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Since 2019, Matheon's application-oriented mathematical research activities are being continued in the framework of the Cluster of Excellence MATH+
www.mathplus.de
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Project archive 2002 - 2014

Projekte der Förderperiode 2010 - 2014

  • D26

    Asymptotic analysis of the wave-propagation in realistic photonic crystal wave-guides

    Project heads: -
    Project members: -
    Duration: 04/11 - 05/14
    Status: completed

    Description

    The technical progress of the last decades has been enormously stimulated by two technological revolutions: the invention of the transistor in 1947 (Nobel prize 1956) and the invention of the laser in 1958 (Nobel prize 1964). The impact of both inventions on modern life is an evident fact.

    Already in 1950, a system of partial differential equations was published that models adequately the essential charge transport processes in semiconductor devices. On the basis of this drift-diffusion model the first bipolar transistor was successfully simulated in 1964. Just in that time the first integrated circuits containing a few transistors became commercially available. Since then, the electronics industry has achieved a phenomenal growth, mainly due to the rapid advances in integration technologies, large-scale systems design and numerical simulation. The number of applications of integrated circuits in high-performance computing, telecommunications, and consumer electronics has been rising steadily, and at a very fast pace. As microelectronic research moves into the nanometer scale device regime with GHz or higher operating speeds, the physics of electron flow through devices becomes more complicated, and physical effects, which previously could be safely ignored, become significant. Consequently, models of a higher abstraction level are needed. Conversely, faster simulation is typically required, which places a constraint on the model refinement if conventional simulation techniques are applied.

    Like the invention of the transistor triggered research in circuit simulation, the invention of the laser had a major impact on optical technologies. Classical optics turned into photonics. In todays telecommunication technologies, photons have already become the main carrier of information, regardless of the fact that even today most of the applied optical devices are based on conventional optical fibers and low index-contrast waveguides. Recently, a number of pioneering developments - all based on nanotechnologies - opened up the door to completely new working principles, hence to new classes of optoelectronic devices. Among them are nanostructured periodic materials (photonic crystals) and optically active nanostructures like quantum layers and quantum dots. A proper modelling of such structures has to describe simultaneously electrical charge transport, light generation, light propagation and scattering. Moreover, optical active nanostructures have to be described by quantum mechanics.

    In spite of the achievements of electronic/optoelectronic device and circuit simulation obtained so far, new nanotechnologies create new challenging tasks for mathematical modeling and numerical simulation in this field.

    Topics:
    • shape memory alloys in airfoils
    • production of semiconductor crystals
    • methanole fuel cell optimization
    • online production planning metamaterials


    http://www.tu-berlin.de/?Matheon-d26
  • F13

    Combinatorics and geometry restrictions on triangulations and meshes

    Project heads: -
    Project members: -
    Duration: 03/11 - 05/14
    Status: completed

    Description

    Visualization has the task to create insight from given data. Image analysis is to extract information from data and to make it explicit in the form of a geometric model. The two areas have tight relations on both the methodical and the application level. Prominent examples are image-based rendering and visual analysis of 3D image data, e.g. in tomography or confocal microscopy.

    In recent years we have seen a rapid development of fundamentally new techniques for the visualization of complex physical phenomena as well as for imaging applications. At the very heart of these new technologies we encounter fundamentally new data structures and algorithms, all with a quest for a new level of abstraction. Here is where mathematics enters the scene.

    Especially in visualization, it is still a challenge to give the underlying objects a solid mathematical description. Here the research field of mathematical visualization faces the challenge to develop precise abstractions which eventually enables the development of new algorithms and visualization tools. Efforts in this direction can build on broad mathematical foundations, laid among others in the fields of discrete geometry, computational geometry, discrete differential geometry, and combinatorial topology. Results of this development are not only needed in research, where scientifically correct visualization is essential, but also meant to provide a solid basis for applications, for example, in computer graphics as well as in mathematics education projects.

    Even more so, the fields of visualization and image processing are key technologies for very current fields of research, among them many of the natural sciences (physics, chemistry, climate research), the life sciences (medicine, biochemistry, biotechnology, pharmacy), but also for various problems of engineering and production. Due to the multiple applications, but also due to technological reasons such as the availability of new imaging devices and display technology, imaging and visualization have been - and will be - areas of impressive growth.

    Topics:
    • discrete differential geometry
    • geometry processing
    • image processing
    • virtual reality PORTAL


    http://userpage.fu-berlin.de/mws/f13
  • ZO8*

    Panorama der Mathematik

    Project heads: -
    Project members: -
    Duration: 03/11 - 05/14
    Status: completed

    Description

    The recent TIMSS studies have displayed and highlighted considerable deficits in the mathematical education in Germany, in particular on the gymnasium level. According to the study, in general, German pupils seem to be able to master calculations in a satisfactory way, but their abilities to solve application oriented problems are below average. Moreover, the mathematics taught at schools is not experienced as something interesting and attractive, so pupils are not well-motivated. This in turn leads to the fact that the mathematical knowledge acquired by the pupils is not sufficient for their orientation in the real-world. In particular, we observe corresponding problems in our mathematical education of students at the university. Such deficits were also stressed in the influential lecture Drawbridge Up by the noted German poet and essayist H. M. Enzensberger.

    There are a number of reasons for the unfavourable situation. Among others, we mention first that the sensitivity for mathematics in the German public is rather low, despite the fact that mathematics is more and more present in everyday life: most of the public many acknowledge that mathematics is difficult and impressive, but they do not view it as something interesting, or as a genuine part of culture. Secondly, the mathematics taught at schools often misses a certain amount of attractivity: very little of what the pupils see or learn is new, and there are typically very few references to any current mathematical developments; it does not become clear that there are new mathematical discoveries made every day, that there is recent and current progress on many different questions. A third reason is a deficit in the practice orientation of the mathematics taught at high schools: pupils do not see that mathematics is relevant and important in the real-world, that there are lots of interesting applications and developments.

    To improve the situation the following measures seem promising. The very experts have to give more emphasis to the popularization of current mathematics. Moreover, the teaching of mathematics, including the corresponding mathematics curricula, at schools and universities has to be made more attractive and problem-solving-oriented. Last but not least, the teacher students education has to obtain a more practice-oriented component.

    The basis to attack and solve the problems that we have described lies in greater educational activity of university mathematicians, and in a much closer cooperation between schools and universities than the present one.

    Topics:
    • modern mathematics at school
    • school teachers at universities
    • network of math-science oriented schools
    • public awareness of mathematics
    • media presence


    http://www.userpage.fu-berlin.de/aloos/ZO8star.htm
  • B26

    Information extracting sensor networks

    Project heads: -
    Project members: -
    Duration: 04/12 - 06/13
    Status: completed

    Description

    Networks, such as telephone networks, the internet, airline, railway, and bus networks are omnipresent and play a fundamental role for communication and mobility in our society. We almost take their permanent availability, reliability, and quality at low cost for granted. However, traffic jams, ill-designed train schedules, canceled flights, break-downs of telephone and computing networks, and slow internet access are reminders that networks are not automatically good networks.

    In fact, designing and operating communication and traffic networks are extremely complex tasks that lead directly to mathematical problems. A good example is the design of telecommunication networks. They were implemented with simple low-cost tree topologies until 15 years ago. Then, in 1988, a telco hub broke down in Chicago. This brought O Hare airport to a stand-still and caused an estimated business loss of billions of US dollars. Disasters of this kind made it clear that more sophisticated designs were needed. Nowadays, telecommunication companies use mathematically designed networks with built-in failure safety and rerouting capacities. Similar developments are expected in road traffic. We are now facing the installation of the first generation of load measuring, signalling, pricing, and route finding devices. These will soon integrate into a network-wide telematic system based on mathematical methods of traffic prediction, simulation, and control.

    Network design and operation tasks of this type are traditionally handled under the responsibility of various engineering disciplines (electrical engineering, traffic management and logistics, industrial engineering). While these disciplines can contribute to the improvement of the engineering components of such networks, todays demand on global optimization of the entire system poses problems where qualitative progress has to come from a better theoretical understanding of the structural aspects of the networks.

    This is where mathematics must come into play. The appearance of the word "network" in all the systems described above is not accidental, but hints at a common feature that has deep mathematical roots: networks are fundamental structures of graph theory and combinatorial optimization. Their study has become a prosperous subject in recent years, with impressive successes in many applications. The groups in Berlin are among the driving forces in this development.

    Nowadays, mathematical optimization techniques are used to locate switches and hubs in a phone system, to schedule buses and bus drivers in metropolitan transportation systems, etc. These tasks are individual steps in a hierarchical and sequential network planning process. In public transport, for example, this sequential process encompasses line planning, finding a periodic time table, assigning buses to lines, and creating individual bus driver schedules.

    Topics:
    • planning of optical, multilayer, and UMTS telecommunication networks
    • line planning, periodic timetabling, and revenue management in public transport networks
    • optimization in logistics, scheduling and material flows
    • optimization under uncertainty
    • symmetries in integer programming
    • game theoretic methods in network design


    http://www.math.tu-berlin.de/fachgebiete_ag_modnumdiff/angewandtefunktionalanalysis/v-menue/projekte/informationextractsensornetworks/parameter/de/
  • E12

    Optimal Order Placement in Illiquid Markets

    Project heads: -
    Project members: -
    Duration: 04/12 - 06/13
    Status: completed

    Description

    Mathematics has become highly visible as a key technology in the area of finance and insurance. Increasingly, advanced probabilistic and statistical methods are being applied to the analysis of financial risk in its various forms. Their impact is not only felt on a computational level. To a surprising extent, concepts of stochastic analysis are shaping the discourse of the field, both in academia and in the financial industry. Conversely, finance has become a significant source of new research problems in mathematical modelling, simulation and optimization.

    Such problems arise typically beyond the idealized context of a complete financial market model without frictions, where derivatives admit a perfect hedge and hence can be priced by arbitrage. As one moves on to more realistic models, the Black-Scholes paradigm of a perfect hedge breaks down. Instead, one is confronted with an incomplete financial market model where derivatives carry an intrinsic risk which cannot be hedged away. In an incomplete model, the challenge is to construct hedging strategies which are optimal in terms of some criterion of risk minimization. Considerable progress has been made over the last years in understanding the mathematical structure of such strategies, and Berlin has played a leading role in this development.

    At the same time, demand by the financial industry for advanced mathematical methods of assessing and hedging financial risk has increased dramatically. One major factor is the growing pressure of supervising agencies on banks to improve their internal models for quantifying risk exposure, triggered by the 1995 guidelines of the Basel Committee on Banking Supervision and their ongoing improvements. Banks are now competing not only in the innovation of financial products but also in the development of new methods of risk management. Another important factor is the breakdown of traditional boundaries between the financial and the insurance industry, in particular the growing trend towards financial securitization of insurance risks. This leads to the design of new products which combine very different sources of risk and pose new valuation and hedging problems.

    Topics:
    • measurement and hedging of risks
    • interaction models for asset price fluctuation


  • D27

    Numerical methods for coupled micro- und nanoflows with strong electrostatic forces

    Project heads: -
    Project members: -
    Duration: 05/12 - 06/13
    Status: completed

    Description

    The technical progress of the last decades has been enormously stimulated by two technological revolutions: the invention of the transistor in 1947 (Nobel prize 1956) and the invention of the laser in 1958 (Nobel prize 1964). The impact of both inventions on modern life is an evident fact.

    Already in 1950, a system of partial differential equations was published that models adequately the essential charge transport processes in semiconductor devices. On the basis of this drift-diffusion model the first bipolar transistor was successfully simulated in 1964. Just in that time the first integrated circuits containing a few transistors became commercially available. Since then, the electronics industry has achieved a phenomenal growth, mainly due to the rapid advances in integration technologies, large-scale systems design and numerical simulation. The number of applications of integrated circuits in high-performance computing, telecommunications, and consumer electronics has been rising steadily, and at a very fast pace. As microelectronic research moves into the nanometer scale device regime with GHz or higher operating speeds, the physics of electron flow through devices becomes more complicated, and physical effects, which previously could be safely ignored, become significant. Consequently, models of a higher abstraction level are needed. Conversely, faster simulation is typically required, which places a constraint on the model refinement if conventional simulation techniques are applied.

    Like the invention of the transistor triggered research in circuit simulation, the invention of the laser had a major impact on optical technologies. Classical optics turned into photonics. In todays telecommunication technologies, photons have already become the main carrier of information, regardless of the fact that even today most of the applied optical devices are based on conventional optical fibers and low index-contrast waveguides. Recently, a number of pioneering developments - all based on nanotechnologies - opened up the door to completely new working principles, hence to new classes of optoelectronic devices. Among them are nanostructured periodic materials (photonic crystals) and optically active nanostructures like quantum layers and quantum dots. A proper modelling of such structures has to describe simultaneously electrical charge transport, light generation, light propagation and scattering. Moreover, optical active nanostructures have to be described by quantum mechanics.

    In spite of the achievements of electronic/optoelectronic device and circuit simulation obtained so far, new nanotechnologies create new challenging tasks for mathematical modeling and numerical simulation in this field.

    Topics:
    • shape memory alloys in airfoils
    • production of semiconductor crystals
    • methanole fuel cell optimization
    • online production planning metamaterials


    http://www.wias-berlin.de/people/linke/D27.html
  • E13

    Affine processes in finance: LIBOR modeling and estimation

    Project heads: -
    Project members: -
    Duration: 04/12 - 06/13
    Status: completed

    Description

    Mathematics has become highly visible as a key technology in the area of finance and insurance. Increasingly, advanced probabilistic and statistical methods are being applied to the analysis of financial risk in its various forms. Their impact is not only felt on a computational level. To a surprising extent, concepts of stochastic analysis are shaping the discourse of the field, both in academia and in the financial industry. Conversely, finance has become a significant source of new research problems in mathematical modelling, simulation and optimization.

    Such problems arise typically beyond the idealized context of a complete financial market model without frictions, where derivatives admit a perfect hedge and hence can be priced by arbitrage. As one moves on to more realistic models, the Black-Scholes paradigm of a perfect hedge breaks down. Instead, one is confronted with an incomplete financial market model where derivatives carry an intrinsic risk which cannot be hedged away. In an incomplete model, the challenge is to construct hedging strategies which are optimal in terms of some criterion of risk minimization. Considerable progress has been made over the last years in understanding the mathematical structure of such strategies, and Berlin has played a leading role in this development.

    At the same time, demand by the financial industry for advanced mathematical methods of assessing and hedging financial risk has increased dramatically. One major factor is the growing pressure of supervising agencies on banks to improve their internal models for quantifying risk exposure, triggered by the 1995 guidelines of the Basel Committee on Banking Supervision and their ongoing improvements. Banks are now competing not only in the innovation of financial products but also in the development of new methods of risk management. Another important factor is the breakdown of traditional boundaries between the financial and the insurance industry, in particular the growing trend towards financial securitization of insurance risks. This leads to the design of new products which combine very different sources of risk and pose new valuation and hedging problems.

    Topics:
    • measurement and hedging of risks
    • interaction models for asset price fluctuation


  • A21

    Modeling, Simulation and Therapy Optimization for Infectious Diseases

    Project heads: -
    Project members: -
    Duration: 05/12-05/14
    Status: completed

    Description

    "Life sciences" describe a wide research area with enormous technological and social impact. However, there exist specific areas where mathematics has just begun to take on an active role.

    In medicine, the already traditional role of mathematics in medical imaging (e.g., computer tomography) has been successfully extended. Mathematical progress has proved to directly influence medical progress towards the design of patient-specific therapies - e.g., in the cancer therapy hyperthermia. As another example, computer-assisted surgery planning allows the comparison of various operation options before the actual operation on the basis of a simulation of more and more realistic models describing soft tissue, bone, or typical human gaits such as stair climbing. Further mathematization of the field is expected to open entirely new perspectives for the optimal design of joint prostheses adapted to individual anatomy.

    In biotechnology, the present situation is clearly dominated by the generation of huge datasets about biomolecular, genetic, metabolic or other bio-processes. Algorithms from discrete mathematics or computer science (e.g., in multiple alignment) already play a publicly visible role in the decoding of the human and other genomes. In contrast to that, the mathematical treatment of the dynamics of bio-processes is still rather limited - even though this aspect seems to be crucial for the detailed understanding of virus diseases or the design of narrow band drugs. Therefore, beyond the well-established core areas of bioinformatics, numerical biocomputing has recently become more and more accepted as one of the keys to data-based reliable prediction, control and design of real-life bio-processes: As it turns out, a significant increase in our ability in a reliable quantitative simulation of the dynamics of large biomolecules is essential for a detailed understanding of, e.g., the enzymatic mechanisms of prion diseases (like the mad cow disease or its human counterpart, the Creutzfeldt-Jacob syndrome).

    Topics:
    • computer-assisted surgery
    • patient-specific therapy planning
    • protein data base analysis
    • protein conformation dynamics
    • systems biology
    • pharmacokinetics


  • A22

    Geometric methods for optimization problems with singularities

    Project heads: -
    Project members: -
    Duration: 04/12 - 05/14
    Status: completed

    Description

    "Life sciences" describe a wide research area with enormous technological and social impact. However, there exist specific areas where mathematics has just begun to take on an active role.

    In medicine, the already traditional role of mathematics in medical imaging (e.g., computer tomography) has been successfully extended. Mathematical progress has proved to directly influence medical progress towards the design of patient-specific therapies - e.g., in the cancer therapy hyperthermia. As another example, computer-assisted surgery planning allows the comparison of various operation options before the actual operation on the basis of a simulation of more and more realistic models describing soft tissue, bone, or typical human gaits such as stair climbing. Further mathematization of the field is expected to open entirely new perspectives for the optimal design of joint prostheses adapted to individual anatomy.

    In biotechnology, the present situation is clearly dominated by the generation of huge datasets about biomolecular, genetic, metabolic or other bio-processes. Algorithms from discrete mathematics or computer science (e.g., in multiple alignment) already play a publicly visible role in the decoding of the human and other genomes. In contrast to that, the mathematical treatment of the dynamics of bio-processes is still rather limited - even though this aspect seems to be crucial for the detailed understanding of virus diseases or the design of narrow band drugs. Therefore, beyond the well-established core areas of bioinformatics, numerical biocomputing has recently become more and more accepted as one of the keys to data-based reliable prediction, control and design of real-life bio-processes: As it turns out, a significant increase in our ability in a reliable quantitative simulation of the dynamics of large biomolecules is essential for a detailed understanding of, e.g., the enzymatic mechanisms of prion diseases (like the mad cow disease or its human counterpart, the Creutzfeldt-Jacob syndrome).

    Topics:
    • computer-assisted surgery
    • patient-specific therapy planning
    • protein data base analysis
    • protein conformation dynamics
    • systems biology
    • pharmacokinetics


  • C36

    Fluid-Driven Fracture Growth

    Project heads: -
    Project members: -
    Duration: 06/12-12/12
    Status: completed

    Description

    Production is one of the most important parts of the economy and at the very heart of the creation of value. Due to the central importance of production, big efforts have been made to improve production processes ever since the beginning of the industrial revolution. Nowadays, many production processes are highly automated. Computer programs based on numerical algorithms monitor the processes, improve efficiency and robustness, and guarantee high quality products. Consequently, mathematics is playing a steadily increasing role in this field. The possibilities of applying mathematical methods in production are wide-ranging. The Application Area cannot cover their full scale. For that reason, the projects concentrate on the development of new mathematical methods for special topics in manufacturing and production planning, two central aspects of production, in which the participating groups have longstanding expertise in mathematical modeling, simulation and optimization.

    In the field of manufacturing, we focus on innovative technologies having a big impact on technological progress: growth and processing of semiconductor bulk single crystals, phase transitions in modern steels and solder alloys, modeling of active and passive behavior of functional materials like shape-memory materials, growth of thin films. In the projects devoted to production planning, the main aim is the effective control of the whole production flow. Among the subjects to be studied, there is also electricity portfolio management.

    Topics:
    • phase transitions in steels and solder alloys
    • production of semiconductor crystals
    • modeling of active and passive behavior of functional materials
    • online production planning
    • growth of thin films


  • C37

    Shape/Topology optimization methods for inverse problems

    Project heads: -
    Project members: -
    Duration: 05/12 - 05/14
    Status: completed

    Description

    Production is one of the most important parts of the economy and at the very heart of the creation of value. Due to the central importance of production, big efforts have been made to improve production processes ever since the beginning of the industrial revolution. Nowadays, many production processes are highly automated. Computer programs based on numerical algorithms monitor the processes, improve efficiency and robustness, and guarantee high quality products. Consequently, mathematics is playing a steadily increasing role in this field. The possibilities of applying mathematical methods in production are wide-ranging. The Application Area cannot cover their full scale. For that reason, the projects concentrate on the development of new mathematical methods for special topics in manufacturing and production planning, two central aspects of production, in which the participating groups have longstanding expertise in mathematical modeling, simulation and optimization.

    In the field of manufacturing, we focus on innovative technologies having a big impact on technological progress: growth and processing of semiconductor bulk single crystals, phase transitions in modern steels and solder alloys, modeling of active and passive behavior of functional materials like shape-memory materials, growth of thin films. In the projects devoted to production planning, the main aim is the effective control of the whole production flow. Among the subjects to be studied, there is also electricity portfolio management.

    Topics:
    • phase transitions in steels and solder alloys
    • production of semiconductor crystals
    • modeling of active and passive behavior of functional materials
    • online production planning
    • growth of thin films


    http://www.antoinelaurain.com/
  • B27

    Stable Transient Modeling and Simulation of Flow Networks

    Project heads: -
    Project members: -
    Duration: 05/12-05/14
    Status: completed

    Description

    Networks, such as telephone networks, the internet, airline, railway, and bus networks are omnipresent and play a fundamental role for communication and mobility in our society. We almost take their permanent availability, reliability, and quality at low cost for granted. However, traffic jams, ill-designed train schedules, canceled flights, break-downs of telephone and computing networks, and slow internet access are reminders that networks are not automatically good networks.

    In fact, designing and operating communication and traffic networks are extremely complex tasks that lead directly to mathematical problems. A good example is the design of telecommunication networks. They were implemented with simple low-cost tree topologies until 15 years ago. Then, in 1988, a telco hub broke down in Chicago. This brought O Hare airport to a stand-still and caused an estimated business loss of billions of US dollars. Disasters of this kind made it clear that more sophisticated designs were needed. Nowadays, telecommunication companies use mathematically designed networks with built-in failure safety and rerouting capacities. Similar developments are expected in road traffic. We are now facing the installation of the first generation of load measuring, signalling, pricing, and route finding devices. These will soon integrate into a network-wide telematic system based on mathematical methods of traffic prediction, simulation, and control.

    Network design and operation tasks of this type are traditionally handled under the responsibility of various engineering disciplines (electrical engineering, traffic management and logistics, industrial engineering). While these disciplines can contribute to the improvement of the engineering components of such networks, todays demand on global optimization of the entire system poses problems where qualitative progress has to come from a better theoretical understanding of the structural aspects of the networks.

    This is where mathematics must come into play. The appearance of the word "network" in all the systems described above is not accidental, but hints at a common feature that has deep mathematical roots: networks are fundamental structures of graph theory and combinatorial optimization. Their study has become a prosperous subject in recent years, with impressive successes in many applications. The groups in Berlin are among the driving forces in this development.

    Nowadays, mathematical optimization techniques are used to locate switches and hubs in a phone system, to schedule buses and bus drivers in metropolitan transportation systems, etc. These tasks are individual steps in a hierarchical and sequential network planning process. In public transport, for example, this sequential process encompasses line planning, finding a periodic time table, assigning buses to lines, and creating individual bus driver schedules.

    Topics:
    • planning of optical, multilayer, and UMTS telecommunication networks
    • line planning, periodic timetabling, and revenue management in public transport networks
    • optimization in logistics, scheduling and material flows
    • optimization under uncertainty
    • symmetries in integer programming
    • game theoretic methods in network design


  • A23

    Tractabel recovery of multivariate functions from limited number of samples

    Project heads: -
    Project members: -
    Duration: 11/12 - 05/14
    Status: completed

    Description

    "Life sciences" describe a wide research area with enormous technological and social impact. However, there exist specific areas where mathematics has just begun to take on an active role.

    In medicine, the already traditional role of mathematics in medical imaging (e.g., computer tomography) has been successfully extended. Mathematical progress has proved to directly influence medical progress towards the design of patient-specific therapies - e.g., in the cancer therapy hyperthermia. As another example, computer-assisted surgery planning allows the comparison of various operation options before the actual operation on the basis of a simulation of more and more realistic models describing soft tissue, bone, or typical human gaits such as stair climbing. Further mathematization of the field is expected to open entirely new perspectives for the optimal design of joint prostheses adapted to individual anatomy.

    In biotechnology, the present situation is clearly dominated by the generation of huge datasets about biomolecular, genetic, metabolic or other bio-processes. Algorithms from discrete mathematics or computer science (e.g., in multiple alignment) already play a publicly visible role in the decoding of the human and other genomes. In contrast to that, the mathematical treatment of the dynamics of bio-processes is still rather limited - even though this aspect seems to be crucial for the detailed understanding of virus diseases or the design of narrow band drugs. Therefore, beyond the well-established core areas of bioinformatics, numerical biocomputing has recently become more and more accepted as one of the keys to data-based reliable prediction, control and design of real-life bio-processes: As it turns out, a significant increase in our ability in a reliable quantitative simulation of the dynamics of large biomolecules is essential for a detailed understanding of, e.g., the enzymatic mechanisms of prion diseases (like the mad cow disease or its human counterpart, the Creutzfeldt-Jacob syndrome).

    Topics:
    • computer-assisted surgery
    • patient-specific therapy planning
    • protein data base analysis
    • protein conformation dynamics
    • systems biology
    • pharmacokinetics


  • A24

    Top-down modeling and experimental design for molecular networks

    Project heads: -
    Project members: -
    Duration: 04/13 - 12/13
    Status: completed

    Description

    "Life sciences" describe a wide research area with enormous technological and social impact. However, there exist specific areas where mathematics has just begun to take on an active role.

    In medicine, the already traditional role of mathematics in medical imaging (e.g., computer tomography) has been successfully extended. Mathematical progress has proved to directly influence medical progress towards the design of patient-specific therapies - e.g., in the cancer therapy hyperthermia. As another example, computer-assisted surgery planning allows the comparison of various operation options before the actual operation on the basis of a simulation of more and more realistic models describing soft tissue, bone, or typical human gaits such as stair climbing. Further mathematization of the field is expected to open entirely new perspectives for the optimal design of joint prostheses adapted to individual anatomy.

    In biotechnology, the present situation is clearly dominated by the generation of huge datasets about biomolecular, genetic, metabolic or other bio-processes. Algorithms from discrete mathematics or computer science (e.g., in multiple alignment) already play a publicly visible role in the decoding of the human and other genomes. In contrast to that, the mathematical treatment of the dynamics of bio-processes is still rather limited - even though this aspect seems to be crucial for the detailed understanding of virus diseases or the design of narrow band drugs. Therefore, beyond the well-established core areas of bioinformatics, numerical biocomputing has recently become more and more accepted as one of the keys to data-based reliable prediction, control and design of real-life bio-processes: As it turns out, a significant increase in our ability in a reliable quantitative simulation of the dynamics of large biomolecules is essential for a detailed understanding of, e.g., the enzymatic mechanisms of prion diseases (like the mad cow disease or its human counterpart, the Creutzfeldt-Jacob syndrome).

    Topics:
    • computer-assisted surgery
    • patient-specific therapy planning
    • protein data base analysis
    • protein conformation dynamics
    • systems biology
    • pharmacokinetics


  • A25

    Weak convergence of numerical methods for stochastic partial differential equations with applications to neurosciences

    Project heads: -
    Project members: -
    Duration: 05/14-05/17
    Status: completed

    Description

    "Life sciences" describe a wide research area with enormous technological and social impact. However, there exist specific areas where mathematics has just begun to take on an active role.

    In medicine, the already traditional role of mathematics in medical imaging (e.g., computer tomography) has been successfully extended. Mathematical progress has proved to directly influence medical progress towards the design of patient-specific therapies - e.g., in the cancer therapy hyperthermia. As another example, computer-assisted surgery planning allows the comparison of various operation options before the actual operation on the basis of a simulation of more and more realistic models describing soft tissue, bone, or typical human gaits such as stair climbing. Further mathematization of the field is expected to open entirely new perspectives for the optimal design of joint prostheses adapted to individual anatomy.

    In biotechnology, the present situation is clearly dominated by the generation of huge datasets about biomolecular, genetic, metabolic or other bio-processes. Algorithms from discrete mathematics or computer science (e.g., in multiple alignment) already play a publicly visible role in the decoding of the human and other genomes. In contrast to that, the mathematical treatment of the dynamics of bio-processes is still rather limited - even though this aspect seems to be crucial for the detailed understanding of virus diseases or the design of narrow band drugs. Therefore, beyond the well-established core areas of bioinformatics, numerical biocomputing has recently become more and more accepted as one of the keys to data-based reliable prediction, control and design of real-life bio-processes: As it turns out, a significant increase in our ability in a reliable quantitative simulation of the dynamics of large biomolecules is essential for a detailed understanding of, e.g., the enzymatic mechanisms of prion diseases (like the mad cow disease or its human counterpart, the Creutzfeldt-Jacob syndrome).

    Topics:
    • computer-assisted surgery
    • patient-specific therapy planning
    • protein data base analysis
    • protein conformation dynamics
    • systems biology
    • pharmacokinetics






Projekte der Förderperiode 2006 - 2010

  • C23

    Mass conservative coupling of fluid flow and species transport in electrochemical flow cells

    Project heads: -
    Project members: -
    Duration: 04/07-12/08
    Status: completed

    Description

    Production is one of the most important parts of the economy and at the very heart of the creation of value. Due to the central importance of production, big efforts have been made to improve production processes ever since the beginning of the industrial revolution. Nowadays, many production processes are highly automated. Computer programs based on numerical algorithms monitor the processes, improve efficiency and robustness, and guarantee high quality products. Consequently, mathematics is playing a steadily increasing role in this field. The possibilities of applying mathematical methods in production are wide-ranging. The Application Area cannot cover their full scale. For that reason, the projects concentrate on the development of new mathematical methods for special topics in manufacturing and production planning, two central aspects of production, in which the participating groups have longstanding expertise in mathematical modeling, simulation and optimization.

    In the field of manufacturing, we focus on innovative technologies having a big impact on technological progress: growth and processing of semiconductor bulk single crystals, phase transitions in modern steels and solder alloys, modeling of active and passive behavior of functional materials like shape-memory materials, growth of thin films. In the projects devoted to production planning, the main aim is the effective control of the whole production flow. Among the subjects to be studied, there is also electricity portfolio management.

    Topics:
    • phase transitions in steels and solder alloys
    • production of semiconductor crystals
    • modeling of active and passive behavior of functional materials
    • online production planning
    • growth of thin films


    http://www.wias-berlin.de/projects/Matheon_c23/index.html
  • C22

    Adaptive solution of parametric eigenvalue problems for partial differential equations

    Project heads: -
    Project members: -
    Duration: 08/07 - 05/14
    Status: completed

    Description

    Production is one of the most important parts of the economy and at the very heart of the creation of value. Due to the central importance of production, big efforts have been made to improve production processes ever since the beginning of the industrial revolution. Nowadays, many production processes are highly automated. Computer programs based on numerical algorithms monitor the processes, improve efficiency and robustness, and guarantee high quality products. Consequently, mathematics is playing a steadily increasing role in this field. The possibilities of applying mathematical methods in production are wide-ranging. The Application Area cannot cover their full scale. For that reason, the projects concentrate on the development of new mathematical methods for special topics in manufacturing and production planning, two central aspects of production, in which the participating groups have longstanding expertise in mathematical modeling, simulation and optimization.

    In the field of manufacturing, we focus on innovative technologies having a big impact on technological progress: growth and processing of semiconductor bulk single crystals, phase transitions in modern steels and solder alloys, modeling of active and passive behavior of functional materials like shape-memory materials, growth of thin films. In the projects devoted to production planning, the main aim is the effective control of the whole production flow. Among the subjects to be studied, there is also electricity portfolio management.

    Topics:
    • phase transitions in steels and solder alloys
    • production of semiconductor crystals
    • modeling of active and passive behavior of functional materials
    • online production planning
    • growth of thin films


    http://www3.math.tu-berlin.de/Matheon/projects/C22/
  • A13

    Meshless Discrete Galerkin Methods for Polymer Chemistry and Systems Biology

    Project heads: -
    Project members: -
    Duration: 04/07 - 05/10
    Status: completed

    Description

    "Life sciences" describe a wide research area with enormous technological and social impact. However, there exist specific areas where mathematics has just begun to take on an active role.

    In medicine, the already traditional role of mathematics in medical imaging (e.g., computer tomography) has been successfully extended. Mathematical progress has proved to directly influence medical progress towards the design of patient-specific therapies - e.g., in the cancer therapy hyperthermia. As another example, computer-assisted surgery planning allows the comparison of various operation options before the actual operation on the basis of a simulation of more and more realistic models describing soft tissue, bone, or typical human gaits such as stair climbing. Further mathematization of the field is expected to open entirely new perspectives for the optimal design of joint prostheses adapted to individual anatomy.

    In biotechnology, the present situation is clearly dominated by the generation of huge datasets about biomolecular, genetic, metabolic or other bio-processes. Algorithms from discrete mathematics or computer science (e.g., in multiple alignment) already play a publicly visible role in the decoding of the human and other genomes. In contrast to that, the mathematical treatment of the dynamics of bio-processes is still rather limited - even though this aspect seems to be crucial for the detailed understanding of virus diseases or the design of narrow band drugs. Therefore, beyond the well-established core areas of bioinformatics, numerical biocomputing has recently become more and more accepted as one of the keys to data-based reliable prediction, control and design of real-life bio-processes: As it turns out, a significant increase in our ability in a reliable quantitative simulation of the dynamics of large biomolecules is essential for a detailed understanding of, e.g., the enzymatic mechanisms of prion diseases (like the mad cow disease or its human counterpart, the Creutzfeldt-Jacob syndrome).

    Topics:
    • computer-assisted surgery
    • patient-specific therapy planning
    • protein data base analysis
    • protein conformation dynamics
    • systems biology
    • pharmacokinetics


    http://www.zib.de/Numerik/projects/Matheon-A13/project.frameset.en.html
  • D19

    Local existence, uniqueness, and smooth dependence for quasilinear parabolic problems with non-smooth data

    Project heads: -
    Project members: -
    Duration: 07/07-12/08
    Status: completed

    Description

    The technical progress of the last decades has been enormously stimulated by two technological revolutions: the invention of the transistor in 1947 (Nobel prize 1956) and the invention of the laser in 1958 (Nobel prize 1964). The impact of both inventions on modern life is an evident fact.

    Already in 1950, a system of partial differential equations was published that models adequately the essential charge transport processes in semiconductor devices. On the basis of this drift-diffusion model the first bipolar transistor was successfully simulated in 1964. Just in that time the first integrated circuits containing a few transistors became commercially available. Since then, the electronics industry has achieved a phenomenal growth, mainly due to the rapid advances in integration technologies, large-scale systems design and numerical simulation. The number of applications of integrated circuits in high-performance computing, telecommunications, and consumer electronics has been rising steadily, and at a very fast pace. As microelectronic research moves into the nanometer scale device regime with GHz or higher operating speeds, the physics of electron flow through devices becomes more complicated, and physical effects, which previously could be safely ignored, become significant. Consequently, models of a higher abstraction level are needed. Conversely, faster simulation is typically required, which places a constraint on the model refinement if conventional simulation techniques are applied.

    Like the invention of the transistor triggered research in circuit simulation, the invention of the laser had a major impact on optical technologies. Classical optics turned into photonics. In todays telecommunication technologies, photons have already become the main carrier of information, regardless of the fact that even today most of the applied optical devices are based on conventional optical fibers and low index-contrast waveguides. Recently, a number of pioneering developments - all based on nanotechnologies - opened up the door to completely new working principles, hence to new classes of optoelectronic devices. Among them are nanostructured periodic materials (photonic crystals) and optically active nanostructures like quantum layers and quantum dots. A proper modelling of such structures has to describe simultaneously electrical charge transport, light generation, light propagation and scattering. Moreover, optical active nanostructures have to be described by quantum mechanics.

    In spite of the achievements of electronic/optoelectronic device and circuit simulation obtained so far, new nanotechnologies create new challenging tasks for mathematical modeling and numerical simulation in this field.

    Topics:
    • shape memory alloys in airfoils
    • production of semiconductor crystals
    • methanole fuel cell optimization
    • online production planning metamaterials


    http://www.wias-berlin.de/project-areas/micro-el/Matheon-D19
  • D20

    Pulse shaping in photonic crystal-fibers

    Project heads: -
    Project members: -
    Duration: 05/07 - 12/08
    Status: completed

    Description

    The technical progress of the last decades has been enormously stimulated by two technological revolutions: the invention of the transistor in 1947 (Nobel prize 1956) and the invention of the laser in 1958 (Nobel prize 1964). The impact of both inventions on modern life is an evident fact.

    Already in 1950, a system of partial differential equations was published that models adequately the essential charge transport processes in semiconductor devices. On the basis of this drift-diffusion model the first bipolar transistor was successfully simulated in 1964. Just in that time the first integrated circuits containing a few transistors became commercially available. Since then, the electronics industry has achieved a phenomenal growth, mainly due to the rapid advances in integration technologies, large-scale systems design and numerical simulation. The number of applications of integrated circuits in high-performance computing, telecommunications, and consumer electronics has been rising steadily, and at a very fast pace. As microelectronic research moves into the nanometer scale device regime with GHz or higher operating speeds, the physics of electron flow through devices becomes more complicated, and physical effects, which previously could be safely ignored, become significant. Consequently, models of a higher abstraction level are needed. Conversely, faster simulation is typically required, which places a constraint on the model refinement if conventional simulation techniques are applied.

    Like the invention of the transistor triggered research in circuit simulation, the invention of the laser had a major impact on optical technologies. Classical optics turned into photonics. In todays telecommunication technologies, photons have already become the main carrier of information, regardless of the fact that even today most of the applied optical devices are based on conventional optical fibers and low index-contrast waveguides. Recently, a number of pioneering developments - all based on nanotechnologies - opened up the door to completely new working principles, hence to new classes of optoelectronic devices. Among them are nanostructured periodic materials (photonic crystals) and optically active nanostructures like quantum layers and quantum dots. A proper modelling of such structures has to describe simultaneously electrical charge transport, light generation, light propagation and scattering. Moreover, optical active nanostructures have to be described by quantum mechanics.

    In spite of the achievements of electronic/optoelectronic device and circuit simulation obtained so far, new nanotechnologies create new challenging tasks for mathematical modeling and numerical simulation in this field.

    Topics:
    • shape memory alloys in airfoils
    • production of semiconductor crystals
    • methanole fuel cell optimization
    • online production planning metamaterials


    http://www.wias-berlin.de/research-groups/laser/projects/FZ86_D20/
  • A14

    Optimal Models for the Structure and Dynamics of Macromolecular Complexes using Actin as an Example

    Project heads: -
    Project members: -
    Duration: 10/07 - 05/10
    Status: completed

    Description

    "Life sciences" describe a wide research area with enormous technological and social impact. However, there exist specific areas where mathematics has just begun to take on an active role.

    In medicine, the already traditional role of mathematics in medical imaging (e.g., computer tomography) has been successfully extended. Mathematical progress has proved to directly influence medical progress towards the design of patient-specific therapies - e.g., in the cancer therapy hyperthermia. As another example, computer-assisted surgery planning allows the comparison of various operation options before the actual operation on the basis of a simulation of more and more realistic models describing soft tissue, bone, or typical human gaits such as stair climbing. Further mathematization of the field is expected to open entirely new perspectives for the optimal design of joint prostheses adapted to individual anatomy.

    In biotechnology, the present situation is clearly dominated by the generation of huge datasets about biomolecular, genetic, metabolic or other bio-processes. Algorithms from discrete mathematics or computer science (e.g., in multiple alignment) already play a publicly visible role in the decoding of the human and other genomes. In contrast to that, the mathematical treatment of the dynamics of bio-processes is still rather limited - even though this aspect seems to be crucial for the detailed understanding of virus diseases or the design of narrow band drugs. Therefore, beyond the well-established core areas of bioinformatics, numerical biocomputing has recently become more and more accepted as one of the keys to data-based reliable prediction, control and design of real-life bio-processes: As it turns out, a significant increase in our ability in a reliable quantitative simulation of the dynamics of large biomolecules is essential for a detailed understanding of, e.g., the enzymatic mechanisms of prion diseases (like the mad cow disease or its human counterpart, the Creutzfeldt-Jacob syndrome).

    Topics:
    • computer-assisted surgery
    • patient-specific therapy planning
    • protein data base analysis
    • protein conformation dynamics
    • systems biology
    • pharmacokinetics


    http://compmolbio.biocomputing-berlin.de/index.php
  • B18

    Applications of Network Flows in Evacuation Planning

    Project heads: -
    Project members: -
    Duration: 10/07 - 05/14
    Status: completed

    Description

    Networks, such as telephone networks, the internet, airline, railway, and bus networks are omnipresent and play a fundamental role for communication and mobility in our society. We almost take their permanent availability, reliability, and quality at low cost for granted. However, traffic jams, ill-designed train schedules, canceled flights, break-downs of telephone and computing networks, and slow internet access are reminders that networks are not automatically good networks.

    In fact, designing and operating communication and traffic networks are extremely complex tasks that lead directly to mathematical problems. A good example is the design of telecommunication networks. They were implemented with simple low-cost tree topologies until 15 years ago. Then, in 1988, a telco hub broke down in Chicago. This brought O Hare airport to a stand-still and caused an estimated business loss of billions of US dollars. Disasters of this kind made it clear that more sophisticated designs were needed. Nowadays, telecommunication companies use mathematically designed networks with built-in failure safety and rerouting capacities. Similar developments are expected in road traffic. We are now facing the installation of the first generation of load measuring, signalling, pricing, and route finding devices. These will soon integrate into a network-wide telematic system based on mathematical methods of traffic prediction, simulation, and control.

    Network design and operation tasks of this type are traditionally handled under the responsibility of various engineering disciplines (electrical engineering, traffic management and logistics, industrial engineering). While these disciplines can contribute to the improvement of the engineering components of such networks, todays demand on global optimization of the entire system poses problems where qualitative progress has to come from a better theoretical understanding of the structural aspects of the networks.

    This is where mathematics must come into play. The appearance of the word "network" in all the systems described above is not accidental, but hints at a common feature that has deep mathematical roots: networks are fundamental structures of graph theory and combinatorial optimization. Their study has become a prosperous subject in recent years, with impressive successes in many applications. The groups in Berlin are among the driving forces in this development.

    Nowadays, mathematical optimization techniques are used to locate switches and hubs in a phone system, to schedule buses and bus drivers in metropolitan transportation systems, etc. These tasks are individual steps in a hierarchical and sequential network planning process. In public transport, for example, this sequential process encompasses line planning, finding a periodic time table, assigning buses to lines, and creating individual bus driver schedules.

    Topics:
    • planning of optical, multilayer, and UMTS telecommunication networks
    • line planning, periodic timetabling, and revenue management in public transport networks
    • optimization in logistics, scheduling and material flows
    • optimization under uncertainty
    • symmetries in integer programming
    • game theoretic methods in network design


    http://www.math.tu-berlin.de/coga/projects/Matheon/B18/
  • F8

    Discrete differential geometry and kinematics in architectural design

    Project heads: -
    Project members: -
    Duration: 01/09 - 12/09
    Status: completed

    Description

    Visualization has the task to create insight from given data. Image analysis is to extract information from data and to make it explicit in the form of a geometric model. The two areas have tight relations on both the methodical and the application level. Prominent examples are image-based rendering and visual analysis of 3D image data, e.g. in tomography or confocal microscopy.

    In recent years we have seen a rapid development of fundamentally new techniques for the visualization of complex physical phenomena as well as for imaging applications. At the very heart of these new technologies we encounter fundamentally new data structures and algorithms, all with a quest for a new level of abstraction. Here is where mathematics enters the scene.

    Especially in visualization, it is still a challenge to give the underlying objects a solid mathematical description. Here the research field of mathematical visualization faces the challenge to develop precise abstractions which eventually enables the development of new algorithms and visualization tools. Efforts in this direction can build on broad mathematical foundations, laid among others in the fields of discrete geometry, computational geometry, discrete differential geometry, and combinatorial topology. Results of this development are not only needed in research, where scientifically correct visualization is essential, but also meant to provide a solid basis for applications, for example, in computer graphics as well as in mathematics education projects.

    Even more so, the fields of visualization and image processing are key technologies for very current fields of research, among them many of the natural sciences (physics, chemistry, climate research), the life sciences (medicine, biochemistry, biotechnology, pharmacy), but also for various problems of engineering and production. Due to the multiple applications, but also due to technological reasons such as the availability of new imaging devices and display technology, imaging and visualization have been - and will be - areas of impressive growth.

    Topics:
    • discrete differential geometry
    • geometry processing
    • image processing
    • virtual reality PORTAL


    http://www3.math.tu-berlin.de/Matheon/projects/f8/
  • E8

    "Multidimensional Portfolio Optimization"

    Project heads: -
    Project members: -
    Duration: 07/08 - 05/14
    Status: completed

    Description

    Mathematics has become highly visible as a key technology in the area of finance and insurance. Increasingly, advanced probabilistic and statistical methods are being applied to the analysis of financial risk in its various forms. Their impact is not only felt on a computational level. To a surprising extent, concepts of stochastic analysis are shaping the discourse of the field, both in academia and in the financial industry. Conversely, finance has become a significant source of new research problems in mathematical modelling, simulation and optimization.

    Such problems arise typically beyond the idealized context of a complete financial market model without frictions, where derivatives admit a perfect hedge and hence can be priced by arbitrage. As one moves on to more realistic models, the Black-Scholes paradigm of a perfect hedge breaks down. Instead, one is confronted with an incomplete financial market model where derivatives carry an intrinsic risk which cannot be hedged away. In an incomplete model, the challenge is to construct hedging strategies which are optimal in terms of some criterion of risk minimization. Considerable progress has been made over the last years in understanding the mathematical structure of such strategies, and Berlin has played a leading role in this development.

    At the same time, demand by the financial industry for advanced mathematical methods of assessing and hedging financial risk has increased dramatically. One major factor is the growing pressure of supervising agencies on banks to improve their internal models for quantifying risk exposure, triggered by the 1995 guidelines of the Basel Committee on Banking Supervision and their ongoing improvements. Banks are now competing not only in the innovation of financial products but also in the development of new methods of risk management. Another important factor is the breakdown of traditional boundaries between the financial and the insurance industry, in particular the growing trend towards financial securitization of insurance risks. This leads to the design of new products which combine very different sources of risk and pose new valuation and hedging problems.

    Topics:
    • measurement and hedging of risks
    • interaction models for asset price fluctuation


    http://www.math.hu-berlin.de/~becherer
  • C24

    "Modelling and Optimization of Biogas Reactors"

    Project heads: -
    Project members: -
    Duration: 11/08-10/09
    Status: completed

    Description

    Production is one of the most important parts of the economy and at the very heart of the creation of value. Due to the central importance of production, big efforts have been made to improve production processes ever since the beginning of the industrial revolution. Nowadays, many production processes are highly automated. Computer programs based on numerical algorithms monitor the processes, improve efficiency and robustness, and guarantee high quality products. Consequently, mathematics is playing a steadily increasing role in this field. The possibilities of applying mathematical methods in production are wide-ranging. The Application Area cannot cover their full scale. For that reason, the projects concentrate on the development of new mathematical methods for special topics in manufacturing and production planning, two central aspects of production, in which the participating groups have longstanding expertise in mathematical modeling, simulation and optimization.

    In the field of manufacturing, we focus on innovative technologies having a big impact on technological progress: growth and processing of semiconductor bulk single crystals, phase transitions in modern steels and solder alloys, modeling of active and passive behavior of functional materials like shape-memory materials, growth of thin films. In the projects devoted to production planning, the main aim is the effective control of the whole production flow. Among the subjects to be studied, there is also electricity portfolio management.

    Topics:
    • phase transitions in steels and solder alloys
    • production of semiconductor crystals
    • modeling of active and passive behavior of functional materials
    • online production planning
    • growth of thin films


  • C25

    "State trajectory compression in optimal control"

    Project heads: -
    Project members: -
    Duration: 10/08-07/09
    Status: completed

    Description

    Production is one of the most important parts of the economy and at the very heart of the creation of value. Due to the central importance of production, big efforts have been made to improve production processes ever since the beginning of the industrial revolution. Nowadays, many production processes are highly automated. Computer programs based on numerical algorithms monitor the processes, improve efficiency and robustness, and guarantee high quality products. Consequently, mathematics is playing a steadily increasing role in this field. The possibilities of applying mathematical methods in production are wide-ranging. The Application Area cannot cover their full scale. For that reason, the projects concentrate on the development of new mathematical methods for special topics in manufacturing and production planning, two central aspects of production, in which the participating groups have longstanding expertise in mathematical modeling, simulation and optimization.

    In the field of manufacturing, we focus on innovative technologies having a big impact on technological progress: growth and processing of semiconductor bulk single crystals, phase transitions in modern steels and solder alloys, modeling of active and passive behavior of functional materials like shape-memory materials, growth of thin films. In the projects devoted to production planning, the main aim is the effective control of the whole production flow. Among the subjects to be studied, there is also electricity portfolio management.

    Topics:
    • phase transitions in steels and solder alloys
    • production of semiconductor crystals
    • modeling of active and passive behavior of functional materials
    • online production planning
    • growth of thin films


    http://geom.mi.fu-berlin.de/projects/Matheon/f9/index.html
  • B19

    Nonconvex Mixed-Integer Nonlinear Programming

    Project heads: -
    Project members: -
    Duration: 10/08 - 04/09
    Status: completed

    Description

    Networks, such as telephone networks, the internet, airline, railway, and bus networks are omnipresent and play a fundamental role for communication and mobility in our society. We almost take their permanent availability, reliability, and quality at low cost for granted. However, traffic jams, ill-designed train schedules, canceled flights, break-downs of telephone and computing networks, and slow internet access are reminders that networks are not automatically good networks.

    In fact, designing and operating communication and traffic networks are extremely complex tasks that lead directly to mathematical problems. A good example is the design of telecommunication networks. They were implemented with simple low-cost tree topologies until 15 years ago. Then, in 1988, a telco hub broke down in Chicago. This brought O Hare airport to a stand-still and caused an estimated business loss of billions of US dollars. Disasters of this kind made it clear that more sophisticated designs were needed. Nowadays, telecommunication companies use mathematically designed networks with built-in failure safety and rerouting capacities. Similar developments are expected in road traffic. We are now facing the installation of the first generation of load measuring, signalling, pricing, and route finding devices. These will soon integrate into a network-wide telematic system based on mathematical methods of traffic prediction, simulation, and control.

    Network design and operation tasks of this type are traditionally handled under the responsibility of various engineering disciplines (electrical engineering, traffic management and logistics, industrial engineering). While these disciplines can contribute to the improvement of the engineering components of such networks, todays demand on global optimization of the entire system poses problems where qualitative progress has to come from a better theoretical understanding of the structural aspects of the networks.

    This is where mathematics must come into play. The appearance of the word "network" in all the systems described above is not accidental, but hints at a common feature that has deep mathematical roots: networks are fundamental structures of graph theory and combinatorial optimization. Their study has become a prosperous subject in recent years, with impressive successes in many applications. The groups in Berlin are among the driving forces in this development.

    Nowadays, mathematical optimization techniques are used to locate switches and hubs in a phone system, to schedule buses and bus drivers in metropolitan transportation systems, etc. These tasks are individual steps in a hierarchical and sequential network planning process. In public transport, for example, this sequential process encompasses line planning, finding a periodic time table, assigning buses to lines, and creating individual bus driver schedules.

    Topics:
    • planning of optical, multilayer, and UMTS telecommunication networks
    • line planning, periodic timetabling, and revenue management in public transport networks
    • optimization in logistics, scheduling and material flows
    • optimization under uncertainty
    • symmetries in integer programming
    • game theoretic methods in network design


    http://www.math.hu-berlin.de/~stefan/B19
  • C26

    "Storage of hydrogen in hydrides"

    Project heads: -
    Project members: -
    Duration: 05/08 - 05/14
    Status: completed

    Description

    Production is one of the most important parts of the economy and at the very heart of the creation of value. Due to the central importance of production, big efforts have been made to improve production processes ever since the beginning of the industrial revolution. Nowadays, many production processes are highly automated. Computer programs based on numerical algorithms monitor the processes, improve efficiency and robustness, and guarantee high quality products. Consequently, mathematics is playing a steadily increasing role in this field. The possibilities of applying mathematical methods in production are wide-ranging. The Application Area cannot cover their full scale. For that reason, the projects concentrate on the development of new mathematical methods for special topics in manufacturing and production planning, two central aspects of production, in which the participating groups have longstanding expertise in mathematical modeling, simulation and optimization.

    In the field of manufacturing, we focus on innovative technologies having a big impact on technological progress: growth and processing of semiconductor bulk single crystals, phase transitions in modern steels and solder alloys, modeling of active and passive behavior of functional materials like shape-memory materials, growth of thin films. In the projects devoted to production planning, the main aim is the effective control of the whole production flow. Among the subjects to be studied, there is also electricity portfolio management.

    Topics:
    • phase transitions in steels and solder alloys
    • production of semiconductor crystals
    • modeling of active and passive behavior of functional materials
    • online production planning
    • growth of thin films


    http://www.wias-berlin.de/projects/Matheon-c26/C26/MatheonC26b.html
  • E9

    "Beyond replication: Hedging in markets with frictions"

    Project heads: -
    Project members: -
    Duration: 08/08 - 05/14
    Status: completed

    Description

    Mathematics has become highly visible as a key technology in the area of finance and insurance. Increasingly, advanced probabilistic and statistical methods are being applied to the analysis of financial risk in its various forms. Their impact is not only felt on a computational level. To a surprising extent, concepts of stochastic analysis are shaping the discourse of the field, both in academia and in the financial industry. Conversely, finance has become a significant source of new research problems in mathematical modelling, simulation and optimization.

    Such problems arise typically beyond the idealized context of a complete financial market model without frictions, where derivatives admit a perfect hedge and hence can be priced by arbitrage. As one moves on to more realistic models, the Black-Scholes paradigm of a perfect hedge breaks down. Instead, one is confronted with an incomplete financial market model where derivatives carry an intrinsic risk which cannot be hedged away. In an incomplete model, the challenge is to construct hedging strategies which are optimal in terms of some criterion of risk minimization. Considerable progress has been made over the last years in understanding the mathematical structure of such strategies, and Berlin has played a leading role in this development.

    At the same time, demand by the financial industry for advanced mathematical methods of assessing and hedging financial risk has increased dramatically. One major factor is the growing pressure of supervising agencies on banks to improve their internal models for quantifying risk exposure, triggered by the 1995 guidelines of the Basel Committee on Banking Supervision and their ongoing improvements. Banks are now competing not only in the innovation of financial products but also in the development of new methods of risk management. Another important factor is the breakdown of traditional boundaries between the financial and the insurance industry, in particular the growing trend towards financial securitization of insurance risks. This leads to the design of new products which combine very different sources of risk and pose new valuation and hedging problems.

    Topics:
    • measurement and hedging of risks
    • interaction models for asset price fluctuation


    http://wws.mathematik.hu-berlin.de/~penner/E9.html
  • D21

    Synchronization phenomena in coupled dynamical systems

    Project heads: -
    Project members: -
    Duration: 06/08-05/14
    Status: completed

    Description

    The technical progress of the last decades has been enormously stimulated by two technological revolutions: the invention of the transistor in 1947 (Nobel prize 1956) and the invention of the laser in 1958 (Nobel prize 1964). The impact of both inventions on modern life is an evident fact.

    Already in 1950, a system of partial differential equations was published that models adequately the essential charge transport processes in semiconductor devices. On the basis of this drift-diffusion model the first bipolar transistor was successfully simulated in 1964. Just in that time the first integrated circuits containing a few transistors became commercially available. Since then, the electronics industry has achieved a phenomenal growth, mainly due to the rapid advances in integration technologies, large-scale systems design and numerical simulation. The number of applications of integrated circuits in high-performance computing, telecommunications, and consumer electronics has been rising steadily, and at a very fast pace. As microelectronic research moves into the nanometer scale device regime with GHz or higher operating speeds, the physics of electron flow through devices becomes more complicated, and physical effects, which previously could be safely ignored, become significant. Consequently, models of a higher abstraction level are needed. Conversely, faster simulation is typically required, which places a constraint on the model refinement if conventional simulation techniques are applied.

    Like the invention of the transistor triggered research in circuit simulation, the invention of the laser had a major impact on optical technologies. Classical optics turned into photonics. In todays telecommunication technologies, photons have already become the main carrier of information, regardless of the fact that even today most of the applied optical devices are based on conventional optical fibers and low index-contrast waveguides. Recently, a number of pioneering developments - all based on nanotechnologies - opened up the door to completely new working principles, hence to new classes of optoelectronic devices. Among them are nanostructured periodic materials (photonic crystals) and optically active nanostructures like quantum layers and quantum dots. A proper modelling of such structures has to describe simultaneously electrical charge transport, light generation, light propagation and scattering. Moreover, optical active nanostructures have to be described by quantum mechanics.

    In spite of the achievements of electronic/optoelectronic device and circuit simulation obtained so far, new nanotechnologies create new challenging tasks for mathematical modeling and numerical simulation in this field.

    Topics:
    • shape memory alloys in airfoils
    • production of semiconductor crystals
    • methanole fuel cell optimization
    • online production planning metamaterials


    http://www.math.hu-berlin.de/~yanchuk/RG/
  • C27

    Simulation of magnetic rotary shaft seals

    Project heads: -
    Project members: -
    Duration: 01/09-04/09
    Status: completed

    Description

    Production is one of the most important parts of the economy and at the very heart of the creation of value. Due to the central importance of production, big efforts have been made to improve production processes ever since the beginning of the industrial revolution. Nowadays, many production processes are highly automated. Computer programs based on numerical algorithms monitor the processes, improve efficiency and robustness, and guarantee high quality products. Consequently, mathematics is playing a steadily increasing role in this field. The possibilities of applying mathematical methods in production are wide-ranging. The Application Area cannot cover their full scale. For that reason, the projects concentrate on the development of new mathematical methods for special topics in manufacturing and production planning, two central aspects of production, in which the participating groups have longstanding expertise in mathematical modeling, simulation and optimization.

    In the field of manufacturing, we focus on innovative technologies having a big impact on technological progress: growth and processing of semiconductor bulk single crystals, phase transitions in modern steels and solder alloys, modeling of active and passive behavior of functional materials like shape-memory materials, growth of thin films. In the projects devoted to production planning, the main aim is the effective control of the whole production flow. Among the subjects to be studied, there is also electricity portfolio management.

    Topics:
    • phase transitions in steels and solder alloys
    • production of semiconductor crystals
    • modeling of active and passive behavior of functional materials
    • online production planning
    • growth of thin films


    http://www.math.hu-berlin.de/~muellerr/C27
  • C28

    Optimal control of phase separation phenomena

    Project heads: -
    Project members: -
    Duration: 07/09-05/14
    Status: completed

    Description

    Production is one of the most important parts of the economy and at the very heart of the creation of value. Due to the central importance of production, big efforts have been made to improve production processes ever since the beginning of the industrial revolution. Nowadays, many production processes are highly automated. Computer programs based on numerical algorithms monitor the processes, improve efficiency and robustness, and guarantee high quality products. Consequently, mathematics is playing a steadily increasing role in this field. The possibilities of applying mathematical methods in production are wide-ranging. The Application Area cannot cover their full scale. For that reason, the projects concentrate on the development of new mathematical methods for special topics in manufacturing and production planning, two central aspects of production, in which the participating groups have longstanding expertise in mathematical modeling, simulation and optimization.

    In the field of manufacturing, we focus on innovative technologies having a big impact on technological progress: growth and processing of semiconductor bulk single crystals, phase transitions in modern steels and solder alloys, modeling of active and passive behavior of functional materials like shape-memory materials, growth of thin films. In the projects devoted to production planning, the main aim is the effective control of the whole production flow. Among the subjects to be studied, there is also electricity portfolio management.

    Topics:
    • phase transitions in steels and solder alloys
    • production of semiconductor crystals
    • modeling of active and passive behavior of functional materials
    • online production planning
    • growth of thin films


    http://www.math.hu-berlin.de/~hp_hint/C28
  • A15

    Viscosity properties of biomembrane surfaces

    Project heads: -
    Project members: -
    Duration: 02/09 - 05/14
    Status: completed

    Description

    "Life sciences" describe a wide research area with enormous technological and social impact. However, there exist specific areas where mathematics has just begun to take on an active role.

    In medicine, the already traditional role of mathematics in medical imaging (e.g., computer tomography) has been successfully extended. Mathematical progress has proved to directly influence medical progress towards the design of patient-specific therapies - e.g., in the cancer therapy hyperthermia. As another example, computer-assisted surgery planning allows the comparison of various operation options before the actual operation on the basis of a simulation of more and more realistic models describing soft tissue, bone, or typical human gaits such as stair climbing. Further mathematization of the field is expected to open entirely new perspectives for the optimal design of joint prostheses adapted to individual anatomy.

    In biotechnology, the present situation is clearly dominated by the generation of huge datasets about biomolecular, genetic, metabolic or other bio-processes. Algorithms from discrete mathematics or computer science (e.g., in multiple alignment) already play a publicly visible role in the decoding of the human and other genomes. In contrast to that, the mathematical treatment of the dynamics of bio-processes is still rather limited - even though this aspect seems to be crucial for the detailed understanding of virus diseases or the design of narrow band drugs. Therefore, beyond the well-established core areas of bioinformatics, numerical biocomputing has recently become more and more accepted as one of the keys to data-based reliable prediction, control and design of real-life bio-processes: As it turns out, a significant increase in our ability in a reliable quantitative simulation of the dynamics of large biomolecules is essential for a detailed understanding of, e.g., the enzymatic mechanisms of prion diseases (like the mad cow disease or its human counterpart, the Creutzfeldt-Jacob syndrome).

    Topics:
    • computer-assisted surgery
    • patient-specific therapy planning
    • protein data base analysis
    • protein conformation dynamics
    • systems biology
    • pharmacokinetics


    http://www.math.fu-berlin.de/en/groups/cellmechanics/
  • A16

    Numerical treatment of the chemical master equation using sums of separable functions

    Project heads: -
    Project members: -
    Duration: 03/09-05/10
    Status: completed

    Description

    "Life sciences" describe a wide research area with enormous technological and social impact. However, there exist specific areas where mathematics has just begun to take on an active role.

    In medicine, the already traditional role of mathematics in medical imaging (e.g., computer tomography) has been successfully extended. Mathematical progress has proved to directly influence medical progress towards the design of patient-specific therapies - e.g., in the cancer therapy hyperthermia. As another example, computer-assisted surgery planning allows the comparison of various operation options before the actual operation on the basis of a simulation of more and more realistic models describing soft tissue, bone, or typical human gaits such as stair climbing. Further mathematization of the field is expected to open entirely new perspectives for the optimal design of joint prostheses adapted to individual anatomy.

    In biotechnology, the present situation is clearly dominated by the generation of huge datasets about biomolecular, genetic, metabolic or other bio-processes. Algorithms from discrete mathematics or computer science (e.g., in multiple alignment) already play a publicly visible role in the decoding of the human and other genomes. In contrast to that, the mathematical treatment of the dynamics of bio-processes is still rather limited - even though this aspect seems to be crucial for the detailed understanding of virus diseases or the design of narrow band drugs. Therefore, beyond the well-established core areas of bioinformatics, numerical biocomputing has recently become more and more accepted as one of the keys to data-based reliable prediction, control and design of real-life bio-processes: As it turns out, a significant increase in our ability in a reliable quantitative simulation of the dynamics of large biomolecules is essential for a detailed understanding of, e.g., the enzymatic mechanisms of prion diseases (like the mad cow disease or its human counterpart, the Creutzfeldt-Jacob syndrome).

    Topics:
    • computer-assisted surgery
    • patient-specific therapy planning
    • protein data base analysis
    • protein conformation dynamics
    • systems biology
    • pharmacokinetics


    http://www.math.tu-berlin.de/~garcke/Files/Matheon_project.html
  • B20

    Optimization of gas transport

    Project heads: -
    Project members: -
    Duration: 05/09 - 05/14
    Status: completed

    Description

    Networks, such as telephone networks, the internet, airline, railway, and bus networks are omnipresent and play a fundamental role for communication and mobility in our society. We almost take their permanent availability, reliability, and quality at low cost for granted. However, traffic jams, ill-designed train schedules, canceled flights, break-downs of telephone and computing networks, and slow internet access are reminders that networks are not automatically good networks.

    In fact, designing and operating communication and traffic networks are extremely complex tasks that lead directly to mathematical problems. A good example is the design of telecommunication networks. They were implemented with simple low-cost tree topologies until 15 years ago. Then, in 1988, a telco hub broke down in Chicago. This brought O Hare airport to a stand-still and caused an estimated business loss of billions of US dollars. Disasters of this kind made it clear that more sophisticated designs were needed. Nowadays, telecommunication companies use mathematically designed networks with built-in failure safety and rerouting capacities. Similar developments are expected in road traffic. We are now facing the installation of the first generation of load measuring, signalling, pricing, and route finding devices. These will soon integrate into a network-wide telematic system based on mathematical methods of traffic prediction, simulation, and control.

    Network design and operation tasks of this type are traditionally handled under the responsibility of various engineering disciplines (electrical engineering, traffic management and logistics, industrial engineering). While these disciplines can contribute to the improvement of the engineering components of such networks, todays demand on global optimization of the entire system poses problems where qualitative progress has to come from a better theoretical understanding of the structural aspects of the networks.

    This is where mathematics must come into play. The appearance of the word "network" in all the systems described above is not accidental, but hints at a common feature that has deep mathematical roots: networks are fundamental structures of graph theory and combinatorial optimization. Their study has become a prosperous subject in recent years, with impressive successes in many applications. The groups in Berlin are among the driving forces in this development.

    Nowadays, mathematical optimization techniques are used to locate switches and hubs in a phone system, to schedule buses and bus drivers in metropolitan transportation systems, etc. These tasks are individual steps in a hierarchical and sequential network planning process. In public transport, for example, this sequential process encompasses line planning, finding a periodic time table, assigning buses to lines, and creating individual bus driver schedules.

    Topics:
    • planning of optical, multilayer, and UMTS telecommunication networks
    • line planning, periodic timetabling, and revenue management in public transport networks
    • optimization in logistics, scheduling and material flows
    • optimization under uncertainty
    • symmetries in integer programming
    • game theoretic methods in network design


    http://www.zib.de/en/optimization/mip/projects-long/Matheon-b20-optimization-of-gas-transport.html
  • B21

    Optical Access Networks

    Project heads: -
    Project members: -
    Duration: 06/09-05/14
    Status: completed

    Description

    Networks, such as telephone networks, the internet, airline, railway, and bus networks are omnipresent and play a fundamental role for communication and mobility in our society. We almost take their permanent availability, reliability, and quality at low cost for granted. However, traffic jams, ill-designed train schedules, canceled flights, break-downs of telephone and computing networks, and slow internet access are reminders that networks are not automatically good networks.

    In fact, designing and operating communication and traffic networks are extremely complex tasks that lead directly to mathematical problems. A good example is the design of telecommunication networks. They were implemented with simple low-cost tree topologies until 15 years ago. Then, in 1988, a telco hub broke down in Chicago. This brought O Hare airport to a stand-still and caused an estimated business loss of billions of US dollars. Disasters of this kind made it clear that more sophisticated designs were needed. Nowadays, telecommunication companies use mathematically designed networks with built-in failure safety and rerouting capacities. Similar developments are expected in road traffic. We are now facing the installation of the first generation of load measuring, signalling, pricing, and route finding devices. These will soon integrate into a network-wide telematic system based on mathematical methods of traffic prediction, simulation, and control.

    Network design and operation tasks of this type are traditionally handled under the responsibility of various engineering disciplines (electrical engineering, traffic management and logistics, industrial engineering). While these disciplines can contribute to the improvement of the engineering components of such networks, todays demand on global optimization of the entire system poses problems where qualitative progress has to come from a better theoretical understanding of the structural aspects of the networks.

    This is where mathematics must come into play. The appearance of the word "network" in all the systems described above is not accidental, but hints at a common feature that has deep mathematical roots: networks are fundamental structures of graph theory and combinatorial optimization. Their study has become a prosperous subject in recent years, with impressive successes in many applications. The groups in Berlin are among the driving forces in this development.

    Nowadays, mathematical optimization techniques are used to locate switches and hubs in a phone system, to schedule buses and bus drivers in metropolitan transportation systems, etc. These tasks are individual steps in a hierarchical and sequential network planning process. In public transport, for example, this sequential process encompasses line planning, finding a periodic time table, assigning buses to lines, and creating individual bus driver schedules.

    Topics:
    • planning of optical, multilayer, and UMTS telecommunication networks
    • line planning, periodic timetabling, and revenue management in public transport networks
    • optimization in logistics, scheduling and material flows
    • optimization under uncertainty
    • symmetries in integer programming
    • game theoretic methods in network design


    http://www3.math.tu-berlin.de/coga/projects/Matheon/B21/
  • C29

    Numerical methods for large-scale parameter-dependent systems

    Project heads: -
    Project members: -
    Duration: 06/09-05/14
    Status: completed

    Description

    Production is one of the most important parts of the economy and at the very heart of the creation of value. Due to the central importance of production, big efforts have been made to improve production processes ever since the beginning of the industrial revolution. Nowadays, many production processes are highly automated. Computer programs based on numerical algorithms monitor the processes, improve efficiency and robustness, and guarantee high quality products. Consequently, mathematics is playing a steadily increasing role in this field. The possibilities of applying mathematical methods in production are wide-ranging. The Application Area cannot cover their full scale. For that reason, the projects concentrate on the development of new mathematical methods for special topics in manufacturing and production planning, two central aspects of production, in which the participating groups have longstanding expertise in mathematical modeling, simulation and optimization.

    In the field of manufacturing, we focus on innovative technologies having a big impact on technological progress: growth and processing of semiconductor bulk single crystals, phase transitions in modern steels and solder alloys, modeling of active and passive behavior of functional materials like shape-memory materials, growth of thin films. In the projects devoted to production planning, the main aim is the effective control of the whole production flow. Among the subjects to be studied, there is also electricity portfolio management.

    Topics:
    • phase transitions in steels and solder alloys
    • production of semiconductor crystals
    • modeling of active and passive behavior of functional materials
    • online production planning
    • growth of thin films


    http://www3.math.tu-berlin.de/Matheon/projects/C29
  • F9

    Trajectory compression

    Project heads: -
    Project members: -
    Duration: 08/09 - 05/14
    Status: completed

    Description

    Visualization has the task to create insight from given data. Image analysis is to extract information from data and to make it explicit in the form of a geometric model. The two areas have tight relations on both the methodical and the application level. Prominent examples are image-based rendering and visual analysis of 3D image data, e.g. in tomography or confocal microscopy.

    In recent years we have seen a rapid development of fundamentally new techniques for the visualization of complex physical phenomena as well as for imaging applications. At the very heart of these new technologies we encounter fundamentally new data structures and algorithms, all with a quest for a new level of abstraction. Here is where mathematics enters the scene.

    Especially in visualization, it is still a challenge to give the underlying objects a solid mathematical description. Here the research field of mathematical visualization faces the challenge to develop precise abstractions which eventually enables the development of new algorithms and visualization tools. Efforts in this direction can build on broad mathematical foundations, laid among others in the fields of discrete geometry, computational geometry, discrete differential geometry, and combinatorial topology. Results of this development are not only needed in research, where scientifically correct visualization is essential, but also meant to provide a solid basis for applications, for example, in computer graphics as well as in mathematics education projects.

    Even more so, the fields of visualization and image processing are key technologies for very current fields of research, among them many of the natural sciences (physics, chemistry, climate research), the life sciences (medicine, biochemistry, biotechnology, pharmacy), but also for various problems of engineering and production. Due to the multiple applications, but also due to technological reasons such as the availability of new imaging devices and display technology, imaging and visualization have been - and will be - areas of impressive growth.

    Topics:
    • discrete differential geometry
    • geometry processing
    • image processing
    • virtual reality PORTAL


    http://www.zib.de/de/numerik/projekte/projektdetails/article/Matheon-f9-1.html
  • E11

    Beyond Value at Risk: Dynamic Risk Measures and Applications

    Project heads: -
    Project members: -
    Duration: 09/09-06/13
    Status: completed

    Description

    Mathematics has become highly visible as a key technology in the area of finance and insurance. Increasingly, advanced probabilistic and statistical methods are being applied to the analysis of financial risk in its various forms. Their impact is not only felt on a computational level. To a surprising extent, concepts of stochastic analysis are shaping the discourse of the field, both in academia and in the financial industry. Conversely, finance has become a significant source of new research problems in mathematical modelling, simulation and optimization.

    Such problems arise typically beyond the idealized context of a complete financial market model without frictions, where derivatives admit a perfect hedge and hence can be priced by arbitrage. As one moves on to more realistic models, the Black-Scholes paradigm of a perfect hedge breaks down. Instead, one is confronted with an incomplete financial market model where derivatives carry an intrinsic risk which cannot be hedged away. In an incomplete model, the challenge is to construct hedging strategies which are optimal in terms of some criterion of risk minimization. Considerable progress has been made over the last years in understanding the mathematical structure of such strategies, and Berlin has played a leading role in this development.

    At the same time, demand by the financial industry for advanced mathematical methods of assessing and hedging financial risk has increased dramatically. One major factor is the growing pressure of supervising agencies on banks to improve their internal models for quantifying risk exposure, triggered by the 1995 guidelines of the Basel Committee on Banking Supervision and their ongoing improvements. Banks are now competing not only in the innovation of financial products but also in the development of new methods of risk management. Another important factor is the breakdown of traditional boundaries between the financial and the insurance industry, in particular the growing trend towards financial securitization of insurance risks. This leads to the design of new products which combine very different sources of risk and pose new valuation and hedging problems.

    Topics:
    • measurement and hedging of risks
    • interaction models for asset price fluctuation


    http://www.mathematik.hu-berlin.de/~kupper
  • E10

    Large deviation-, heat kernel- and PDE methods in the study of volatility of financial markets

    Project heads: -
    Project members: -
    Duration: 11/09-05/14
    Status: completed

    Description

    Mathematics has become highly visible as a key technology in the area of finance and insurance. Increasingly, advanced probabilistic and statistical methods are being applied to the analysis of financial risk in its various forms. Their impact is not only felt on a computational level. To a surprising extent, concepts of stochastic analysis are shaping the discourse of the field, both in academia and in the financial industry. Conversely, finance has become a significant source of new research problems in mathematical modelling, simulation and optimization.

    Such problems arise typically beyond the idealized context of a complete financial market model without frictions, where derivatives admit a perfect hedge and hence can be priced by arbitrage. As one moves on to more realistic models, the Black-Scholes paradigm of a perfect hedge breaks down. Instead, one is confronted with an incomplete financial market model where derivatives carry an intrinsic risk which cannot be hedged away. In an incomplete model, the challenge is to construct hedging strategies which are optimal in terms of some criterion of risk minimization. Considerable progress has been made over the last years in understanding the mathematical structure of such strategies, and Berlin has played a leading role in this development.

    At the same time, demand by the financial industry for advanced mathematical methods of assessing and hedging financial risk has increased dramatically. One major factor is the growing pressure of supervising agencies on banks to improve their internal models for quantifying risk exposure, triggered by the 1995 guidelines of the Basel Committee on Banking Supervision and their ongoing improvements. Banks are now competing not only in the innovation of financial products but also in the development of new methods of risk management. Another important factor is the breakdown of traditional boundaries between the financial and the insurance industry, in particular the growing trend towards financial securitization of insurance risks. This leads to the design of new products which combine very different sources of risk and pose new valuation and hedging problems.

    Topics:
    • measurement and hedging of risks
    • interaction models for asset price fluctuation


    http://www.math.tu-berlin.de/~friz/
  • A17

    Computational surgery planning

    Project heads: -
    Project members: -
    Duration: 06/10-05/14
    Status: completed

    Description

    "Life sciences" describe a wide research area with enormous technological and social impact. However, there exist specific areas where mathematics has just begun to take on an active role.

    In medicine, the already traditional role of mathematics in medical imaging (e.g., computer tomography) has been successfully extended. Mathematical progress has proved to directly influence medical progress towards the design of patient-specific therapies - e.g., in the cancer therapy hyperthermia. As another example, computer-assisted surgery planning allows the comparison of various operation options before the actual operation on the basis of a simulation of more and more realistic models describing soft tissue, bone, or typical human gaits such as stair climbing. Further mathematization of the field is expected to open entirely new perspectives for the optimal design of joint prostheses adapted to individual anatomy.

    In biotechnology, the present situation is clearly dominated by the generation of huge datasets about biomolecular, genetic, metabolic or other bio-processes. Algorithms from discrete mathematics or computer science (e.g., in multiple alignment) already play a publicly visible role in the decoding of the human and other genomes. In contrast to that, the mathematical treatment of the dynamics of bio-processes is still rather limited - even though this aspect seems to be crucial for the detailed understanding of virus diseases or the design of narrow band drugs. Therefore, beyond the well-established core areas of bioinformatics, numerical biocomputing has recently become more and more accepted as one of the keys to data-based reliable prediction, control and design of real-life bio-processes: As it turns out, a significant increase in our ability in a reliable quantitative simulation of the dynamics of large biomolecules is essential for a detailed understanding of, e.g., the enzymatic mechanisms of prion diseases (like the mad cow disease or its human counterpart, the Creutzfeldt-Jacob syndrome).

    Topics:
    • computer-assisted surgery
    • patient-specific therapy planning
    • protein data base analysis
    • protein conformation dynamics
    • systems biology
    • pharmacokinetics


    http://www.zib.de/de/numerik/projekte/projektdetails/article/Matheon-a17.html
  • A18

    Mathematical system biology

    Project heads: -
    Project members: -
    Duration: 06/10-05/14
    Status: completed

    Description

    "Life sciences" describe a wide research area with enormous technological and social impact. However, there exist specific areas where mathematics has just begun to take on an active role.

    In medicine, the already traditional role of mathematics in medical imaging (e.g., computer tomography) has been successfully extended. Mathematical progress has proved to directly influence medical progress towards the design of patient-specific therapies - e.g., in the cancer therapy hyperthermia. As another example, computer-assisted surgery planning allows the comparison of various operation options before the actual operation on the basis of a simulation of more and more realistic models describing soft tissue, bone, or typical human gaits such as stair climbing. Further mathematization of the field is expected to open entirely new perspectives for the optimal design of joint prostheses adapted to individual anatomy.

    In biotechnology, the present situation is clearly dominated by the generation of huge datasets about biomolecular, genetic, metabolic or other bio-processes. Algorithms from discrete mathematics or computer science (e.g., in multiple alignment) already play a publicly visible role in the decoding of the human and other genomes. In contrast to that, the mathematical treatment of the dynamics of bio-processes is still rather limited - even though this aspect seems to be crucial for the detailed understanding of virus diseases or the design of narrow band drugs. Therefore, beyond the well-established core areas of bioinformatics, numerical biocomputing has recently become more and more accepted as one of the keys to data-based reliable prediction, control and design of real-life bio-processes: As it turns out, a significant increase in our ability in a reliable quantitative simulation of the dynamics of large biomolecules is essential for a detailed understanding of, e.g., the enzymatic mechanisms of prion diseases (like the mad cow disease or its human counterpart, the Creutzfeldt-Jacob syndrome).

    Topics:
    • computer-assisted surgery
    • patient-specific therapy planning
    • protein data base analysis
    • protein conformation dynamics
    • systems biology
    • pharmacokinetics


    http://www.math.fu-berlin.de/en/groups/mathlife/projects/A18/index.html
  • A19

    Modeling and optimization of functional molecules

    Project heads: -
    Project members: -
    Duration: 06/10-05/14
    Status: completed

    Description

    "Life sciences" describe a wide research area with enormous technological and social impact. However, there exist specific areas where mathematics has just begun to take on an active role.

    In medicine, the already traditional role of mathematics in medical imaging (e.g., computer tomography) has been successfully extended. Mathematical progress has proved to directly influence medical progress towards the design of patient-specific therapies - e.g., in the cancer therapy hyperthermia. As another example, computer-assisted surgery planning allows the comparison of various operation options before the actual operation on the basis of a simulation of more and more realistic models describing soft tissue, bone, or typical human gaits such as stair climbing. Further mathematization of the field is expected to open entirely new perspectives for the optimal design of joint prostheses adapted to individual anatomy.

    In biotechnology, the present situation is clearly dominated by the generation of huge datasets about biomolecular, genetic, metabolic or other bio-processes. Algorithms from discrete mathematics or computer science (e.g., in multiple alignment) already play a publicly visible role in the decoding of the human and other genomes. In contrast to that, the mathematical treatment of the dynamics of bio-processes is still rather limited - even though this aspect seems to be crucial for the detailed understanding of virus diseases or the design of narrow band drugs. Therefore, beyond the well-established core areas of bioinformatics, numerical biocomputing has recently become more and more accepted as one of the keys to data-based reliable prediction, control and design of real-life bio-processes: As it turns out, a significant increase in our ability in a reliable quantitative simulation of the dynamics of large biomolecules is essential for a detailed understanding of, e.g., the enzymatic mechanisms of prion diseases (like the mad cow disease or its human counterpart, the Creutzfeldt-Jacob syndrome).

    Topics:
    • computer-assisted surgery
    • patient-specific therapy planning
    • protein data base analysis
    • protein conformation dynamics
    • systems biology
    • pharmacokinetics


    http://www.biocomputing-berlin.de/biocomputing/en/projects/Matheon_project_a19_modelling_and_optimization_of_functional_molecules/
  • A20

    Numerical methods in quantum chemistry

    Project heads: -
    Project members: -
    Duration: 06/10-05/14
    Status: completed

    Description

    "Life sciences" describe a wide research area with enormous technological and social impact. However, there exist specific areas where mathematics has just begun to take on an active role.

    In medicine, the already traditional role of mathematics in medical imaging (e.g., computer tomography) has been successfully extended. Mathematical progress has proved to directly influence medical progress towards the design of patient-specific therapies - e.g., in the cancer therapy hyperthermia. As another example, computer-assisted surgery planning allows the comparison of various operation options before the actual operation on the basis of a simulation of more and more realistic models describing soft tissue, bone, or typical human gaits such as stair climbing. Further mathematization of the field is expected to open entirely new perspectives for the optimal design of joint prostheses adapted to individual anatomy.

    In biotechnology, the present situation is clearly dominated by the generation of huge datasets about biomolecular, genetic, metabolic or other bio-processes. Algorithms from discrete mathematics or computer science (e.g., in multiple alignment) already play a publicly visible role in the decoding of the human and other genomes. In contrast to that, the mathematical treatment of the dynamics of bio-processes is still rather limited - even though this aspect seems to be crucial for the detailed understanding of virus diseases or the design of narrow band drugs. Therefore, beyond the well-established core areas of bioinformatics, numerical biocomputing has recently become more and more accepted as one of the keys to data-based reliable prediction, control and design of real-life bio-processes: As it turns out, a significant increase in our ability in a reliable quantitative simulation of the dynamics of large biomolecules is essential for a detailed understanding of, e.g., the enzymatic mechanisms of prion diseases (like the mad cow disease or its human counterpart, the Creutzfeldt-Jacob syndrome).

    Topics:
    • computer-assisted surgery
    • patient-specific therapy planning
    • protein data base analysis
    • protein conformation dynamics
    • systems biology
    • pharmacokinetics


    http://page.math.tu-berlin.de/~gauckler/a20/
  • B22

    Rolling stock roster planning for railways

    Project heads: -
    Project members: -
    Duration: 06/10-05/14
    Status: completed

    Description

    Networks, such as telephone networks, the internet, airline, railway, and bus networks are omnipresent and play a fundamental role for communication and mobility in our society. We almost take their permanent availability, reliability, and quality at low cost for granted. However, traffic jams, ill-designed train schedules, canceled flights, break-downs of telephone and computing networks, and slow internet access are reminders that networks are not automatically good networks.

    In fact, designing and operating communication and traffic networks are extremely complex tasks that lead directly to mathematical problems. A good example is the design of telecommunication networks. They were implemented with simple low-cost tree topologies until 15 years ago. Then, in 1988, a telco hub broke down in Chicago. This brought O Hare airport to a stand-still and caused an estimated business loss of billions of US dollars. Disasters of this kind made it clear that more sophisticated designs were needed. Nowadays, telecommunication companies use mathematically designed networks with built-in failure safety and rerouting capacities. Similar developments are expected in road traffic. We are now facing the installation of the first generation of load measuring, signalling, pricing, and route finding devices. These will soon integrate into a network-wide telematic system based on mathematical methods of traffic prediction, simulation, and control.

    Network design and operation tasks of this type are traditionally handled under the responsibility of various engineering disciplines (electrical engineering, traffic management and logistics, industrial engineering). While these disciplines can contribute to the improvement of the engineering components of such networks, todays demand on global optimization of the entire system poses problems where qualitative progress has to come from a better theoretical understanding of the structural aspects of the networks.

    This is where mathematics must come into play. The appearance of the word "network" in all the systems described above is not accidental, but hints at a common feature that has deep mathematical roots: networks are fundamental structures of graph theory and combinatorial optimization. Their study has become a prosperous subject in recent years, with impressive successes in many applications. The groups in Berlin are among the driving forces in this development.

    Nowadays, mathematical optimization techniques are used to locate switches and hubs in a phone system, to schedule buses and bus drivers in metropolitan transportation systems, etc. These tasks are individual steps in a hierarchical and sequential network planning process. In public transport, for example, this sequential process encompasses line planning, finding a periodic time table, assigning buses to lines, and creating individual bus driver schedules.

    Topics:
    • planning of optical, multilayer, and UMTS telecommunication networks
    • line planning, periodic timetabling, and revenue management in public transport networks
    • optimization in logistics, scheduling and material flows
    • optimization under uncertainty
    • symmetries in integer programming
    • game theoretic methods in network design


    http://www.zib.de/en/projects/current-projects/project-details/article/Matheon-b22-rolling-stock-roster-planning.html
  • B23

    Robust optimization for network applications

    Project heads: -
    Project members: -
    Duration: 06/10-05/14
    Status: completed

    Description

    Networks, such as telephone networks, the internet, airline, railway, and bus networks are omnipresent and play a fundamental role for communication and mobility in our society. We almost take their permanent availability, reliability, and quality at low cost for granted. However, traffic jams, ill-designed train schedules, canceled flights, break-downs of telephone and computing networks, and slow internet access are reminders that networks are not automatically good networks.

    In fact, designing and operating communication and traffic networks are extremely complex tasks that lead directly to mathematical problems. A good example is the design of telecommunication networks. They were implemented with simple low-cost tree topologies until 15 years ago. Then, in 1988, a telco hub broke down in Chicago. This brought O Hare airport to a stand-still and caused an estimated business loss of billions of US dollars. Disasters of this kind made it clear that more sophisticated designs were needed. Nowadays, telecommunication companies use mathematically designed networks with built-in failure safety and rerouting capacities. Similar developments are expected in road traffic. We are now facing the installation of the first generation of load measuring, signalling, pricing, and route finding devices. These will soon integrate into a network-wide telematic system based on mathematical methods of traffic prediction, simulation, and control.

    Network design and operation tasks of this type are traditionally handled under the responsibility of various engineering disciplines (electrical engineering, traffic management and logistics, industrial engineering). While these disciplines can contribute to the improvement of the engineering components of such networks, todays demand on global optimization of the entire system poses problems where qualitative progress has to come from a better theoretical understanding of the structural aspects of the networks.

    This is where mathematics must come into play. The appearance of the word "network" in all the systems described above is not accidental, but hints at a common feature that has deep mathematical roots: networks are fundamental structures of graph theory and combinatorial optimization. Their study has become a prosperous subject in recent years, with impressive successes in many applications. The groups in Berlin are among the driving forces in this development.

    Nowadays, mathematical optimization techniques are used to locate switches and hubs in a phone system, to schedule buses and bus drivers in metropolitan transportation systems, etc. These tasks are individual steps in a hierarchical and sequential network planning process. In public transport, for example, this sequential process encompasses line planning, finding a periodic time table, assigning buses to lines, and creating individual bus driver schedules.

    Topics:
    • planning of optical, multilayer, and UMTS telecommunication networks
    • line planning, periodic timetabling, and revenue management in public transport networks
    • optimization in logistics, scheduling and material flows
    • optimization under uncertainty
    • symmetries in integer programming
    • game theoretic methods in network design


    http://www.coga.tu-berlin.de/v-menue/projekte/Matheon_b23/parameter/en/
  • B24

    Scheduling material flows in logistic networks

    Project heads: -
    Project members: -
    Duration: 06/10-05/14
    Status: completed

    Description

    Networks, such as telephone networks, the internet, airline, railway, and bus networks are omnipresent and play a fundamental role for communication and mobility in our society. We almost take their permanent availability, reliability, and quality at low cost for granted. However, traffic jams, ill-designed train schedules, canceled flights, break-downs of telephone and computing networks, and slow internet access are reminders that networks are not automatically good networks.

    In fact, designing and operating communication and traffic networks are extremely complex tasks that lead directly to mathematical problems. A good example is the design of telecommunication networks. They were implemented with simple low-cost tree topologies until 15 years ago. Then, in 1988, a telco hub broke down in Chicago. This brought O Hare airport to a stand-still and caused an estimated business loss of billions of US dollars. Disasters of this kind made it clear that more sophisticated designs were needed. Nowadays, telecommunication companies use mathematically designed networks with built-in failure safety and rerouting capacities. Similar developments are expected in road traffic. We are now facing the installation of the first generation of load measuring, signalling, pricing, and route finding devices. These will soon integrate into a network-wide telematic system based on mathematical methods of traffic prediction, simulation, and control.

    Network design and operation tasks of this type are traditionally handled under the responsibility of various engineering disciplines (electrical engineering, traffic management and logistics, industrial engineering). While these disciplines can contribute to the improvement of the engineering components of such networks, todays demand on global optimization of the entire system poses problems where qualitative progress has to come from a better theoretical understanding of the structural aspects of the networks.

    This is where mathematics must come into play. The appearance of the word "network" in all the systems described above is not accidental, but hints at a common feature that has deep mathematical roots: networks are fundamental structures of graph theory and combinatorial optimization. Their study has become a prosperous subject in recent years, with impressive successes in many applications. The groups in Berlin are among the driving forces in this development.

    Nowadays, mathematical optimization techniques are used to locate switches and hubs in a phone system, to schedule buses and bus drivers in metropolitan transportation systems, etc. These tasks are individual steps in a hierarchical and sequential network planning process. In public transport, for example, this sequential process encompasses line planning, finding a periodic time table, assigning buses to lines, and creating individual bus driver schedules.

    Topics:
    • planning of optical, multilayer, and UMTS telecommunication networks
    • line planning, periodic timetabling, and revenue management in public transport networks
    • optimization in logistics, scheduling and material flows
    • optimization under uncertainty
    • symmetries in integer programming
    • game theoretic methods in network design


    http://www.coga.tu-berlin.de/v-menue/projekte/Matheon_b24/parameter/en/
  • C30

    Automatic reconfiguration of robotic welding cells

    Project heads: -
    Project members: -
    Duration: 06/10-05/14
    Status: completed

    Description

    Production is one of the most important parts of the economy and at the very heart of the creation of value. Due to the central importance of production, big efforts have been made to improve production processes ever since the beginning of the industrial revolution. Nowadays, many production processes are highly automated. Computer programs based on numerical algorithms monitor the processes, improve efficiency and robustness, and guarantee high quality products. Consequently, mathematics is playing a steadily increasing role in this field. The possibilities of applying mathematical methods in production are wide-ranging. The Application Area cannot cover their full scale. For that reason, the projects concentrate on the development of new mathematical methods for special topics in manufacturing and production planning, two central aspects of production, in which the participating groups have longstanding expertise in mathematical modeling, simulation and optimization.

    In the field of manufacturing, we focus on innovative technologies having a big impact on technological progress: growth and processing of semiconductor bulk single crystals, phase transitions in modern steels and solder alloys, modeling of active and passive behavior of functional materials like shape-memory materials, growth of thin films. In the projects devoted to production planning, the main aim is the effective control of the whole production flow. Among the subjects to be studied, there is also electricity portfolio management.

    Topics:
    • phase transitions in steels and solder alloys
    • production of semiconductor crystals
    • modeling of active and passive behavior of functional materials
    • online production planning
    • growth of thin films


    http://www.coga.tu-berlin.de/v-menue/projekte/Matheon_c30/parameter/en/
  • C31

    Numerical minimization of nonsmooth energy functionals in multiphase materials

    Project heads: -
    Project members: -
    Duration: 06/10-07/12
    Status: completed

    Description

    Production is one of the most important parts of the economy and at the very heart of the creation of value. Due to the central importance of production, big efforts have been made to improve production processes ever since the beginning of the industrial revolution. Nowadays, many production processes are highly automated. Computer programs based on numerical algorithms monitor the processes, improve efficiency and robustness, and guarantee high quality products. Consequently, mathematics is playing a steadily increasing role in this field. The possibilities of applying mathematical methods in production are wide-ranging. The Application Area cannot cover their full scale. For that reason, the projects concentrate on the development of new mathematical methods for special topics in manufacturing and production planning, two central aspects of production, in which the participating groups have longstanding expertise in mathematical modeling, simulation and optimization.

    In the field of manufacturing, we focus on innovative technologies having a big impact on technological progress: growth and processing of semiconductor bulk single crystals, phase transitions in modern steels and solder alloys, modeling of active and passive behavior of functional materials like shape-memory materials, growth of thin films. In the projects devoted to production planning, the main aim is the effective control of the whole production flow. Among the subjects to be studied, there is also electricity portfolio management.

    Topics:
    • phase transitions in steels and solder alloys
    • production of semiconductor crystals
    • modeling of active and passive behavior of functional materials
    • online production planning
    • growth of thin films


    http://www.math.hu-berlin.de/~hp_hint/C31
  • C32

    Modeling of phase separation and damage processes in alloys

    Project heads: -
    Project members: -
    Duration: 06/10-05/14
    Status: completed

    Description

    Production is one of the most important parts of the economy and at the very heart of the creation of value. Due to the central importance of production, big efforts have been made to improve production processes ever since the beginning of the industrial revolution. Nowadays, many production processes are highly automated. Computer programs based on numerical algorithms monitor the processes, improve efficiency and robustness, and guarantee high quality products. Consequently, mathematics is playing a steadily increasing role in this field. The possibilities of applying mathematical methods in production are wide-ranging. The Application Area cannot cover their full scale. For that reason, the projects concentrate on the development of new mathematical methods for special topics in manufacturing and production planning, two central aspects of production, in which the participating groups have longstanding expertise in mathematical modeling, simulation and optimization.

    In the field of manufacturing, we focus on innovative technologies having a big impact on technological progress: growth and processing of semiconductor bulk single crystals, phase transitions in modern steels and solder alloys, modeling of active and passive behavior of functional materials like shape-memory materials, growth of thin films. In the projects devoted to production planning, the main aim is the effective control of the whole production flow. Among the subjects to be studied, there is also electricity portfolio management.

    Topics:
    • phase transitions in steels and solder alloys
    • production of semiconductor crystals
    • modeling of active and passive behavior of functional materials
    • online production planning
    • growth of thin films


    http://www.wias-berlin.de/people/griepent/C32.html
  • D22

    Modeling of electronic properties of interfaces in solar cells

    Project heads: -
    Project members: -
    Duration: 06/10-05/14
    Status: completed

    Description

    The technical progress of the last decades has been enormously stimulated by two technological revolutions: the invention of the transistor in 1947 (Nobel prize 1956) and the invention of the laser in 1958 (Nobel prize 1964). The impact of both inventions on modern life is an evident fact.

    Already in 1950, a system of partial differential equations was published that models adequately the essential charge transport processes in semiconductor devices. On the basis of this drift-diffusion model the first bipolar transistor was successfully simulated in 1964. Just in that time the first integrated circuits containing a few transistors became commercially available. Since then, the electronics industry has achieved a phenomenal growth, mainly due to the rapid advances in integration technologies, large-scale systems design and numerical simulation. The number of applications of integrated circuits in high-performance computing, telecommunications, and consumer electronics has been rising steadily, and at a very fast pace. As microelectronic research moves into the nanometer scale device regime with GHz or higher operating speeds, the physics of electron flow through devices becomes more complicated, and physical effects, which previously could be safely ignored, become significant. Consequently, models of a higher abstraction level are needed. Conversely, faster simulation is typically required, which places a constraint on the model refinement if conventional simulation techniques are applied.

    Like the invention of the transistor triggered research in circuit simulation, the invention of the laser had a major impact on optical technologies. Classical optics turned into photonics. In todays telecommunication technologies, photons have already become the main carrier of information, regardless of the fact that even today most of the applied optical devices are based on conventional optical fibers and low index-contrast waveguides. Recently, a number of pioneering developments - all based on nanotechnologies - opened up the door to completely new working principles, hence to new classes of optoelectronic devices. Among them are nanostructured periodic materials (photonic crystals) and optically active nanostructures like quantum layers and quantum dots. A proper modelling of such structures has to describe simultaneously electrical charge transport, light generation, light propagation and scattering. Moreover, optical active nanostructures have to be described by quantum mechanics.

    In spite of the achievements of electronic/optoelectronic device and circuit simulation obtained so far, new nanotechnologies create new challenging tasks for mathematical modeling and numerical simulation in this field.

    Topics:
    • shape memory alloys in airfoils
    • production of semiconductor crystals
    • methanole fuel cell optimization
    • online production planning metamaterials


    http://www.wias-berlin.de/people/liero/glitzky_projects_7.jsp
  • D23

    Design of nanophotonic devices and materials

    Project heads: -
    Project members: -
    Duration: 06/10-05/14
    Status: completed

    Description

    The technical progress of the last decades has been enormously stimulated by two technological revolutions: the invention of the transistor in 1947 (Nobel prize 1956) and the invention of the laser in 1958 (Nobel prize 1964). The impact of both inventions on modern life is an evident fact.

    Already in 1950, a system of partial differential equations was published that models adequately the essential charge transport processes in semiconductor devices. On the basis of this drift-diffusion model the first bipolar transistor was successfully simulated in 1964. Just in that time the first integrated circuits containing a few transistors became commercially available. Since then, the electronics industry has achieved a phenomenal growth, mainly due to the rapid advances in integration technologies, large-scale systems design and numerical simulation. The number of applications of integrated circuits in high-performance computing, telecommunications, and consumer electronics has been rising steadily, and at a very fast pace. As microelectronic research moves into the nanometer scale device regime with GHz or higher operating speeds, the physics of electron flow through devices becomes more complicated, and physical effects, which previously could be safely ignored, become significant. Consequently, models of a higher abstraction level are needed. Conversely, faster simulation is typically required, which places a constraint on the model refinement if conventional simulation techniques are applied.

    Like the invention of the transistor triggered research in circuit simulation, the invention of the laser had a major impact on optical technologies. Classical optics turned into photonics. In todays telecommunication technologies, photons have already become the main carrier of information, regardless of the fact that even today most of the applied optical devices are based on conventional optical fibers and low index-contrast waveguides. Recently, a number of pioneering developments - all based on nanotechnologies - opened up the door to completely new working principles, hence to new classes of optoelectronic devices. Among them are nanostructured periodic materials (photonic crystals) and optically active nanostructures like quantum layers and quantum dots. A proper modelling of such structures has to describe simultaneously electrical charge transport, light generation, light propagation and scattering. Moreover, optical active nanostructures have to be described by quantum mechanics.

    In spite of the achievements of electronic/optoelectronic device and circuit simulation obtained so far, new nanotechnologies create new challenging tasks for mathematical modeling and numerical simulation in this field.

    Topics:
    • shape memory alloys in airfoils
    • production of semiconductor crystals
    • methanole fuel cell optimization
    • online production planning metamaterials


    http://www.zib.de/en/numerik/computational-nano-optics/projects/details/article/Matheon-d23.html
  • ZE1

    Teachers at university

    Project heads: -
    Project members: -
    Duration: 06/10-05/14
    Status: completed

    Description

    The recent TIMSS studies have displayed and highlighted considerable deficits in the mathematical education in Germany, in particular on the gymnasium level. According to the study, in general, German pupils seem to be able to master calculations in a satisfactory way, but their abilities to solve application oriented problems are below average. Moreover, the mathematics taught at schools is not experienced as something interesting and attractive, so pupils are not well-motivated. This in turn leads to the fact that the mathematical knowledge acquired by the pupils is not sufficient for their orientation in the real-world. In particular, we observe corresponding problems in our mathematical education of students at the university. Such deficits were also stressed in the influential lecture Drawbridge Up by the noted German poet and essayist H. M. Enzensberger.

    There are a number of reasons for the unfavourable situation. Among others, we mention first that the sensitivity for mathematics in the German public is rather low, despite the fact that mathematics is more and more present in everyday life: most of the public many acknowledge that mathematics is difficult and impressive, but they do not view it as something interesting, or as a genuine part of culture. Secondly, the mathematics taught at schools often misses a certain amount of attractivity: very little of what the pupils see or learn is new, and there are typically very few references to any current mathematical developments; it does not become clear that there are new mathematical discoveries made every day, that there is recent and current progress on many different questions. A third reason is a deficit in the practice orientation of the mathematics taught at high schools: pupils do not see that mathematics is relevant and important in the real-world, that there are lots of interesting applications and developments.

    To improve the situation the following measures seem promising. The very experts have to give more emphasis to the popularization of current mathematics. Moreover, the teaching of mathematics, including the corresponding mathematics curricula, at schools and universities has to be made more attractive and problem-solving-oriented. Last but not least, the teacher students education has to obtain a more practice-oriented component.

    The basis to attack and solve the problems that we have described lies in greater educational activity of university mathematicians, and in a much closer cooperation between schools and universities than the present one.

    Topics:
    • modern mathematics at school
    • school teachers at universities
    • network of math-science oriented schools
    • public awareness of mathematics
    • media presence


    http://didaktik1.mathematik.hu-berlin.de/index.php?article_id=49
  • ZE2

    Mathematics teacher training initiative

    Project heads: -
    Project members: -
    Duration: 06/10-05/14
    Status: completed

    Description

    The recent TIMSS studies have displayed and highlighted considerable deficits in the mathematical education in Germany, in particular on the gymnasium level. According to the study, in general, German pupils seem to be able to master calculations in a satisfactory way, but their abilities to solve application oriented problems are below average. Moreover, the mathematics taught at schools is not experienced as something interesting and attractive, so pupils are not well-motivated. This in turn leads to the fact that the mathematical knowledge acquired by the pupils is not sufficient for their orientation in the real-world. In particular, we observe corresponding problems in our mathematical education of students at the university. Such deficits were also stressed in the influential lecture Drawbridge Up by the noted German poet and essayist H. M. Enzensberger.

    There are a number of reasons for the unfavourable situation. Among others, we mention first that the sensitivity for mathematics in the German public is rather low, despite the fact that mathematics is more and more present in everyday life: most of the public many acknowledge that mathematics is difficult and impressive, but they do not view it as something interesting, or as a genuine part of culture. Secondly, the mathematics taught at schools often misses a certain amount of attractivity: very little of what the pupils see or learn is new, and there are typically very few references to any current mathematical developments; it does not become clear that there are new mathematical discoveries made every day, that there is recent and current progress on many different questions. A third reason is a deficit in the practice orientation of the mathematics taught at high schools: pupils do not see that mathematics is relevant and important in the real-world, that there are lots of interesting applications and developments.

    To improve the situation the following measures seem promising. The very experts have to give more emphasis to the popularization of current mathematics. Moreover, the teaching of mathematics, including the corresponding mathematics curricula, at schools and universities has to be made more attractive and problem-solving-oriented. Last but not least, the teacher students education has to obtain a more practice-oriented component.

    The basis to attack and solve the problems that we have described lies in greater educational activity of university mathematicians, and in a much closer cooperation between schools and universities than the present one.

    Topics:
    • modern mathematics at school
    • school teachers at universities
    • network of math-science oriented schools
    • public awareness of mathematics
    • media presence


    http://didaktik.mathematik.hu-berlin.de/index.php?article_id=387&clang=0
  • ZE3

    Industry-driven applications of mathematics in the classroom

    Project heads: -
    Project members: -
    Duration: 10/10-05/14
    Status: completed

    Description

    The recent TIMSS studies have displayed and highlighted considerable deficits in the mathematical education in Germany, in particular on the gymnasium level. According to the study, in general, German pupils seem to be able to master calculations in a satisfactory way, but their abilities to solve application oriented problems are below average. Moreover, the mathematics taught at schools is not experienced as something interesting and attractive, so pupils are not well-motivated. This in turn leads to the fact that the mathematical knowledge acquired by the pupils is not sufficient for their orientation in the real-world. In particular, we observe corresponding problems in our mathematical education of students at the university. Such deficits were also stressed in the influential lecture Drawbridge Up by the noted German poet and essayist H. M. Enzensberger.

    There are a number of reasons for the unfavourable situation. Among others, we mention first that the sensitivity for mathematics in the German public is rather low, despite the fact that mathematics is more and more present in everyday life: most of the public many acknowledge that mathematics is difficult and impressive, but they do not view it as something interesting, or as a genuine part of culture. Secondly, the mathematics taught at schools often misses a certain amount of attractivity: very little of what the pupils see or learn is new, and there are typically very few references to any current mathematical developments; it does not become clear that there are new mathematical discoveries made every day, that there is recent and current progress on many different questions. A third reason is a deficit in the practice orientation of the mathematics taught at high schools: pupils do not see that mathematics is relevant and important in the real-world, that there are lots of interesting applications and developments.

    To improve the situation the following measures seem promising. The very experts have to give more emphasis to the popularization of current mathematics. Moreover, the teaching of mathematics, including the corresponding mathematics curricula, at schools and universities has to be made more attractive and problem-solving-oriented. Last but not least, the teacher students education has to obtain a more practice-oriented component.

    The basis to attack and solve the problems that we have described lies in greater educational activity of university mathematicians, and in a much closer cooperation between schools and universities than the present one.

    Topics:
    • modern mathematics at school
    • school teachers at universities
    • network of math-science oriented schools
    • public awareness of mathematics
    • media presence


  • ZE5

    Enhancing engineering students perception of mathematical concepts (UNITUS)

    Project heads: -
    Project members: -
    Duration: 06/10-05/14
    Status: completed

    Description

    The recent TIMSS studies have displayed and highlighted considerable deficits in the mathematical education in Germany, in particular on the gymnasium level. According to the study, in general, German pupils seem to be able to master calculations in a satisfactory way, but their abilities to solve application oriented problems are below average. Moreover, the mathematics taught at schools is not experienced as something interesting and attractive, so pupils are not well-motivated. This in turn leads to the fact that the mathematical knowledge acquired by the pupils is not sufficient for their orientation in the real-world. In particular, we observe corresponding problems in our mathematical education of students at the university. Such deficits were also stressed in the influential lecture Drawbridge Up by the noted German poet and essayist H. M. Enzensberger.

    There are a number of reasons for the unfavourable situation. Among others, we mention first that the sensitivity for mathematics in the German public is rather low, despite the fact that mathematics is more and more present in everyday life: most of the public many acknowledge that mathematics is difficult and impressive, but they do not view it as something interesting, or as a genuine part of culture. Secondly, the mathematics taught at schools often misses a certain amount of attractivity: very little of what the pupils see or learn is new, and there are typically very few references to any current mathematical developments; it does not become clear that there are new mathematical discoveries made every day, that there is recent and current progress on many different questions. A third reason is a deficit in the practice orientation of the mathematics taught at high schools: pupils do not see that mathematics is relevant and important in the real-world, that there are lots of interesting applications and developments.

    To improve the situation the following measures seem promising. The very experts have to give more emphasis to the popularization of current mathematics. Moreover, the teaching of mathematics, including the corresponding mathematics curricula, at schools and universities has to be made more attractive and problem-solving-oriented. Last but not least, the teacher students education has to obtain a more practice-oriented component.

    The basis to attack and solve the problems that we have described lies in greater educational activity of university mathematicians, and in a much closer cooperation between schools and universities than the present one.

    Topics:
    • modern mathematics at school
    • school teachers at universities
    • network of math-science oriented schools
    • public awareness of mathematics
    • media presence


  • F10

    Image and signal processing in the biomedical sciences: diffusion weighted imaging - modeling and beyond

    Project heads: -
    Project members: -
    Duration: 06/10-05/14
    Status: completed

    Description

    Visualization has the task to create insight from given data. Image analysis is to extract information from data and to make it explicit in the form of a geometric model. The two areas have tight relations on both the methodical and the application level. Prominent examples are image-based rendering and visual analysis of 3D image data, e.g. in tomography or confocal microscopy.

    In recent years we have seen a rapid development of fundamentally new techniques for the visualization of complex physical phenomena as well as for imaging applications. At the very heart of these new technologies we encounter fundamentally new data structures and algorithms, all with a quest for a new level of abstraction. Here is where mathematics enters the scene.

    Especially in visualization, it is still a challenge to give the underlying objects a solid mathematical description. Here the research field of mathematical visualization faces the challenge to develop precise abstractions which eventually enables the development of new algorithms and visualization tools. Efforts in this direction can build on broad mathematical foundations, laid among others in the fields of discrete geometry, computational geometry, discrete differential geometry, and combinatorial topology. Results of this development are not only needed in research, where scientifically correct visualization is essential, but also meant to provide a solid basis for applications, for example, in computer graphics as well as in mathematics education projects.

    Even more so, the fields of visualization and image processing are key technologies for very current fields of research, among them many of the natural sciences (physics, chemistry, climate research), the life sciences (medicine, biochemistry, biotechnology, pharmacy), but also for various problems of engineering and production. Due to the multiple applications, but also due to technological reasons such as the availability of new imaging devices and display technology, imaging and visualization have been - and will be - areas of impressive growth.

    Topics:
    • discrete differential geometry
    • geometry processing
    • image processing
    • virtual reality PORTAL


    http://www.wias-berlin.de/projects/Matheon_a3
  • C33

    Modeling and Simulation of Composite Materials

    Project heads: -
    Project members: -
    Duration: 06/10-05/14
    Status: completed

    Description

    Production is one of the most important parts of the economy and at the very heart of the creation of value. Due to the central importance of production, big efforts have been made to improve production processes ever since the beginning of the industrial revolution. Nowadays, many production processes are highly automated. Computer programs based on numerical algorithms monitor the processes, improve efficiency and robustness, and guarantee high quality products. Consequently, mathematics is playing a steadily increasing role in this field. The possibilities of applying mathematical methods in production are wide-ranging. The Application Area cannot cover their full scale. For that reason, the projects concentrate on the development of new mathematical methods for special topics in manufacturing and production planning, two central aspects of production, in which the participating groups have longstanding expertise in mathematical modeling, simulation and optimization.

    In the field of manufacturing, we focus on innovative technologies having a big impact on technological progress: growth and processing of semiconductor bulk single crystals, phase transitions in modern steels and solder alloys, modeling of active and passive behavior of functional materials like shape-memory materials, growth of thin films. In the projects devoted to production planning, the main aim is the effective control of the whole production flow. Among the subjects to be studied, there is also electricity portfolio management.

    Topics:
    • phase transitions in steels and solder alloys
    • production of semiconductor crystals
    • modeling of active and passive behavior of functional materials
    • online production planning
    • growth of thin films


    http://www2.mathematik.hu-berlin.de/~numa/C33/
  • B25

    Scheduling Techniques in Constraint Integer Programming

    Project heads: -
    Project members: -
    Duration: 07/10-12/10
    Status: completed

    Description

    Networks, such as telephone networks, the internet, airline, railway, and bus networks are omnipresent and play a fundamental role for communication and mobility in our society. We almost take their permanent availability, reliability, and quality at low cost for granted. However, traffic jams, ill-designed train schedules, canceled flights, break-downs of telephone and computing networks, and slow internet access are reminders that networks are not automatically good networks.

    In fact, designing and operating communication and traffic networks are extremely complex tasks that lead directly to mathematical problems. A good example is the design of telecommunication networks. They were implemented with simple low-cost tree topologies until 15 years ago. Then, in 1988, a telco hub broke down in Chicago. This brought O Hare airport to a stand-still and caused an estimated business loss of billions of US dollars. Disasters of this kind made it clear that more sophisticated designs were needed. Nowadays, telecommunication companies use mathematically designed networks with built-in failure safety and rerouting capacities. Similar developments are expected in road traffic. We are now facing the installation of the first generation of load measuring, signalling, pricing, and route finding devices. These will soon integrate into a network-wide telematic system based on mathematical methods of traffic prediction, simulation, and control.

    Network design and operation tasks of this type are traditionally handled under the responsibility of various engineering disciplines (electrical engineering, traffic management and logistics, industrial engineering). While these disciplines can contribute to the improvement of the engineering components of such networks, todays demand on global optimization of the entire system poses problems where qualitative progress has to come from a better theoretical understanding of the structural aspects of the networks.

    This is where mathematics must come into play. The appearance of the word "network" in all the systems described above is not accidental, but hints at a common feature that has deep mathematical roots: networks are fundamental structures of graph theory and combinatorial optimization. Their study has become a prosperous subject in recent years, with impressive successes in many applications. The groups in Berlin are among the driving forces in this development.

    Nowadays, mathematical optimization techniques are used to locate switches and hubs in a phone system, to schedule buses and bus drivers in metropolitan transportation systems, etc. These tasks are individual steps in a hierarchical and sequential network planning process. In public transport, for example, this sequential process encompasses line planning, finding a periodic time table, assigning buses to lines, and creating individual bus driver schedules.

    Topics:
    • planning of optical, multilayer, and UMTS telecommunication networks
    • line planning, periodic timetabling, and revenue management in public transport networks
    • optimization in logistics, scheduling and material flows
    • optimization under uncertainty
    • symmetries in integer programming
    • game theoretic methods in network design


    http://www3.math.tu-berlin.de/Matheon/projects/B25
  • C34

    Open Pit Mine planning via a Continuous Optimization Approach

    Project heads: -
    Project members: -
    Duration: 07/10-12/10
    Status: completed

    Description

    Production is one of the most important parts of the economy and at the very heart of the creation of value. Due to the central importance of production, big efforts have been made to improve production processes ever since the beginning of the industrial revolution. Nowadays, many production processes are highly automated. Computer programs based on numerical algorithms monitor the processes, improve efficiency and robustness, and guarantee high quality products. Consequently, mathematics is playing a steadily increasing role in this field. The possibilities of applying mathematical methods in production are wide-ranging. The Application Area cannot cover their full scale. For that reason, the projects concentrate on the development of new mathematical methods for special topics in manufacturing and production planning, two central aspects of production, in which the participating groups have longstanding expertise in mathematical modeling, simulation and optimization.

    In the field of manufacturing, we focus on innovative technologies having a big impact on technological progress: growth and processing of semiconductor bulk single crystals, phase transitions in modern steels and solder alloys, modeling of active and passive behavior of functional materials like shape-memory materials, growth of thin films. In the projects devoted to production planning, the main aim is the effective control of the whole production flow. Among the subjects to be studied, there is also electricity portfolio management.

    Topics:
    • phase transitions in steels and solder alloys
    • production of semiconductor crystals
    • modeling of active and passive behavior of functional materials
    • online production planning
    • growth of thin films


  • C35

    Global higher integrability of minimizers of variational problems with mixed boundary conditions

    Project heads: -
    Project members: -
    Duration: 07/10-12/10
    Status: completed

    Description

    Production is one of the most important parts of the economy and at the very heart of the creation of value. Due to the central importance of production, big efforts have been made to improve production processes ever since the beginning of the industrial revolution. Nowadays, many production processes are highly automated. Computer programs based on numerical algorithms monitor the processes, improve efficiency and robustness, and guarantee high quality products. Consequently, mathematics is playing a steadily increasing role in this field. The possibilities of applying mathematical methods in production are wide-ranging. The Application Area cannot cover their full scale. For that reason, the projects concentrate on the development of new mathematical methods for special topics in manufacturing and production planning, two central aspects of production, in which the participating groups have longstanding expertise in mathematical modeling, simulation and optimization.

    In the field of manufacturing, we focus on innovative technologies having a big impact on technological progress: growth and processing of semiconductor bulk single crystals, phase transitions in modern steels and solder alloys, modeling of active and passive behavior of functional materials like shape-memory materials, growth of thin films. In the projects devoted to production planning, the main aim is the effective control of the whole production flow. Among the subjects to be studied, there is also electricity portfolio management.

    Topics:
    • phase transitions in steels and solder alloys
    • production of semiconductor crystals
    • modeling of active and passive behavior of functional materials
    • online production planning
    • growth of thin films


  • D24

    Network-Based Remodeling of Mechanical and Mechatronic Devices

    Project heads: -
    Project members: -
    Duration: 07/10-12/10
    Status: completed

    Description

    The technical progress of the last decades has been enormously stimulated by two technological revolutions: the invention of the transistor in 1947 (Nobel prize 1956) and the invention of the laser in 1958 (Nobel prize 1964). The impact of both inventions on modern life is an evident fact.

    Already in 1950, a system of partial differential equations was published that models adequately the essential charge transport processes in semiconductor devices. On the basis of this drift-diffusion model the first bipolar transistor was successfully simulated in 1964. Just in that time the first integrated circuits containing a few transistors became commercially available. Since then, the electronics industry has achieved a phenomenal growth, mainly due to the rapid advances in integration technologies, large-scale systems design and numerical simulation. The number of applications of integrated circuits in high-performance computing, telecommunications, and consumer electronics has been rising steadily, and at a very fast pace. As microelectronic research moves into the nanometer scale device regime with GHz or higher operating speeds, the physics of electron flow through devices becomes more complicated, and physical effects, which previously could be safely ignored, become significant. Consequently, models of a higher abstraction level are needed. Conversely, faster simulation is typically required, which places a constraint on the model refinement if conventional simulation techniques are applied.

    Like the invention of the transistor triggered research in circuit simulation, the invention of the laser had a major impact on optical technologies. Classical optics turned into photonics. In todays telecommunication technologies, photons have already become the main carrier of information, regardless of the fact that even today most of the applied optical devices are based on conventional optical fibers and low index-contrast waveguides. Recently, a number of pioneering developments - all based on nanotechnologies - opened up the door to completely new working principles, hence to new classes of optoelectronic devices. Among them are nanostructured periodic materials (photonic crystals) and optically active nanostructures like quantum layers and quantum dots. A proper modelling of such structures has to describe simultaneously electrical charge transport, light generation, light propagation and scattering. Moreover, optical active nanostructures have to be described by quantum mechanics.

    In spite of the achievements of electronic/optoelectronic device and circuit simulation obtained so far, new nanotechnologies create new challenging tasks for mathematical modeling and numerical simulation in this field.

    Topics:
    • shape memory alloys in airfoils
    • production of semiconductor crystals
    • methanole fuel cell optimization
    • online production planning metamaterials


    http://www3.math.tu-berlin.de/Matheon/projects/D24/
  • D25

    Computation of shape derivatives for conical diffraction by polygonal gratings

    Project heads: -
    Project members: -
    Duration: 07/10-12/10
    Status: completed

    Description

    The technical progress of the last decades has been enormously stimulated by two technological revolutions: the invention of the transistor in 1947 (Nobel prize 1956) and the invention of the laser in 1958 (Nobel prize 1964). The impact of both inventions on modern life is an evident fact.

    Already in 1950, a system of partial differential equations was published that models adequately the essential charge transport processes in semiconductor devices. On the basis of this drift-diffusion model the first bipolar transistor was successfully simulated in 1964. Just in that time the first integrated circuits containing a few transistors became commercially available. Since then, the electronics industry has achieved a phenomenal growth, mainly due to the rapid advances in integration technologies, large-scale systems design and numerical simulation. The number of applications of integrated circuits in high-performance computing, telecommunications, and consumer electronics has been rising steadily, and at a very fast pace. As microelectronic research moves into the nanometer scale device regime with GHz or higher operating speeds, the physics of electron flow through devices becomes more complicated, and physical effects, which previously could be safely ignored, become significant. Consequently, models of a higher abstraction level are needed. Conversely, faster simulation is typically required, which places a constraint on the model refinement if conventional simulation techniques are applied.

    Like the invention of the transistor triggered research in circuit simulation, the invention of the laser had a major impact on optical technologies. Classical optics turned into photonics. In todays telecommunication technologies, photons have already become the main carrier of information, regardless of the fact that even today most of the applied optical devices are based on conventional optical fibers and low index-contrast waveguides. Recently, a number of pioneering developments - all based on nanotechnologies - opened up the door to completely new working principles, hence to new classes of optoelectronic devices. Among them are nanostructured periodic materials (photonic crystals) and optically active nanostructures like quantum layers and quantum dots. A proper modelling of such structures has to describe simultaneously electrical charge transport, light generation, light propagation and scattering. Moreover, optical active nanostructures have to be described by quantum mechanics.

    In spite of the achievements of electronic/optoelectronic device and circuit simulation obtained so far, new nanotechnologies create new challenging tasks for mathematical modeling and numerical simulation in this field.

    Topics:
    • shape memory alloys in airfoils
    • production of semiconductor crystals
    • methanole fuel cell optimization
    • online production planning metamaterials


    http://www.wias-berlin.de/projects/Matheon-d25/
  • F11

    Accelerating Curvature Flows on the GPU

    Project heads: -
    Project members: -
    Duration: 07/10-12/10
    Status: completed

    Description

    Visualization has the task to create insight from given data. Image analysis is to extract information from data and to make it explicit in the form of a geometric model. The two areas have tight relations on both the methodical and the application level. Prominent examples are image-based rendering and visual analysis of 3D image data, e.g. in tomography or confocal microscopy.

    In recent years we have seen a rapid development of fundamentally new techniques for the visualization of complex physical phenomena as well as for imaging applications. At the very heart of these new technologies we encounter fundamentally new data structures and algorithms, all with a quest for a new level of abstraction. Here is where mathematics enters the scene.

    Especially in visualization, it is still a challenge to give the underlying objects a solid mathematical description. Here the research field of mathematical visualization faces the challenge to develop precise abstractions which eventually enables the development of new algorithms and visualization tools. Efforts in this direction can build on broad mathematical foundations, laid among others in the fields of discrete geometry, computational geometry, discrete differential geometry, and combinatorial topology. Results of this development are not only needed in research, where scientifically correct visualization is essential, but also meant to provide a solid basis for applications, for example, in computer graphics as well as in mathematics education projects.

    Even more so, the fields of visualization and image processing are key technologies for very current fields of research, among them many of the natural sciences (physics, chemistry, climate research), the life sciences (medicine, biochemistry, biotechnology, pharmacy), but also for various problems of engineering and production. Due to the multiple applications, but also due to technological reasons such as the availability of new imaging devices and display technology, imaging and visualization have been - and will be - areas of impressive growth.

    Topics:
    • discrete differential geometry
    • geometry processing
    • image processing
    • virtual reality PORTAL


    http://geom.mi.fu-berlin.de/projects/Matheon/f11/index.html
  • ZE6

    Learner as Creator - The Portal PlayMolecule

    Project heads: -
    Project members: -
    Duration: 07/10-03/11
    Status: completed

    Description

    The recent TIMSS studies have displayed and highlighted considerable deficits in the mathematical education in Germany, in particular on the gymnasium level. According to the study, in general, German pupils seem to be able to master calculations in a satisfactory way, but their abilities to solve application oriented problems are below average. Moreover, the mathematics taught at schools is not experienced as something interesting and attractive, so pupils are not well-motivated. This in turn leads to the fact that the mathematical knowledge acquired by the pupils is not sufficient for their orientation in the real-world. In particular, we observe corresponding problems in our mathematical education of students at the university. Such deficits were also stressed in the influential lecture Drawbridge Up by the noted German poet and essayist H. M. Enzensberger.

    There are a number of reasons for the unfavourable situation. Among others, we mention first that the sensitivity for mathematics in the German public is rather low, despite the fact that mathematics is more and more present in everyday life: most of the public many acknowledge that mathematics is difficult and impressive, but they do not view it as something interesting, or as a genuine part of culture. Secondly, the mathematics taught at schools often misses a certain amount of attractivity: very little of what the pupils see or learn is new, and there are typically very few references to any current mathematical developments; it does not become clear that there are new mathematical discoveries made every day, that there is recent and current progress on many different questions. A third reason is a deficit in the practice orientation of the mathematics taught at high schools: pupils do not see that mathematics is relevant and important in the real-world, that there are lots of interesting applications and developments.

    To improve the situation the following measures seem promising. The very experts have to give more emphasis to the popularization of current mathematics. Moreover, the teaching of mathematics, including the corresponding mathematics curricula, at schools and universities has to be made more attractive and problem-solving-oriented. Last but not least, the teacher students education has to obtain a more practice-oriented component.

    The basis to attack and solve the problems that we have described lies in greater educational activity of university mathematicians, and in a much closer cooperation between schools and universities than the present one.

    Topics:
    • modern mathematics at school
    • school teachers at universities
    • network of math-science oriented schools
    • public awareness of mathematics
    • media presence


    http://www.playmolecule.de
  • F12

    Fast algorithms for fluids

    Project heads: -
    Project members: -
    Duration: 07/10-05/12
    Status: completed

    Description

    Visualization has the task to create insight from given data. Image analysis is to extract information from data and to make it explicit in the form of a geometric model. The two areas have tight relations on both the methodical and the application level. Prominent examples are image-based rendering and visual analysis of 3D image data, e.g. in tomography or confocal microscopy.

    In recent years we have seen a rapid development of fundamentally new techniques for the visualization of complex physical phenomena as well as for imaging applications. At the very heart of these new technologies we encounter fundamentally new data structures and algorithms, all with a quest for a new level of abstraction. Here is where mathematics enters the scene.

    Especially in visualization, it is still a challenge to give the underlying objects a solid mathematical description. Here the research field of mathematical visualization faces the challenge to develop precise abstractions which eventually enables the development of new algorithms and visualization tools. Efforts in this direction can build on broad mathematical foundations, laid among others in the fields of discrete geometry, computational geometry, discrete differential geometry, and combinatorial topology. Results of this development are not only needed in research, where scientifically correct visualization is essential, but also meant to provide a solid basis for applications, for example, in computer graphics as well as in mathematics education projects.

    Even more so, the fields of visualization and image processing are key technologies for very current fields of research, among them many of the natural sciences (physics, chemistry, climate research), the life sciences (medicine, biochemistry, biotechnology, pharmacy), but also for various problems of engineering and production. Due to the multiple applications, but also due to technological reasons such as the availability of new imaging devices and display technology, imaging and visualization have been - and will be - areas of impressive growth.

    Topics:
    • discrete differential geometry
    • geometry processing
    • image processing
    • virtual reality PORTAL


    http://www3.math.tu-berlin.de/geometrie/f12/
  • ZO7

    Mathematische Installationen/ Mathematical Installations

    Project heads: -
    Project members: -
    Duration: 10/10-05/14
    Status: completed

    Description

    The recent TIMSS studies have displayed and highlighted considerable deficits in the mathematical education in Germany, in particular on the gymnasium level. According to the study, in general, German pupils seem to be able to master calculations in a satisfactory way, but their abilities to solve application oriented problems are below average. Moreover, the mathematics taught at schools is not experienced as something interesting and attractive, so pupils are not well-motivated. This in turn leads to the fact that the mathematical knowledge acquired by the pupils is not sufficient for their orientation in the real-world. In particular, we observe corresponding problems in our mathematical education of students at the university. Such deficits were also stressed in the influential lecture Drawbridge Up by the noted German poet and essayist H. M. Enzensberger.

    There are a number of reasons for the unfavourable situation. Among others, we mention first that the sensitivity for mathematics in the German public is rather low, despite the fact that mathematics is more and more present in everyday life: most of the public many acknowledge that mathematics is difficult and impressive, but they do not view it as something interesting, or as a genuine part of culture. Secondly, the mathematics taught at schools often misses a certain amount of attractivity: very little of what the pupils see or learn is new, and there are typically very few references to any current mathematical developments; it does not become clear that there are new mathematical discoveries made every day, that there is recent and current progress on many different questions. A third reason is a deficit in the practice orientation of the mathematics taught at high schools: pupils do not see that mathematics is relevant and important in the real-world, that there are lots of interesting applications and developments.

    To improve the situation the following measures seem promising. The very experts have to give more emphasis to the popularization of current mathematics. Moreover, the teaching of mathematics, including the corresponding mathematics curricula, at schools and universities has to be made more attractive and problem-solving-oriented. Last but not least, the teacher students education has to obtain a more practice-oriented component.

    The basis to attack and solve the problems that we have described lies in greater educational activity of university mathematicians, and in a much closer cooperation between schools and universities than the present one.

    Topics:
    • modern mathematics at school
    • school teachers at universities
    • network of math-science oriented schools
    • public awareness of mathematics
    • media presence


    http://www3.math.tu-berlin.de/geometrie/zo7/




Projekte der Förderperiode 2002 - 2006

  • A1

    Modelling, simulation, and optimal control of thermoregulation in the human vascular system

    Project heads: -
    Project members: -
    Duration: 06/02-05/10
    Status: completed

    Description

    "Life sciences" describe a wide research area with enormous technological and social impact. However, there exist specific areas where mathematics has just begun to take on an active role.

    In medicine, the already traditional role of mathematics in medical imaging (e.g., computer tomography) has been successfully extended. Mathematical progress has proved to directly influence medical progress towards the design of patient-specific therapies - e.g., in the cancer therapy hyperthermia. As another example, computer-assisted surgery planning allows the comparison of various operation options before the actual operation on the basis of a simulation of more and more realistic models describing soft tissue, bone, or typical human gaits such as stair climbing. Further mathematization of the field is expected to open entirely new perspectives for the optimal design of joint prostheses adapted to individual anatomy.

    In biotechnology, the present situation is clearly dominated by the generation of huge datasets about biomolecular, genetic, metabolic or other bio-processes. Algorithms from discrete mathematics or computer science (e.g., in multiple alignment) already play a publicly visible role in the decoding of the human and other genomes. In contrast to that, the mathematical treatment of the dynamics of bio-processes is still rather limited - even though this aspect seems to be crucial for the detailed understanding of virus diseases or the design of narrow band drugs. Therefore, beyond the well-established core areas of bioinformatics, numerical biocomputing has recently become more and more accepted as one of the keys to data-based reliable prediction, control and design of real-life bio-processes: As it turns out, a significant increase in our ability in a reliable quantitative simulation of the dynamics of large biomolecules is essential for a detailed understanding of, e.g., the enzymatic mechanisms of prion diseases (like the mad cow disease or its human counterpart, the Creutzfeldt-Jacob syndrome).

    Topics:
    • computer-assisted surgery
    • patient-specific therapy planning
    • protein data base analysis
    • protein conformation dynamics
    • systems biology
    • pharmacokinetics


    http://www.zib.de/weiser/projekte/Matheon-A1/projectlong.en.html
  • A2

    Modelling and simulation of human motion for osteotomic surgery

    Project heads: -
    Project members: -
    Duration: 06/02-05/10
    Status: completed

    Description

    "Life sciences" describe a wide research area with enormous technological and social impact. However, there exist specific areas where mathematics has just begun to take on an active role.

    In medicine, the already traditional role of mathematics in medical imaging (e.g., computer tomography) has been successfully extended. Mathematical progress has proved to directly influence medical progress towards the design of patient-specific therapies - e.g., in the cancer therapy hyperthermia. As another example, computer-assisted surgery planning allows the comparison of various operation options before the actual operation on the basis of a simulation of more and more realistic models describing soft tissue, bone, or typical human gaits such as stair climbing. Further mathematization of the field is expected to open entirely new perspectives for the optimal design of joint prostheses adapted to individual anatomy.

    In biotechnology, the present situation is clearly dominated by the generation of huge datasets about biomolecular, genetic, metabolic or other bio-processes. Algorithms from discrete mathematics or computer science (e.g., in multiple alignment) already play a publicly visible role in the decoding of the human and other genomes. In contrast to that, the mathematical treatment of the dynamics of bio-processes is still rather limited - even though this aspect seems to be crucial for the detailed understanding of virus diseases or the design of narrow band drugs. Therefore, beyond the well-established core areas of bioinformatics, numerical biocomputing has recently become more and more accepted as one of the keys to data-based reliable prediction, control and design of real-life bio-processes: As it turns out, a significant increase in our ability in a reliable quantitative simulation of the dynamics of large biomolecules is essential for a detailed understanding of, e.g., the enzymatic mechanisms of prion diseases (like the mad cow disease or its human counterpart, the Creutzfeldt-Jacob syndrome).

    Topics:
    • computer-assisted surgery
    • patient-specific therapy planning
    • protein data base analysis
    • protein conformation dynamics
    • systems biology
    • pharmacokinetics


    http://www.mi.fu-berlin.de/Matheon-A2
  • A3

    Image and signal processing in medicine and biosciences

    Project heads: -
    Project members: -
    Duration: 06/02-05/10
    Status: completed

    Description

    "Life sciences" describe a wide research area with enormous technological and social impact. However, there exist specific areas where mathematics has just begun to take on an active role.

    In medicine, the already traditional role of mathematics in medical imaging (e.g., computer tomography) has been successfully extended. Mathematical progress has proved to directly influence medical progress towards the design of patient-specific therapies - e.g., in the cancer therapy hyperthermia. As another example, computer-assisted surgery planning allows the comparison of various operation options before the actual operation on the basis of a simulation of more and more realistic models describing soft tissue, bone, or typical human gaits such as stair climbing. Further mathematization of the field is expected to open entirely new perspectives for the optimal design of joint prostheses adapted to individual anatomy.

    In biotechnology, the present situation is clearly dominated by the generation of huge datasets about biomolecular, genetic, metabolic or other bio-processes. Algorithms from discrete mathematics or computer science (e.g., in multiple alignment) already play a publicly visible role in the decoding of the human and other genomes. In contrast to that, the mathematical treatment of the dynamics of bio-processes is still rather limited - even though this aspect seems to be crucial for the detailed understanding of virus diseases or the design of narrow band drugs. Therefore, beyond the well-established core areas of bioinformatics, numerical biocomputing has recently become more and more accepted as one of the keys to data-based reliable prediction, control and design of real-life bio-processes: As it turns out, a significant increase in our ability in a reliable quantitative simulation of the dynamics of large biomolecules is essential for a detailed understanding of, e.g., the enzymatic mechanisms of prion diseases (like the mad cow disease or its human counterpart, the Creutzfeldt-Jacob syndrome).

    Topics:
    • computer-assisted surgery
    • patient-specific therapy planning
    • protein data base analysis
    • protein conformation dynamics
    • systems biology
    • pharmacokinetics


    http://www.wias-berlin.de/projects/Matheon_a3/
  • A4

    Towards a mathematics of biomolecular flexibility: Derivation and fast simulation of reduced models for conformation dynamics

    Project heads: -
    Project members: -
    Duration: 06/02-05/10
    Status: completed

    Description

    "Life sciences" describe a wide research area with enormous technological and social impact. However, there exist specific areas where mathematics has just begun to take on an active role.

    In medicine, the already traditional role of mathematics in medical imaging (e.g., computer tomography) has been successfully extended. Mathematical progress has proved to directly influence medical progress towards the design of patient-specific therapies - e.g., in the cancer therapy hyperthermia. As another example, computer-assisted surgery planning allows the comparison of various operation options before the actual operation on the basis of a simulation of more and more realistic models describing soft tissue, bone, or typical human gaits such as stair climbing. Further mathematization of the field is expected to open entirely new perspectives for the optimal design of joint prostheses adapted to individual anatomy.

    In biotechnology, the present situation is clearly dominated by the generation of huge datasets about biomolecular, genetic, metabolic or other bio-processes. Algorithms from discrete mathematics or computer science (e.g., in multiple alignment) already play a publicly visible role in the decoding of the human and other genomes. In contrast to that, the mathematical treatment of the dynamics of bio-processes is still rather limited - even though this aspect seems to be crucial for the detailed understanding of virus diseases or the design of narrow band drugs. Therefore, beyond the well-established core areas of bioinformatics, numerical biocomputing has recently become more and more accepted as one of the keys to data-based reliable prediction, control and design of real-life bio-processes: As it turns out, a significant increase in our ability in a reliable quantitative simulation of the dynamics of large biomolecules is essential for a detailed understanding of, e.g., the enzymatic mechanisms of prion diseases (like the mad cow disease or its human counterpart, the Creutzfeldt-Jacob syndrome).

    Topics:
    • computer-assisted surgery
    • patient-specific therapy planning
    • protein data base analysis
    • protein conformation dynamics
    • systems biology
    • pharmacokinetics


    http://www.math.fu-berlin.de/groups/biocomputing/projects/projekt_A4/index.html
  • A5

    Analysis and modelling of complex networks

    Project heads: -
    Project members: -
    Duration: 06/02-09/08
    Status: completed

    Description

    "Life sciences" describe a wide research area with enormous technological and social impact. However, there exist specific areas where mathematics has just begun to take on an active role.

    In medicine, the already traditional role of mathematics in medical imaging (e.g., computer tomography) has been successfully extended. Mathematical progress has proved to directly influence medical progress towards the design of patient-specific therapies - e.g., in the cancer therapy hyperthermia. As another example, computer-assisted surgery planning allows the comparison of various operation options before the actual operation on the basis of a simulation of more and more realistic models describing soft tissue, bone, or typical human gaits such as stair climbing. Further mathematization of the field is expected to open entirely new perspectives for the optimal design of joint prostheses adapted to individual anatomy.

    In biotechnology, the present situation is clearly dominated by the generation of huge datasets about biomolecular, genetic, metabolic or other bio-processes. Algorithms from discrete mathematics or computer science (e.g., in multiple alignment) already play a publicly visible role in the decoding of the human and other genomes. In contrast to that, the mathematical treatment of the dynamics of bio-processes is still rather limited - even though this aspect seems to be crucial for the detailed understanding of virus diseases or the design of narrow band drugs. Therefore, beyond the well-established core areas of bioinformatics, numerical biocomputing has recently become more and more accepted as one of the keys to data-based reliable prediction, control and design of real-life bio-processes: As it turns out, a significant increase in our ability in a reliable quantitative simulation of the dynamics of large biomolecules is essential for a detailed understanding of, e.g., the enzymatic mechanisms of prion diseases (like the mad cow disease or its human counterpart, the Creutzfeldt-Jacob syndrome).

    Topics:
    • computer-assisted surgery
    • patient-specific therapy planning
    • protein data base analysis
    • protein conformation dynamics
    • systems biology
    • pharmacokinetics


    http://www2.informatik.hu-berlin.de/alkox/forschung/Matheon_a5/
  • A6

    Stochastic Modelling in Pharmacokinetics

    Project heads: -
    Project members: -
    Duration: 10/02-05/10
    Status: completed

    Description

    "Life sciences" describe a wide research area with enormous technological and social impact. However, there exist specific areas where mathematics has just begun to take on an active role.

    In medicine, the already traditional role of mathematics in medical imaging (e.g., computer tomography) has been successfully extended. Mathematical progress has proved to directly influence medical progress towards the design of patient-specific therapies - e.g., in the cancer therapy hyperthermia. As another example, computer-assisted surgery planning allows the comparison of various operation options before the actual operation on the basis of a simulation of more and more realistic models describing soft tissue, bone, or typical human gaits such as stair climbing. Further mathematization of the field is expected to open entirely new perspectives for the optimal design of joint prostheses adapted to individual anatomy.

    In biotechnology, the present situation is clearly dominated by the generation of huge datasets about biomolecular, genetic, metabolic or other bio-processes. Algorithms from discrete mathematics or computer science (e.g., in multiple alignment) already play a publicly visible role in the decoding of the human and other genomes. In contrast to that, the mathematical treatment of the dynamics of bio-processes is still rather limited - even though this aspect seems to be crucial for the detailed understanding of virus diseases or the design of narrow band drugs. Therefore, beyond the well-established core areas of bioinformatics, numerical biocomputing has recently become more and more accepted as one of the keys to data-based reliable prediction, control and design of real-life bio-processes: As it turns out, a significant increase in our ability in a reliable quantitative simulation of the dynamics of large biomolecules is essential for a detailed understanding of, e.g., the enzymatic mechanisms of prion diseases (like the mad cow disease or its human counterpart, the Creutzfeldt-Jacob syndrome).

    Topics:
    • computer-assisted surgery
    • patient-specific therapy planning
    • protein data base analysis
    • protein conformation dynamics
    • systems biology
    • pharmacokinetics


    http://compphysiol.mi.fu-berlin.de/cms/mathematical_physiology/rubrik/3/3017.mathematical_physiology.htm
  • A7

    Numerical Discretization Methods in Quantum Chemistry

    Project heads: -
    Project members: -
    Duration: 07/04-05/10
    Status: completed

    Description

    "Life sciences" describe a wide research area with enormous technological and social impact. However, there exist specific areas where mathematics has just begun to take on an active role.

    In medicine, the already traditional role of mathematics in medical imaging (e.g., computer tomography) has been successfully extended. Mathematical progress has proved to directly influence medical progress towards the design of patient-specific therapies - e.g., in the cancer therapy hyperthermia. As another example, computer-assisted surgery planning allows the comparison of various operation options before the actual operation on the basis of a simulation of more and more realistic models describing soft tissue, bone, or typical human gaits such as stair climbing. Further mathematization of the field is expected to open entirely new perspectives for the optimal design of joint prostheses adapted to individual anatomy.

    In biotechnology, the present situation is clearly dominated by the generation of huge datasets about biomolecular, genetic, metabolic or other bio-processes. Algorithms from discrete mathematics or computer science (e.g., in multiple alignment) already play a publicly visible role in the decoding of the human and other genomes. In contrast to that, the mathematical treatment of the dynamics of bio-processes is still rather limited - even though this aspect seems to be crucial for the detailed understanding of virus diseases or the design of narrow band drugs. Therefore, beyond the well-established core areas of bioinformatics, numerical biocomputing has recently become more and more accepted as one of the keys to data-based reliable prediction, control and design of real-life bio-processes: As it turns out, a significant increase in our ability in a reliable quantitative simulation of the dynamics of large biomolecules is essential for a detailed understanding of, e.g., the enzymatic mechanisms of prion diseases (like the mad cow disease or its human counterpart, the Creutzfeldt-Jacob syndrome).

    Topics:
    • computer-assisted surgery
    • patient-specific therapy planning
    • protein data base analysis
    • protein conformation dynamics
    • systems biology
    • pharmacokinetics


    http://www.math.tu-berlin.de/~gagelman/A7.html
  • B1

    Strategic planning in public transport

    Project heads: -
    Project members: -
    Duration: 12/02-05/06
    Status: completed

    Description

    Networks, such as telephone networks, the internet, airline, railway, and bus networks are omnipresent and play a fundamental role for communication and mobility in our society. We almost take their permanent availability, reliability, and quality at low cost for granted. However, traffic jams, ill-designed train schedules, canceled flights, break-downs of telephone and computing networks, and slow internet access are reminders that networks are not automatically good networks.

    In fact, designing and operating communication and traffic networks are extremely complex tasks that lead directly to mathematical problems. A good example is the design of telecommunication networks. They were implemented with simple low-cost tree topologies until 15 years ago. Then, in 1988, a telco hub broke down in Chicago. This brought O Hare airport to a stand-still and caused an estimated business loss of billions of US dollars. Disasters of this kind made it clear that more sophisticated designs were needed. Nowadays, telecommunication companies use mathematically designed networks with built-in failure safety and rerouting capacities. Similar developments are expected in road traffic. We are now facing the installation of the first generation of load measuring, signalling, pricing, and route finding devices. These will soon integrate into a network-wide telematic system based on mathematical methods of traffic prediction, simulation, and control.

    Network design and operation tasks of this type are traditionally handled under the responsibility of various engineering disciplines (electrical engineering, traffic management and logistics, industrial engineering). While these disciplines can contribute to the improvement of the engineering components of such networks, todays demand on global optimization of the entire system poses problems where qualitative progress has to come from a better theoretical understanding of the structural aspects of the networks.

    This is where mathematics must come into play. The appearance of the word "network" in all the systems described above is not accidental, but hints at a common feature that has deep mathematical roots: networks are fundamental structures of graph theory and combinatorial optimization. Their study has become a prosperous subject in recent years, with impressive successes in many applications. The groups in Berlin are among the driving forces in this development.

    Nowadays, mathematical optimization techniques are used to locate switches and hubs in a phone system, to schedule buses and bus drivers in metropolitan transportation systems, etc. These tasks are individual steps in a hierarchical and sequential network planning process. In public transport, for example, this sequential process encompasses line planning, finding a periodic time table, assigning buses to lines, and creating individual bus driver schedules.

    Topics:
    • planning of optical, multilayer, and UMTS telecommunication networks
    • line planning, periodic timetabling, and revenue management in public transport networks
    • optimization in logistics, scheduling and material flows
    • optimization under uncertainty
    • symmetries in integer programming
    • game theoretic methods in network design


    http://www.zib.de/Optimization/Projects/TrafficLogistic/Matheon-B1/
  • B2

    Dynamics of nonlinear networks

    Project heads: -
    Project members: -
    Duration: 03/03-04/04
    Status: completed

    Description

    Networks, such as telephone networks, the internet, airline, railway, and bus networks are omnipresent and play a fundamental role for communication and mobility in our society. We almost take their permanent availability, reliability, and quality at low cost for granted. However, traffic jams, ill-designed train schedules, canceled flights, break-downs of telephone and computing networks, and slow internet access are reminders that networks are not automatically good networks.

    In fact, designing and operating communication and traffic networks are extremely complex tasks that lead directly to mathematical problems. A good example is the design of telecommunication networks. They were implemented with simple low-cost tree topologies until 15 years ago. Then, in 1988, a telco hub broke down in Chicago. This brought O Hare airport to a stand-still and caused an estimated business loss of billions of US dollars. Disasters of this kind made it clear that more sophisticated designs were needed. Nowadays, telecommunication companies use mathematically designed networks with built-in failure safety and rerouting capacities. Similar developments are expected in road traffic. We are now facing the installation of the first generation of load measuring, signalling, pricing, and route finding devices. These will soon integrate into a network-wide telematic system based on mathematical methods of traffic prediction, simulation, and control.

    Network design and operation tasks of this type are traditionally handled under the responsibility of various engineering disciplines (electrical engineering, traffic management and logistics, industrial engineering). While these disciplines can contribute to the improvement of the engineering components of such networks, todays demand on global optimization of the entire system poses problems where qualitative progress has to come from a better theoretical understanding of the structural aspects of the networks.

    This is where mathematics must come into play. The appearance of the word "network" in all the systems described above is not accidental, but hints at a common feature that has deep mathematical roots: networks are fundamental structures of graph theory and combinatorial optimization. Their study has become a prosperous subject in recent years, with impressive successes in many applications. The groups in Berlin are among the driving forces in this development.

    Nowadays, mathematical optimization techniques are used to locate switches and hubs in a phone system, to schedule buses and bus drivers in metropolitan transportation systems, etc. These tasks are individual steps in a hierarchical and sequential network planning process. In public transport, for example, this sequential process encompasses line planning, finding a periodic time table, assigning buses to lines, and creating individual bus driver schedules.

    Topics:
    • planning of optical, multilayer, and UMTS telecommunication networks
    • line planning, periodic timetabling, and revenue management in public transport networks
    • optimization in logistics, scheduling and material flows
    • optimization under uncertainty
    • symmetries in integer programming
    • game theoretic methods in network design


    http://dynamics.mi.fu-berlin.de/projects/networks.php
  • B3

    Integrated Planning of Multi-layer Telecommunication Networks

    Project heads: -
    Project members: -
    Duration: 07/02 - 05/14
    Status: completed

    Description

    Networks, such as telephone networks, the internet, airline, railway, and bus networks are omnipresent and play a fundamental role for communication and mobility in our society. We almost take their permanent availability, reliability, and quality at low cost for granted. However, traffic jams, ill-designed train schedules, canceled flights, break-downs of telephone and computing networks, and slow internet access are reminders that networks are not automatically good networks.

    In fact, designing and operating communication and traffic networks are extremely complex tasks that lead directly to mathematical problems. A good example is the design of telecommunication networks. They were implemented with simple low-cost tree topologies until 15 years ago. Then, in 1988, a telco hub broke down in Chicago. This brought O Hare airport to a stand-still and caused an estimated business loss of billions of US dollars. Disasters of this kind made it clear that more sophisticated designs were needed. Nowadays, telecommunication companies use mathematically designed networks with built-in failure safety and rerouting capacities. Similar developments are expected in road traffic. We are now facing the installation of the first generation of load measuring, signalling, pricing, and route finding devices. These will soon integrate into a network-wide telematic system based on mathematical methods of traffic prediction, simulation, and control.

    Network design and operation tasks of this type are traditionally handled under the responsibility of various engineering disciplines (electrical engineering, traffic management and logistics, industrial engineering). While these disciplines can contribute to the improvement of the engineering components of such networks, todays demand on global optimization of the entire system poses problems where qualitative progress has to come from a better theoretical understanding of the structural aspects of the networks.

    This is where mathematics must come into play. The appearance of the word "network" in all the systems described above is not accidental, but hints at a common feature that has deep mathematical roots: networks are fundamental structures of graph theory and combinatorial optimization. Their study has become a prosperous subject in recent years, with impressive successes in many applications. The groups in Berlin are among the driving forces in this development.

    Nowadays, mathematical optimization techniques are used to locate switches and hubs in a phone system, to schedule buses and bus drivers in metropolitan transportation systems, etc. These tasks are individual steps in a hierarchical and sequential network planning process. In public transport, for example, this sequential process encompasses line planning, finding a periodic time table, assigning buses to lines, and creating individual bus driver schedules.

    Topics:
    • planning of optical, multilayer, and UMTS telecommunication networks
    • line planning, periodic timetabling, and revenue management in public transport networks
    • optimization in logistics, scheduling and material flows
    • optimization under uncertainty
    • symmetries in integer programming
    • game theoretic methods in network design


    http://www.zib.de/en/optimization/telecommunications/projects/projectdetails/article/Matheon-b3.html
  • B4

    Optimization in telecommunication: Planning the UMTS radio interface

    Project heads: -
    Project members: -
    Duration: 08/02-05/10
    Status: completed

    Description

    Networks, such as telephone networks, the internet, airline, railway, and bus networks are omnipresent and play a fundamental role for communication and mobility in our society. We almost take their permanent availability, reliability, and quality at low cost for granted. However, traffic jams, ill-designed train schedules, canceled flights, break-downs of telephone and computing networks, and slow internet access are reminders that networks are not automatically good networks.

    In fact, designing and operating communication and traffic networks are extremely complex tasks that lead directly to mathematical problems. A good example is the design of telecommunication networks. They were implemented with simple low-cost tree topologies until 15 years ago. Then, in 1988, a telco hub broke down in Chicago. This brought O Hare airport to a stand-still and caused an estimated business loss of billions of US dollars. Disasters of this kind made it clear that more sophisticated designs were needed. Nowadays, telecommunication companies use mathematically designed networks with built-in failure safety and rerouting capacities. Similar developments are expected in road traffic. We are now facing the installation of the first generation of load measuring, signalling, pricing, and route finding devices. These will soon integrate into a network-wide telematic system based on mathematical methods of traffic prediction, simulation, and control.

    Network design and operation tasks of this type are traditionally handled under the responsibility of various engineering disciplines (electrical engineering, traffic management and logistics, industrial engineering). While these disciplines can contribute to the improvement of the engineering components of such networks, todays demand on global optimization of the entire system poses problems where qualitative progress has to come from a better theoretical understanding of the structural aspects of the networks.

    This is where mathematics must come into play. The appearance of the word "network" in all the systems described above is not accidental, but hints at a common feature that has deep mathematical roots: networks are fundamental structures of graph theory and combinatorial optimization. Their study has become a prosperous subject in recent years, with impressive successes in many applications. The groups in Berlin are among the driving forces in this development.

    Nowadays, mathematical optimization techniques are used to locate switches and hubs in a phone system, to schedule buses and bus drivers in metropolitan transportation systems, etc. These tasks are individual steps in a hierarchical and sequential network planning process. In public transport, for example, this sequential process encompasses line planning, finding a periodic time table, assigning buses to lines, and creating individual bus driver schedules.

    Topics:
    • planning of optical, multilayer, and UMTS telecommunication networks
    • line planning, periodic timetabling, and revenue management in public transport networks
    • optimization in logistics, scheduling and material flows
    • optimization under uncertainty
    • symmetries in integer programming
    • game theoretic methods in network design


    http://www.zib.de/Optimization/Projects/Telecom/Matheon-B4/
  • B5

    Line planning and periodic timetabling in railway traffic

    Project heads: -
    Project members: -
    Duration: 03/03-05/06
    Status: completed

    Description

    Networks, such as telephone networks, the internet, airline, railway, and bus networks are omnipresent and play a fundamental role for communication and mobility in our society. We almost take their permanent availability, reliability, and quality at low cost for granted. However, traffic jams, ill-designed train schedules, canceled flights, break-downs of telephone and computing networks, and slow internet access are reminders that networks are not automatically good networks.

    In fact, designing and operating communication and traffic networks are extremely complex tasks that lead directly to mathematical problems. A good example is the design of telecommunication networks. They were implemented with simple low-cost tree topologies until 15 years ago. Then, in 1988, a telco hub broke down in Chicago. This brought O Hare airport to a stand-still and caused an estimated business loss of billions of US dollars. Disasters of this kind made it clear that more sophisticated designs were needed. Nowadays, telecommunication companies use mathematically designed networks with built-in failure safety and rerouting capacities. Similar developments are expected in road traffic. We are now facing the installation of the first generation of load measuring, signalling, pricing, and route finding devices. These will soon integrate into a network-wide telematic system based on mathematical methods of traffic prediction, simulation, and control.

    Network design and operation tasks of this type are traditionally handled under the responsibility of various engineering disciplines (electrical engineering, traffic management and logistics, industrial engineering). While these disciplines can contribute to the improvement of the engineering components of such networks, todays demand on global optimization of the entire system poses problems where qualitative progress has to come from a better theoretical understanding of the structural aspects of the networks.

    This is where mathematics must come into play. The appearance of the word "network" in all the systems described above is not accidental, but hints at a common feature that has deep mathematical roots: networks are fundamental structures of graph theory and combinatorial optimization. Their study has become a prosperous subject in recent years, with impressive successes in many applications. The groups in Berlin are among the driving forces in this development.

    Nowadays, mathematical optimization techniques are used to locate switches and hubs in a phone system, to schedule buses and bus drivers in metropolitan transportation systems, etc. These tasks are individual steps in a hierarchical and sequential network planning process. In public transport, for example, this sequential process encompasses line planning, finding a periodic time table, assigning buses to lines, and creating individual bus driver schedules.

    Topics:
    • planning of optical, multilayer, and UMTS telecommunication networks
    • line planning, periodic timetabling, and revenue management in public transport networks
    • optimization in logistics, scheduling and material flows
    • optimization under uncertainty
    • symmetries in integer programming
    • game theoretic methods in network design


    http://www3.math.tu-berlin.de/Matheon/projects//B5/
  • B6

    Origin destination control in airline revenue management by dynamic stochastic programming

    Project heads: -
    Project members: -
    Duration: 07/02-05/06
    Status: completed

    Description

    Networks, such as telephone networks, the internet, airline, railway, and bus networks are omnipresent and play a fundamental role for communication and mobility in our society. We almost take their permanent availability, reliability, and quality at low cost for granted. However, traffic jams, ill-designed train schedules, canceled flights, break-downs of telephone and computing networks, and slow internet access are reminders that networks are not automatically good networks.

    In fact, designing and operating communication and traffic networks are extremely complex tasks that lead directly to mathematical problems. A good example is the design of telecommunication networks. They were implemented with simple low-cost tree topologies until 15 years ago. Then, in 1988, a telco hub broke down in Chicago. This brought O Hare airport to a stand-still and caused an estimated business loss of billions of US dollars. Disasters of this kind made it clear that more sophisticated designs were needed. Nowadays, telecommunication companies use mathematically designed networks with built-in failure safety and rerouting capacities. Similar developments are expected in road traffic. We are now facing the installation of the first generation of load measuring, signalling, pricing, and route finding devices. These will soon integrate into a network-wide telematic system based on mathematical methods of traffic prediction, simulation, and control.

    Network design and operation tasks of this type are traditionally handled under the responsibility of various engineering disciplines (electrical engineering, traffic management and logistics, industrial engineering). While these disciplines can contribute to the improvement of the engineering components of such networks, todays demand on global optimization of the entire system poses problems where qualitative progress has to come from a better theoretical understanding of the structural aspects of the networks.

    This is where mathematics must come into play. The appearance of the word "network" in all the systems described above is not accidental, but hints at a common feature that has deep mathematical roots: networks are fundamental structures of graph theory and combinatorial optimization. Their study has become a prosperous subject in recent years, with impressive successes in many applications. The groups in Berlin are among the driving forces in this development.

    Nowadays, mathematical optimization techniques are used to locate switches and hubs in a phone system, to schedule buses and bus drivers in metropolitan transportation systems, etc. These tasks are individual steps in a hierarchical and sequential network planning process. In public transport, for example, this sequential process encompasses line planning, finding a periodic time table, assigning buses to lines, and creating individual bus driver schedules.

    Topics:
    • planning of optical, multilayer, and UMTS telecommunication networks
    • line planning, periodic timetabling, and revenue management in public transport networks
    • optimization in logistics, scheduling and material flows
    • optimization under uncertainty
    • symmetries in integer programming
    • game theoretic methods in network design


    http://www.math.hu-berlin.de/~romisch/projects/FZB6/revenue.html
  • B7

    Computation of performance measures of communication networks

    Project heads: -
    Project members: -
    Duration: 10/02-05/10
    Status: completed

    Description

    Networks, such as telephone networks, the internet, airline, railway, and bus networks are omnipresent and play a fundamental role for communication and mobility in our society. We almost take their permanent availability, reliability, and quality at low cost for granted. However, traffic jams, ill-designed train schedules, canceled flights, break-downs of telephone and computing networks, and slow internet access are reminders that networks are not automatically good networks.

    In fact, designing and operating communication and traffic networks are extremely complex tasks that lead directly to mathematical problems. A good example is the design of telecommunication networks. They were implemented with simple low-cost tree topologies until 15 years ago. Then, in 1988, a telco hub broke down in Chicago. This brought O Hare airport to a stand-still and caused an estimated business loss of billions of US dollars. Disasters of this kind made it clear that more sophisticated designs were needed. Nowadays, telecommunication companies use mathematically designed networks with built-in failure safety and rerouting capacities. Similar developments are expected in road traffic. We are now facing the installation of the first generation of load measuring, signalling, pricing, and route finding devices. These will soon integrate into a network-wide telematic system based on mathematical methods of traffic prediction, simulation, and control.

    Network design and operation tasks of this type are traditionally handled under the responsibility of various engineering disciplines (electrical engineering, traffic management and logistics, industrial engineering). While these disciplines can contribute to the improvement of the engineering components of such networks, todays demand on global optimization of the entire system poses problems where qualitative progress has to come from a better theoretical understanding of the structural aspects of the networks.

    This is where mathematics must come into play. The appearance of the word "network" in all the systems described above is not accidental, but hints at a common feature that has deep mathematical roots: networks are fundamental structures of graph theory and combinatorial optimization. Their study has become a prosperous subject in recent years, with impressive successes in many applications. The groups in Berlin are among the driving forces in this development.

    Nowadays, mathematical optimization techniques are used to locate switches and hubs in a phone system, to schedule buses and bus drivers in metropolitan transportation systems, etc. These tasks are individual steps in a hierarchical and sequential network planning process. In public transport, for example, this sequential process encompasses line planning, finding a periodic time table, assigning buses to lines, and creating individual bus driver schedules.

    Topics:
    • planning of optical, multilayer, and UMTS telecommunication networks
    • line planning, periodic timetabling, and revenue management in public transport networks
    • optimization in logistics, scheduling and material flows
    • optimization under uncertainty
    • symmetries in integer programming
    • game theoretic methods in network design


    http://www.math.tu-berlin.de/~aurzada/project-b7/
  • B8

    Time-dependent multi-commodity flows: Theory and applications

    Project heads: -
    Project members: -
    Duration: 10/02-12/08
    Status: completed

    Description

    Networks, such as telephone networks, the internet, airline, railway, and bus networks are omnipresent and play a fundamental role for communication and mobility in our society. We almost take their permanent availability, reliability, and quality at low cost for granted. However, traffic jams, ill-designed train schedules, canceled flights, break-downs of telephone and computing networks, and slow internet access are reminders that networks are not automatically good networks.

    In fact, designing and operating communication and traffic networks are extremely complex tasks that lead directly to mathematical problems. A good example is the design of telecommunication networks. They were implemented with simple low-cost tree topologies until 15 years ago. Then, in 1988, a telco hub broke down in Chicago. This brought O Hare airport to a stand-still and caused an estimated business loss of billions of US dollars. Disasters of this kind made it clear that more sophisticated designs were needed. Nowadays, telecommunication companies use mathematically designed networks with built-in failure safety and rerouting capacities. Similar developments are expected in road traffic. We are now facing the installation of the first generation of load measuring, signalling, pricing, and route finding devices. These will soon integrate into a network-wide telematic system based on mathematical methods of traffic prediction, simulation, and control.

    Network design and operation tasks of this type are traditionally handled under the responsibility of various engineering disciplines (electrical engineering, traffic management and logistics, industrial engineering). While these disciplines can contribute to the improvement of the engineering components of such networks, todays demand on global optimization of the entire system poses problems where qualitative progress has to come from a better theoretical understanding of the structural aspects of the networks.

    This is where mathematics must come into play. The appearance of the word "network" in all the systems described above is not accidental, but hints at a common feature that has deep mathematical roots: networks are fundamental structures of graph theory and combinatorial optimization. Their study has become a prosperous subject in recent years, with impressive successes in many applications. The groups in Berlin are among the driving forces in this development.

    Nowadays, mathematical optimization techniques are used to locate switches and hubs in a phone system, to schedule buses and bus drivers in metropolitan transportation systems, etc. These tasks are individual steps in a hierarchical and sequential network planning process. In public transport, for example, this sequential process encompasses line planning, finding a periodic time table, assigning buses to lines, and creating individual bus driver schedules.

    Topics:
    • planning of optical, multilayer, and UMTS telecommunication networks
    • line planning, periodic timetabling, and revenue management in public transport networks
    • optimization in logistics, scheduling and material flows
    • optimization under uncertainty
    • symmetries in integer programming
    • game theoretic methods in network design


    http://www3.math.tu-berlin.de/Matheon/projects/B8/
  • B9

    Dual methods for special coloring problems

    Project heads: -
    Project members: -
    Duration: 09/02-05/06
    Status: completed

    Description

    Networks, such as telephone networks, the internet, airline, railway, and bus networks are omnipresent and play a fundamental role for communication and mobility in our society. We almost take their permanent availability, reliability, and quality at low cost for granted. However, traffic jams, ill-designed train schedules, canceled flights, break-downs of telephone and computing networks, and slow internet access are reminders that networks are not automatically good networks.

    In fact, designing and operating communication and traffic networks are extremely complex tasks that lead directly to mathematical problems. A good example is the design of telecommunication networks. They were implemented with simple low-cost tree topologies until 15 years ago. Then, in 1988, a telco hub broke down in Chicago. This brought O Hare airport to a stand-still and caused an estimated business loss of billions of US dollars. Disasters of this kind made it clear that more sophisticated designs were needed. Nowadays, telecommunication companies use mathematically designed networks with built-in failure safety and rerouting capacities. Similar developments are expected in road traffic. We are now facing the installation of the first generation of load measuring, signalling, pricing, and route finding devices. These will soon integrate into a network-wide telematic system based on mathematical methods of traffic prediction, simulation, and control.

    Network design and operation tasks of this type are traditionally handled under the responsibility of various engineering disciplines (electrical engineering, traffic management and logistics, industrial engineering). While these disciplines can contribute to the improvement of the engineering components of such networks, todays demand on global optimization of the entire system poses problems where qualitative progress has to come from a better theoretical understanding of the structural aspects of the networks.

    This is where mathematics must come into play. The appearance of the word "network" in all the systems described above is not accidental, but hints at a common feature that has deep mathematical roots: networks are fundamental structures of graph theory and combinatorial optimization. Their study has become a prosperous subject in recent years, with impressive successes in many applications. The groups in Berlin are among the driving forces in this development.

    Nowadays, mathematical optimization techniques are used to locate switches and hubs in a phone system, to schedule buses and bus drivers in metropolitan transportation systems, etc. These tasks are individual steps in a hierarchical and sequential network planning process. In public transport, for example, this sequential process encompasses line planning, finding a periodic time table, assigning buses to lines, and creating individual bus driver schedules.

    Topics:
    • planning of optical, multilayer, and UMTS telecommunication networks
    • line planning, periodic timetabling, and revenue management in public transport networks
    • optimization in logistics, scheduling and material flows
    • optimization under uncertainty
    • symmetries in integer programming
    • game theoretic methods in network design


    http://www.math.tu-berlin.de/~fpfender/B9.html
  • B10

    Describing polyhedra by polynomial inequalities

    Project heads: -
    Project members: -
    Duration: 07/03-08/04
    Status: completed

    Description

    Networks, such as telephone networks, the internet, airline, railway, and bus networks are omnipresent and play a fundamental role for communication and mobility in our society. We almost take their permanent availability, reliability, and quality at low cost for granted. However, traffic jams, ill-designed train schedules, canceled flights, break-downs of telephone and computing networks, and slow internet access are reminders that networks are not automatically good networks.

    In fact, designing and operating communication and traffic networks are extremely complex tasks that lead directly to mathematical problems. A good example is the design of telecommunication networks. They were implemented with simple low-cost tree topologies until 15 years ago. Then, in 1988, a telco hub broke down in Chicago. This brought O Hare airport to a stand-still and caused an estimated business loss of billions of US dollars. Disasters of this kind made it clear that more sophisticated designs were needed. Nowadays, telecommunication companies use mathematically designed networks with built-in failure safety and rerouting capacities. Similar developments are expected in road traffic. We are now facing the installation of the first generation of load measuring, signalling, pricing, and route finding devices. These will soon integrate into a network-wide telematic system based on mathematical methods of traffic prediction, simulation, and control.

    Network design and operation tasks of this type are traditionally handled under the responsibility of various engineering disciplines (electrical engineering, traffic management and logistics, industrial engineering). While these disciplines can contribute to the improvement of the engineering components of such networks, todays demand on global optimization of the entire system poses problems where qualitative progress has to come from a better theoretical understanding of the structural aspects of the networks.

    This is where mathematics must come into play. The appearance of the word "network" in all the systems described above is not accidental, but hints at a common feature that has deep mathematical roots: networks are fundamental structures of graph theory and combinatorial optimization. Their study has become a prosperous subject in recent years, with impressive successes in many applications. The groups in Berlin are among the driving forces in this development.

    Nowadays, mathematical optimization techniques are used to locate switches and hubs in a phone system, to schedule buses and bus drivers in metropolitan transportation systems, etc. These tasks are individual steps in a hierarchical and sequential network planning process. In public transport, for example, this sequential process encompasses line planning, finding a periodic time table, assigning buses to lines, and creating individual bus driver schedules.

    Topics:
    • planning of optical, multilayer, and UMTS telecommunication networks
    • line planning, periodic timetabling, and revenue management in public transport networks
    • optimization in logistics, scheduling and material flows
    • optimization under uncertainty
    • symmetries in integer programming
    • game theoretic methods in network design


    http://www.math.tu-berlin.de/~bosse/project_B10.html
  • B11

    Randomized methods in network optimization

    Project heads: -
    Project members: -
    Duration: 05/03-05/06
    Status: completed

    Description

    Networks, such as telephone networks, the internet, airline, railway, and bus networks are omnipresent and play a fundamental role for communication and mobility in our society. We almost take their permanent availability, reliability, and quality at low cost for granted. However, traffic jams, ill-designed train schedules, canceled flights, break-downs of telephone and computing networks, and slow internet access are reminders that networks are not automatically good networks.

    In fact, designing and operating communication and traffic networks are extremely complex tasks that lead directly to mathematical problems. A good example is the design of telecommunication networks. They were implemented with simple low-cost tree topologies until 15 years ago. Then, in 1988, a telco hub broke down in Chicago. This brought O Hare airport to a stand-still and caused an estimated business loss of billions of US dollars. Disasters of this kind made it clear that more sophisticated designs were needed. Nowadays, telecommunication companies use mathematically designed networks with built-in failure safety and rerouting capacities. Similar developments are expected in road traffic. We are now facing the installation of the first generation of load measuring, signalling, pricing, and route finding devices. These will soon integrate into a network-wide telematic system based on mathematical methods of traffic prediction, simulation, and control.

    Network design and operation tasks of this type are traditionally handled under the responsibility of various engineering disciplines (electrical engineering, traffic management and logistics, industrial engineering). While these disciplines can contribute to the improvement of the engineering components of such networks, todays demand on global optimization of the entire system poses problems where qualitative progress has to come from a better theoretical understanding of the structural aspects of the networks.

    This is where mathematics must come into play. The appearance of the word "network" in all the systems described above is not accidental, but hints at a common feature that has deep mathematical roots: networks are fundamental structures of graph theory and combinatorial optimization. Their study has become a prosperous subject in recent years, with impressive successes in many applications. The groups in Berlin are among the driving forces in this development.

    Nowadays, mathematical optimization techniques are used to locate switches and hubs in a phone system, to schedule buses and bus drivers in metropolitan transportation systems, etc. These tasks are individual steps in a hierarchical and sequential network planning process. In public transport, for example, this sequential process encompasses line planning, finding a periodic time table, assigning buses to lines, and creating individual bus driver schedules.

    Topics:
    • planning of optical, multilayer, and UMTS telecommunication networks
    • line planning, periodic timetabling, and revenue management in public transport networks
    • optimization in logistics, scheduling and material flows
    • optimization under uncertainty
    • symmetries in integer programming
    • game theoretic methods in network design


    http://www.zib.de/Optimization/Projects/DiscStruct/Matheon-B11/index.en.html
  • C1

    Coupled systems of reaction-diffusion equations and application to the numerical solution of direct methanol fuel cell (DMFC) problems

    Project heads: -
    Project members: -
    Duration: 01/03-05/06
    Status: completed

    Description

    Production is one of the most important parts of the economy and at the very heart of the creation of value. Due to the central importance of production, big efforts have been made to improve production processes ever since the beginning of the industrial revolution. Nowadays, many production processes are highly automated. Computer programs based on numerical algorithms monitor the processes, improve efficiency and robustness, and guarantee high quality products. Consequently, mathematics is playing a steadily increasing role in this field. The possibilities of applying mathematical methods in production are wide-ranging. The Application Area cannot cover their full scale. For that reason, the projects concentrate on the development of new mathematical methods for special topics in manufacturing and production planning, two central aspects of production, in which the participating groups have longstanding expertise in mathematical modeling, simulation and optimization.

    In the field of manufacturing, we focus on innovative technologies having a big impact on technological progress: growth and processing of semiconductor bulk single crystals, phase transitions in modern steels and solder alloys, modeling of active and passive behavior of functional materials like shape-memory materials, growth of thin films. In the projects devoted to production planning, the main aim is the effective control of the whole production flow. Among the subjects to be studied, there is also electricity portfolio management.

    Topics:
    • phase transitions in steels and solder alloys
    • production of semiconductor crystals
    • modeling of active and passive behavior of functional materials
    • online production planning
    • growth of thin films


    http://www.wias-berlin.de/research-groups/nummath/fuelcell/C1/
  • C2

    Efficient simulation of flows in semiconductor melts

    Project heads: -
    Project members: -
    Duration: 08/03-05/06
    Status: completed

    Description

    Production is one of the most important parts of the economy and at the very heart of the creation of value. Due to the central importance of production, big efforts have been made to improve production processes ever since the beginning of the industrial revolution. Nowadays, many production processes are highly automated. Computer programs based on numerical algorithms monitor the processes, improve efficiency and robustness, and guarantee high quality products. Consequently, mathematics is playing a steadily increasing role in this field. The possibilities of applying mathematical methods in production are wide-ranging. The Application Area cannot cover their full scale. For that reason, the projects concentrate on the development of new mathematical methods for special topics in manufacturing and production planning, two central aspects of production, in which the participating groups have longstanding expertise in mathematical modeling, simulation and optimization.

    In the field of manufacturing, we focus on innovative technologies having a big impact on technological progress: growth and processing of semiconductor bulk single crystals, phase transitions in modern steels and solder alloys, modeling of active and passive behavior of functional materials like shape-memory materials, growth of thin films. In the projects devoted to production planning, the main aim is the effective control of the whole production flow. Among the subjects to be studied, there is also electricity portfolio management.

    Topics:
    • phase transitions in steels and solder alloys
    • production of semiconductor crystals
    • modeling of active and passive behavior of functional materials
    • online production planning
    • growth of thin films


    http://www.wias-berlin.de/research-groups/nummath/drittm/c2/index.html
  • C3

    Modelling, analysis, and simulation of modular real-time systems

    Project heads: -
    Project members: -
    Duration: 11/02-12/04
    Status: completed

    Description

    Production is one of the most important parts of the economy and at the very heart of the creation of value. Due to the central importance of production, big efforts have been made to improve production processes ever since the beginning of the industrial revolution. Nowadays, many production processes are highly automated. Computer programs based on numerical algorithms monitor the processes, improve efficiency and robustness, and guarantee high quality products. Consequently, mathematics is playing a steadily increasing role in this field. The possibilities of applying mathematical methods in production are wide-ranging. The Application Area cannot cover their full scale. For that reason, the projects concentrate on the development of new mathematical methods for special topics in manufacturing and production planning, two central aspects of production, in which the participating groups have longstanding expertise in mathematical modeling, simulation and optimization.

    In the field of manufacturing, we focus on innovative technologies having a big impact on technological progress: growth and processing of semiconductor bulk single crystals, phase transitions in modern steels and solder alloys, modeling of active and passive behavior of functional materials like shape-memory materials, growth of thin films. In the projects devoted to production planning, the main aim is the effective control of the whole production flow. Among the subjects to be studied, there is also electricity portfolio management.

    Topics:
    • phase transitions in steels and solder alloys
    • production of semiconductor crystals
    • modeling of active and passive behavior of functional materials
    • online production planning
    • growth of thin films


    http://www.zib.de/Optimization/Projects/Online/Matheon-C3/
  • C4

    Numerical solution of large nonlinear eigenvalue problems

    Project heads: -
    Project members: -
    Duration: 08/02-05/09
    Status: completed

    Description

    Production is one of the most important parts of the economy and at the very heart of the creation of value. Due to the central importance of production, big efforts have been made to improve production processes ever since the beginning of the industrial revolution. Nowadays, many production processes are highly automated. Computer programs based on numerical algorithms monitor the processes, improve efficiency and robustness, and guarantee high quality products. Consequently, mathematics is playing a steadily increasing role in this field. The possibilities of applying mathematical methods in production are wide-ranging. The Application Area cannot cover their full scale. For that reason, the projects concentrate on the development of new mathematical methods for special topics in manufacturing and production planning, two central aspects of production, in which the participating groups have longstanding expertise in mathematical modeling, simulation and optimization.

    In the field of manufacturing, we focus on innovative technologies having a big impact on technological progress: growth and processing of semiconductor bulk single crystals, phase transitions in modern steels and solder alloys, modeling of active and passive behavior of functional materials like shape-memory materials, growth of thin films. In the projects devoted to production planning, the main aim is the effective control of the whole production flow. Among the subjects to be studied, there is also electricity portfolio management.

    Topics:
    • phase transitions in steels and solder alloys
    • production of semiconductor crystals
    • modeling of active and passive behavior of functional materials
    • online production planning
    • growth of thin films


    http://www3.math.tu-berlin.de/Matheon/projects/C4/
  • C5

    Stochastic and nonlinear methods for solving resource constrained scheduling problems

    Project heads: -
    Project members: -
    Duration: 10/02-05/06
    Status: completed

    Description

    Production is one of the most important parts of the economy and at the very heart of the creation of value. Due to the central importance of production, big efforts have been made to improve production processes ever since the beginning of the industrial revolution. Nowadays, many production processes are highly automated. Computer programs based on numerical algorithms monitor the processes, improve efficiency and robustness, and guarantee high quality products. Consequently, mathematics is playing a steadily increasing role in this field. The possibilities of applying mathematical methods in production are wide-ranging. The Application Area cannot cover their full scale. For that reason, the projects concentrate on the development of new mathematical methods for special topics in manufacturing and production planning, two central aspects of production, in which the participating groups have longstanding expertise in mathematical modeling, simulation and optimization.

    In the field of manufacturing, we focus on innovative technologies having a big impact on technological progress: growth and processing of semiconductor bulk single crystals, phase transitions in modern steels and solder alloys, modeling of active and passive behavior of functional materials like shape-memory materials, growth of thin films. In the projects devoted to production planning, the main aim is the effective control of the whole production flow. Among the subjects to be studied, there is also electricity portfolio management.

    Topics:
    • phase transitions in steels and solder alloys
    • production of semiconductor crystals
    • modeling of active and passive behavior of functional materials
    • online production planning
    • growth of thin films


    http://www3.math.tu-berlin.de/Matheon/projects/C5/
  • C6

    Stability, sensitivity, and robustness in combinatorial online-optimization

    Project heads: -
    Project members: -
    Duration: 01/03-05/06
    Status: completed

    Description

    Production is one of the most important parts of the economy and at the very heart of the creation of value. Due to the central importance of production, big efforts have been made to improve production processes ever since the beginning of the industrial revolution. Nowadays, many production processes are highly automated. Computer programs based on numerical algorithms monitor the processes, improve efficiency and robustness, and guarantee high quality products. Consequently, mathematics is playing a steadily increasing role in this field. The possibilities of applying mathematical methods in production are wide-ranging. The Application Area cannot cover their full scale. For that reason, the projects concentrate on the development of new mathematical methods for special topics in manufacturing and production planning, two central aspects of production, in which the participating groups have longstanding expertise in mathematical modeling, simulation and optimization.

    In the field of manufacturing, we focus on innovative technologies having a big impact on technological progress: growth and processing of semiconductor bulk single crystals, phase transitions in modern steels and solder alloys, modeling of active and passive behavior of functional materials like shape-memory materials, growth of thin films. In the projects devoted to production planning, the main aim is the effective control of the whole production flow. Among the subjects to be studied, there is also electricity portfolio management.

    Topics:
    • phase transitions in steels and solder alloys
    • production of semiconductor crystals
    • modeling of active and passive behavior of functional materials
    • online production planning
    • growth of thin films


    http://www.zib.de/Optimization/Projects/Online/Matheon-C6/
  • C7

    Stochastic Optimization Models for Electricity Production in Liberalized Markets

    Project heads: -
    Project members: -
    Duration: 09/02-05/14
    Status: completed

    Description

    Production is one of the most important parts of the economy and at the very heart of the creation of value. Due to the central importance of production, big efforts have been made to improve production processes ever since the beginning of the industrial revolution. Nowadays, many production processes are highly automated. Computer programs based on numerical algorithms monitor the processes, improve efficiency and robustness, and guarantee high quality products. Consequently, mathematics is playing a steadily increasing role in this field. The possibilities of applying mathematical methods in production are wide-ranging. The Application Area cannot cover their full scale. For that reason, the projects concentrate on the development of new mathematical methods for special topics in manufacturing and production planning, two central aspects of production, in which the participating groups have longstanding expertise in mathematical modeling, simulation and optimization.

    In the field of manufacturing, we focus on innovative technologies having a big impact on technological progress: growth and processing of semiconductor bulk single crystals, phase transitions in modern steels and solder alloys, modeling of active and passive behavior of functional materials like shape-memory materials, growth of thin films. In the projects devoted to production planning, the main aim is the effective control of the whole production flow. Among the subjects to be studied, there is also electricity portfolio management.

    Topics:
    • phase transitions in steels and solder alloys
    • production of semiconductor crystals
    • modeling of active and passive behavior of functional materials
    • online production planning
    • growth of thin films


    http://www.math.hu-berlin.de/~romisch/projects/FZC7/electricity.html
  • C8

    Shape optimization and control of curved mechanical structures

    Project heads: -
    Project members: -
    Duration: 02/03-01/05
    Status: completed

    Description

    Production is one of the most important parts of the economy and at the very heart of the creation of value. Due to the central importance of production, big efforts have been made to improve production processes ever since the beginning of the industrial revolution. Nowadays, many production processes are highly automated. Computer programs based on numerical algorithms monitor the processes, improve efficiency and robustness, and guarantee high quality products. Consequently, mathematics is playing a steadily increasing role in this field. The possibilities of applying mathematical methods in production are wide-ranging. The Application Area cannot cover their full scale. For that reason, the projects concentrate on the development of new mathematical methods for special topics in manufacturing and production planning, two central aspects of production, in which the participating groups have longstanding expertise in mathematical modeling, simulation and optimization.

    In the field of manufacturing, we focus on innovative technologies having a big impact on technological progress: growth and processing of semiconductor bulk single crystals, phase transitions in modern steels and solder alloys, modeling of active and passive behavior of functional materials like shape-memory materials, growth of thin films. In the projects devoted to production planning, the main aim is the effective control of the whole production flow. Among the subjects to be studied, there is also electricity portfolio management.

    Topics:
    • phase transitions in steels and solder alloys
    • production of semiconductor crystals
    • modeling of active and passive behavior of functional materials
    • online production planning
    • growth of thin films


    http://www.wias-berlin.de/project-areas/phase-tran/curved-fzt86/
  • C9

    Simulation and Optimization of Semiconductor Crystal Growth from the Melt Controlled by Traveling Magnetic Fields

    Project heads: -
    Project members: -
    Duration: 08/02-05/14
    Status: completed

    Description

    Production is one of the most important parts of the economy and at the very heart of the creation of value. Due to the central importance of production, big efforts have been made to improve production processes ever since the beginning of the industrial revolution. Nowadays, many production processes are highly automated. Computer programs based on numerical algorithms monitor the processes, improve efficiency and robustness, and guarantee high quality products. Consequently, mathematics is playing a steadily increasing role in this field. The possibilities of applying mathematical methods in production are wide-ranging. The Application Area cannot cover their full scale. For that reason, the projects concentrate on the development of new mathematical methods for special topics in manufacturing and production planning, two central aspects of production, in which the participating groups have longstanding expertise in mathematical modeling, simulation and optimization.

    In the field of manufacturing, we focus on innovative technologies having a big impact on technological progress: growth and processing of semiconductor bulk single crystals, phase transitions in modern steels and solder alloys, modeling of active and passive behavior of functional materials like shape-memory materials, growth of thin films. In the projects devoted to production planning, the main aim is the effective control of the whole production flow. Among the subjects to be studied, there is also electricity portfolio management.

    Topics:
    • phase transitions in steels and solder alloys
    • production of semiconductor crystals
    • modeling of active and passive behavior of functional materials
    • online production planning
    • growth of thin films


    http://www.wias-berlin.de/projects/Matheon-c9
  • C10

    Modelling, Asymptotic Analysis and Numerical Simulation of Interface Dynamics on the Nanoscale

    Project heads: -
    Project members: -
    Duration: 12/02-05/14
    Status: completed

    Description

    Production is one of the most important parts of the economy and at the very heart of the creation of value. Due to the central importance of production, big efforts have been made to improve production processes ever since the beginning of the industrial revolution. Nowadays, many production processes are highly automated. Computer programs based on numerical algorithms monitor the processes, improve efficiency and robustness, and guarantee high quality products. Consequently, mathematics is playing a steadily increasing role in this field. The possibilities of applying mathematical methods in production are wide-ranging. The Application Area cannot cover their full scale. For that reason, the projects concentrate on the development of new mathematical methods for special topics in manufacturing and production planning, two central aspects of production, in which the participating groups have longstanding expertise in mathematical modeling, simulation and optimization.

    In the field of manufacturing, we focus on innovative technologies having a big impact on technological progress: growth and processing of semiconductor bulk single crystals, phase transitions in modern steels and solder alloys, modeling of active and passive behavior of functional materials like shape-memory materials, growth of thin films. In the projects devoted to production planning, the main aim is the effective control of the whole production flow. Among the subjects to be studied, there is also electricity portfolio management.

    Topics:
    • phase transitions in steels and solder alloys
    • production of semiconductor crystals
    • modeling of active and passive behavior of functional materials
    • online production planning
    • growth of thin films


    http://www.wias-berlin.de/people/peschka/c10/
  • C11

    Modeling and optimization of phase transitions in steel

    Project heads: -
    Project members: -
    Duration: 04/03-05/14
    Status: completed

    Description

    Production is one of the most important parts of the economy and at the very heart of the creation of value. Due to the central importance of production, big efforts have been made to improve production processes ever since the beginning of the industrial revolution. Nowadays, many production processes are highly automated. Computer programs based on numerical algorithms monitor the processes, improve efficiency and robustness, and guarantee high quality products. Consequently, mathematics is playing a steadily increasing role in this field. The possibilities of applying mathematical methods in production are wide-ranging. The Application Area cannot cover their full scale. For that reason, the projects concentrate on the development of new mathematical methods for special topics in manufacturing and production planning, two central aspects of production, in which the participating groups have longstanding expertise in mathematical modeling, simulation and optimization.

    In the field of manufacturing, we focus on innovative technologies having a big impact on technological progress: growth and processing of semiconductor bulk single crystals, phase transitions in modern steels and solder alloys, modeling of active and passive behavior of functional materials like shape-memory materials, growth of thin films. In the projects devoted to production planning, the main aim is the effective control of the whole production flow. Among the subjects to be studied, there is also electricity portfolio management.

    Topics:
    • phase transitions in steels and solder alloys
    • production of semiconductor crystals
    • modeling of active and passive behavior of functional materials
    • online production planning
    • growth of thin films


    http://www.wias-berlin.de/projects/Matheon-c11/
  • C12

    General purpose, Linearly Invariant Algorithm for Large-Scale Nonlinear Programming

    Project heads: -
    Project members: -
    Duration: 01/04-05/10
    Status: completed

    Description

    Production is one of the most important parts of the economy and at the very heart of the creation of value. Due to the central importance of production, big efforts have been made to improve production processes ever since the beginning of the industrial revolution. Nowadays, many production processes are highly automated. Computer programs based on numerical algorithms monitor the processes, improve efficiency and robustness, and guarantee high quality products. Consequently, mathematics is playing a steadily increasing role in this field. The possibilities of applying mathematical methods in production are wide-ranging. The Application Area cannot cover their full scale. For that reason, the projects concentrate on the development of new mathematical methods for special topics in manufacturing and production planning, two central aspects of production, in which the participating groups have longstanding expertise in mathematical modeling, simulation and optimization.

    In the field of manufacturing, we focus on innovative technologies having a big impact on technological progress: growth and processing of semiconductor bulk single crystals, phase transitions in modern steels and solder alloys, modeling of active and passive behavior of functional materials like shape-memory materials, growth of thin films. In the projects devoted to production planning, the main aim is the effective control of the whole production flow. Among the subjects to be studied, there is also electricity portfolio management.

    Topics:
    • phase transitions in steels and solder alloys
    • production of semiconductor crystals
    • modeling of active and passive behavior of functional materials
    • online production planning
    • growth of thin films


    http://www.math.hu-berlin.de/~griewank/C12/
  • C13

    Adaptive simulation of phase-transitions

    Project heads: -
    Project members: -
    Duration: 11/03-05/10
    Status: completed

    Description

    Production is one of the most important parts of the economy and at the very heart of the creation of value. Due to the central importance of production, big efforts have been made to improve production processes ever since the beginning of the industrial revolution. Nowadays, many production processes are highly automated. Computer programs based on numerical algorithms monitor the processes, improve efficiency and robustness, and guarantee high quality products. Consequently, mathematics is playing a steadily increasing role in this field. The possibilities of applying mathematical methods in production are wide-ranging. The Application Area cannot cover their full scale. For that reason, the projects concentrate on the development of new mathematical methods for special topics in manufacturing and production planning, two central aspects of production, in which the participating groups have longstanding expertise in mathematical modeling, simulation and optimization.

    In the field of manufacturing, we focus on innovative technologies having a big impact on technological progress: growth and processing of semiconductor bulk single crystals, phase transitions in modern steels and solder alloys, modeling of active and passive behavior of functional materials like shape-memory materials, growth of thin films. In the projects devoted to production planning, the main aim is the effective control of the whole production flow. Among the subjects to be studied, there is also electricity portfolio management.

    Topics:
    • phase transitions in steels and solder alloys
    • production of semiconductor crystals
    • modeling of active and passive behavior of functional materials
    • online production planning
    • growth of thin films


    http://www.math.hu-berlin.de/~cc/english/research/dfg_project_c13.html
  • C14

    Macroscopic models for precipitation in crystalline solids

    Project heads: -
    Project members: -
    Duration: 10/04-05/10
    Status: completed

    Description

    Production is one of the most important parts of the economy and at the very heart of the creation of value. Due to the central importance of production, big efforts have been made to improve production processes ever since the beginning of the industrial revolution. Nowadays, many production processes are highly automated. Computer programs based on numerical algorithms monitor the processes, improve efficiency and robustness, and guarantee high quality products. Consequently, mathematics is playing a steadily increasing role in this field. The possibilities of applying mathematical methods in production are wide-ranging. The Application Area cannot cover their full scale. For that reason, the projects concentrate on the development of new mathematical methods for special topics in manufacturing and production planning, two central aspects of production, in which the participating groups have longstanding expertise in mathematical modeling, simulation and optimization.

    In the field of manufacturing, we focus on innovative technologies having a big impact on technological progress: growth and processing of semiconductor bulk single crystals, phase transitions in modern steels and solder alloys, modeling of active and passive behavior of functional materials like shape-memory materials, growth of thin films. In the projects devoted to production planning, the main aim is the effective control of the whole production flow. Among the subjects to be studied, there is also electricity portfolio management.

    Topics:
    • phase transitions in steels and solder alloys
    • production of semiconductor crystals
    • modeling of active and passive behavior of functional materials
    • online production planning
    • growth of thin films


    http://www.math.hu-berlin.de/~wwwaa/MatheonC14
  • C15

    Pattern formation in magnetic thin films

    Project heads: -
    Project members: -
    Duration: 06/05-09/08
    Status: completed

    Description

    Production is one of the most important parts of the economy and at the very heart of the creation of value. Due to the central importance of production, big efforts have been made to improve production processes ever since the beginning of the industrial revolution. Nowadays, many production processes are highly automated. Computer programs based on numerical algorithms monitor the processes, improve efficiency and robustness, and guarantee high quality products. Consequently, mathematics is playing a steadily increasing role in this field. The possibilities of applying mathematical methods in production are wide-ranging. The Application Area cannot cover their full scale. For that reason, the projects concentrate on the development of new mathematical methods for special topics in manufacturing and production planning, two central aspects of production, in which the participating groups have longstanding expertise in mathematical modeling, simulation and optimization.

    In the field of manufacturing, we focus on innovative technologies having a big impact on technological progress: growth and processing of semiconductor bulk single crystals, phase transitions in modern steels and solder alloys, modeling of active and passive behavior of functional materials like shape-memory materials, growth of thin films. In the projects devoted to production planning, the main aim is the effective control of the whole production flow. Among the subjects to be studied, there is also electricity portfolio management.

    Topics:
    • phase transitions in steels and solder alloys
    • production of semiconductor crystals
    • modeling of active and passive behavior of functional materials
    • online production planning
    • growth of thin films


    http://www.mathematik.hu-berlin.de/~wwwaa/web/forschung/fzt86/fzt86-melcher.html
  • D1

    Simulation and control of switched systems of differential-algebraic equations

    Project heads: -
    Project members: -
    Duration: 10/02-05/10
    Status: completed

    Description

    The technical progress of the last decades has been enormously stimulated by two technological revolutions: the invention of the transistor in 1947 (Nobel prize 1956) and the invention of the laser in 1958 (Nobel prize 1964). The impact of both inventions on modern life is an evident fact.

    Already in 1950, a system of partial differential equations was published that models adequately the essential charge transport processes in semiconductor devices. On the basis of this drift-diffusion model the first bipolar transistor was successfully simulated in 1964. Just in that time the first integrated circuits containing a few transistors became commercially available. Since then, the electronics industry has achieved a phenomenal growth, mainly due to the rapid advances in integration technologies, large-scale systems design and numerical simulation. The number of applications of integrated circuits in high-performance computing, telecommunications, and consumer electronics has been rising steadily, and at a very fast pace. As microelectronic research moves into the nanometer scale device regime with GHz or higher operating speeds, the physics of electron flow through devices becomes more complicated, and physical effects, which previously could be safely ignored, become significant. Consequently, models of a higher abstraction level are needed. Conversely, faster simulation is typically required, which places a constraint on the model refinement if conventional simulation techniques are applied.

    Like the invention of the transistor triggered research in circuit simulation, the invention of the laser had a major impact on optical technologies. Classical optics turned into photonics. In todays telecommunication technologies, photons have already become the main carrier of information, regardless of the fact that even today most of the applied optical devices are based on conventional optical fibers and low index-contrast waveguides. Recently, a number of pioneering developments - all based on nanotechnologies - opened up the door to completely new working principles, hence to new classes of optoelectronic devices. Among them are nanostructured periodic materials (photonic crystals) and optically active nanostructures like quantum layers and quantum dots. A proper modelling of such structures has to describe simultaneously electrical charge transport, light generation, light propagation and scattering. Moreover, optical active nanostructures have to be described by quantum mechanics.

    In spite of the achievements of electronic/optoelectronic device and circuit simulation obtained so far, new nanotechnologies create new challenging tasks for mathematical modeling and numerical simulation in this field.

    Topics:
    • shape memory alloys in airfoils
    • production of semiconductor crystals
    • methanole fuel cell optimization
    • online production planning metamaterials


    http://www3.math.tu-berlin.de/Matheon/projects/D1/index.html
  • D2

    Passivation of linear time invariant systems arising in circuit simulation and electric field computation* [*old title: Numerical solution of large unstructured linear systems in circuit simulation]

    Project heads: -
    Project members: -
    Duration: 10/02-05/14
    Status: completed

    Description

    The technical progress of the last decades has been enormously stimulated by two technological revolutions: the invention of the transistor in 1947 (Nobel prize 1956) and the invention of the laser in 1958 (Nobel prize 1964). The impact of both inventions on modern life is an evident fact.

    Already in 1950, a system of partial differential equations was published that models adequately the essential charge transport processes in semiconductor devices. On the basis of this drift-diffusion model the first bipolar transistor was successfully simulated in 1964. Just in that time the first integrated circuits containing a few transistors became commercially available. Since then, the electronics industry has achieved a phenomenal growth, mainly due to the rapid advances in integration technologies, large-scale systems design and numerical simulation. The number of applications of integrated circuits in high-performance computing, telecommunications, and consumer electronics has been rising steadily, and at a very fast pace. As microelectronic research moves into the nanometer scale device regime with GHz or higher operating speeds, the physics of electron flow through devices becomes more complicated, and physical effects, which previously could be safely ignored, become significant. Consequently, models of a higher abstraction level are needed. Conversely, faster simulation is typically required, which places a constraint on the model refinement if conventional simulation techniques are applied.

    Like the invention of the transistor triggered research in circuit simulation, the invention of the laser had a major impact on optical technologies. Classical optics turned into photonics. In todays telecommunication technologies, photons have already become the main carrier of information, regardless of the fact that even today most of the applied optical devices are based on conventional optical fibers and low index-contrast waveguides. Recently, a number of pioneering developments - all based on nanotechnologies - opened up the door to completely new working principles, hence to new classes of optoelectronic devices. Among them are nanostructured periodic materials (photonic crystals) and optically active nanostructures like quantum layers and quantum dots. A proper modelling of such structures has to describe simultaneously electrical charge transport, light generation, light propagation and scattering. Moreover, optical active nanostructures have to be described by quantum mechanics.

    In spite of the achievements of electronic/optoelectronic device and circuit simulation obtained so far, new nanotechnologies create new challenging tasks for mathematical modeling and numerical simulation in this field.

    Topics:
    • shape memory alloys in airfoils
    • production of semiconductor crystals
    • methanole fuel cell optimization
    • online production planning metamaterials


    http://www3.math.tu-berlin.de/Matheon/projects/D2/
  • D3

    Global singular perturbations

    Project heads: -
    Project members: -
    Duration: 03/03-12/04
    Status: completed

    Description

    The technical progress of the last decades has been enormously stimulated by two technological revolutions: the invention of the transistor in 1947 (Nobel prize 1956) and the invention of the laser in 1958 (Nobel prize 1964). The impact of both inventions on modern life is an evident fact.

    Already in 1950, a system of partial differential equations was published that models adequately the essential charge transport processes in semiconductor devices. On the basis of this drift-diffusion model the first bipolar transistor was successfully simulated in 1964. Just in that time the first integrated circuits containing a few transistors became commercially available. Since then, the electronics industry has achieved a phenomenal growth, mainly due to the rapid advances in integration technologies, large-scale systems design and numerical simulation. The number of applications of integrated circuits in high-performance computing, telecommunications, and consumer electronics has been rising steadily, and at a very fast pace. As microelectronic research moves into the nanometer scale device regime with GHz or higher operating speeds, the physics of electron flow through devices becomes more complicated, and physical effects, which previously could be safely ignored, become significant. Consequently, models of a higher abstraction level are needed. Conversely, faster simulation is typically required, which places a constraint on the model refinement if conventional simulation techniques are applied.

    Like the invention of the transistor triggered research in circuit simulation, the invention of the laser had a major impact on optical technologies. Classical optics turned into photonics. In todays telecommunication technologies, photons have already become the main carrier of information, regardless of the fact that even today most of the applied optical devices are based on conventional optical fibers and low index-contrast waveguides. Recently, a number of pioneering developments - all based on nanotechnologies - opened up the door to completely new working principles, hence to new classes of optoelectronic devices. Among them are nanostructured periodic materials (photonic crystals) and optically active nanostructures like quantum layers and quantum dots. A proper modelling of such structures has to describe simultaneously electrical charge transport, light generation, light propagation and scattering. Moreover, optical active nanostructures have to be described by quantum mechanics.

    In spite of the achievements of electronic/optoelectronic device and circuit simulation obtained so far, new nanotechnologies create new challenging tasks for mathematical modeling and numerical simulation in this field.

    Topics:
    • shape memory alloys in airfoils
    • production of semiconductor crystals
    • methanole fuel cell optimization
    • online production planning metamaterials


    http://dynamics.mi.fu-berlin.de/projects/laser1.php
  • D4

    Quantum mechanical and macroscopic models for optoelectronic devices

    Project heads: -
    Project members: -
    Duration: 09/04-05/10
    Status: completed

    Description

    The technical progress of the last decades has been enormously stimulated by two technological revolutions: the invention of the transistor in 1947 (Nobel prize 1956) and the invention of the laser in 1958 (Nobel prize 1964). The impact of both inventions on modern life is an evident fact.

    Already in 1950, a system of partial differential equations was published that models adequately the essential charge transport processes in semiconductor devices. On the basis of this drift-diffusion model the first bipolar transistor was successfully simulated in 1964. Just in that time the first integrated circuits containing a few transistors became commercially available. Since then, the electronics industry has achieved a phenomenal growth, mainly due to the rapid advances in integration technologies, large-scale systems design and numerical simulation. The number of applications of integrated circuits in high-performance computing, telecommunications, and consumer electronics has been rising steadily, and at a very fast pace. As microelectronic research moves into the nanometer scale device regime with GHz or higher operating speeds, the physics of electron flow through devices becomes more complicated, and physical effects, which previously could be safely ignored, become significant. Consequently, models of a higher abstraction level are needed. Conversely, faster simulation is typically required, which places a constraint on the model refinement if conventional simulation techniques are applied.

    Like the invention of the transistor triggered research in circuit simulation, the invention of the laser had a major impact on optical technologies. Classical optics turned into photonics. In todays telecommunication technologies, photons have already become the main carrier of information, regardless of the fact that even today most of the applied optical devices are based on conventional optical fibers and low index-contrast waveguides. Recently, a number of pioneering developments - all based on nanotechnologies - opened up the door to completely new working principles, hence to new classes of optoelectronic devices. Among them are nanostructured periodic materials (photonic crystals) and optically active nanostructures like quantum layers and quantum dots. A proper modelling of such structures has to describe simultaneously electrical charge transport, light generation, light propagation and scattering. Moreover, optical active nanostructures have to be described by quantum mechanics.

    In spite of the achievements of electronic/optoelectronic device and circuit simulation obtained so far, new nanotechnologies create new challenging tasks for mathematical modeling and numerical simulation in this field.

    Topics:
    • shape memory alloys in airfoils
    • production of semiconductor crystals
    • methanole fuel cell optimization
    • online production planning metamaterials


    http://www.wias-berlin.de/projects/Matheon-d4/index.jsp
  • D5

    Structure analysis for simulation and control problems of differential algebraic equations

    Project heads: -
    Project members: -
    Duration: 06/02-05/06
    Status: completed

    Description

    The technical progress of the last decades has been enormously stimulated by two technological revolutions: the invention of the transistor in 1947 (Nobel prize 1956) and the invention of the laser in 1958 (Nobel prize 1964). The impact of both inventions on modern life is an evident fact.

    Already in 1950, a system of partial differential equations was published that models adequately the essential charge transport processes in semiconductor devices. On the basis of this drift-diffusion model the first bipolar transistor was successfully simulated in 1964. Just in that time the first integrated circuits containing a few transistors became commercially available. Since then, the electronics industry has achieved a phenomenal growth, mainly due to the rapid advances in integration technologies, large-scale systems design and numerical simulation. The number of applications of integrated circuits in high-performance computing, telecommunications, and consumer electronics has been rising steadily, and at a very fast pace. As microelectronic research moves into the nanometer scale device regime with GHz or higher operating speeds, the physics of electron flow through devices becomes more complicated, and physical effects, which previously could be safely ignored, become significant. Consequently, models of a higher abstraction level are needed. Conversely, faster simulation is typically required, which places a constraint on the model refinement if conventional simulation techniques are applied.

    Like the invention of the transistor triggered research in circuit simulation, the invention of the laser had a major impact on optical technologies. Classical optics turned into photonics. In todays telecommunication technologies, photons have already become the main carrier of information, regardless of the fact that even today most of the applied optical devices are based on conventional optical fibers and low index-contrast waveguides. Recently, a number of pioneering developments - all based on nanotechnologies - opened up the door to completely new working principles, hence to new classes of optoelectronic devices. Among them are nanostructured periodic materials (photonic crystals) and optically active nanostructures like quantum layers and quantum dots. A proper modelling of such structures has to describe simultaneously electrical charge transport, light generation, light propagation and scattering. Moreover, optical active nanostructures have to be described by quantum mechanics.

    In spite of the achievements of electronic/optoelectronic device and circuit simulation obtained so far, new nanotechnologies create new challenging tasks for mathematical modeling and numerical simulation in this field.

    Topics:
    • shape memory alloys in airfoils
    • production of semiconductor crystals
    • methanole fuel cell optimization
    • online production planning metamaterials


    http://www.mathematik.hu-berlin.de/~lamour/Matheon/
  • D6

    Numerical methods for stochastic differential-algebraic equations applied to transient noise analysis in circuit simulation

    Project heads: -
    Project members: -
    Duration: 10/03-05/06
    Status: completed

    Description

    The technical progress of the last decades has been enormously stimulated by two technological revolutions: the invention of the transistor in 1947 (Nobel prize 1956) and the invention of the laser in 1958 (Nobel prize 1964). The impact of both inventions on modern life is an evident fact.

    Already in 1950, a system of partial differential equations was published that models adequately the essential charge transport processes in semiconductor devices. On the basis of this drift-diffusion model the first bipolar transistor was successfully simulated in 1964. Just in that time the first integrated circuits containing a few transistors became commercially available. Since then, the electronics industry has achieved a phenomenal growth, mainly due to the rapid advances in integration technologies, large-scale systems design and numerical simulation. The number of applications of integrated circuits in high-performance computing, telecommunications, and consumer electronics has been rising steadily, and at a very fast pace. As microelectronic research moves into the nanometer scale device regime with GHz or higher operating speeds, the physics of electron flow through devices becomes more complicated, and physical effects, which previously could be safely ignored, become significant. Consequently, models of a higher abstraction level are needed. Conversely, faster simulation is typically required, which places a constraint on the model refinement if conventional simulation techniques are applied.

    Like the invention of the transistor triggered research in circuit simulation, the invention of the laser had a major impact on optical technologies. Classical optics turned into photonics. In todays telecommunication technologies, photons have already become the main carrier of information, regardless of the fact that even today most of the applied optical devices are based on conventional optical fibers and low index-contrast waveguides. Recently, a number of pioneering developments - all based on nanotechnologies - opened up the door to completely new working principles, hence to new classes of optoelectronic devices. Among them are nanostructured periodic materials (photonic crystals) and optically active nanostructures like quantum layers and quantum dots. A proper modelling of such structures has to describe simultaneously electrical charge transport, light generation, light propagation and scattering. Moreover, optical active nanostructures have to be described by quantum mechanics.

    In spite of the achievements of electronic/optoelectronic device and circuit simulation obtained so far, new nanotechnologies create new challenging tasks for mathematical modeling and numerical simulation in this field.

    Topics:
    • shape memory alloys in airfoils
    • production of semiconductor crystals
    • methanole fuel cell optimization
    • online production planning metamaterials


    http://www.math.hu-berlin.de/~romisch/projects/FZD6/noise.html
  • D7

    Numerical simulation of integrated circuits for future chip generations

    Project heads: -
    Project members: -
    Duration: 09/02-05/08
    Status: completed

    Description

    The technical progress of the last decades has been enormously stimulated by two technological revolutions: the invention of the transistor in 1947 (Nobel prize 1956) and the invention of the laser in 1958 (Nobel prize 1964). The impact of both inventions on modern life is an evident fact.

    Already in 1950, a system of partial differential equations was published that models adequately the essential charge transport processes in semiconductor devices. On the basis of this drift-diffusion model the first bipolar transistor was successfully simulated in 1964. Just in that time the first integrated circuits containing a few transistors became commercially available. Since then, the electronics industry has achieved a phenomenal growth, mainly due to the rapid advances in integration technologies, large-scale systems design and numerical simulation. The number of applications of integrated circuits in high-performance computing, telecommunications, and consumer electronics has been rising steadily, and at a very fast pace. As microelectronic research moves into the nanometer scale device regime with GHz or higher operating speeds, the physics of electron flow through devices becomes more complicated, and physical effects, which previously could be safely ignored, become significant. Consequently, models of a higher abstraction level are needed. Conversely, faster simulation is typically required, which places a constraint on the model refinement if conventional simulation techniques are applied.

    Like the invention of the transistor triggered research in circuit simulation, the invention of the laser had a major impact on optical technologies. Classical optics turned into photonics. In todays telecommunication technologies, photons have already become the main carrier of information, regardless of the fact that even today most of the applied optical devices are based on conventional optical fibers and low index-contrast waveguides. Recently, a number of pioneering developments - all based on nanotechnologies - opened up the door to completely new working principles, hence to new classes of optoelectronic devices. Among them are nanostructured periodic materials (photonic crystals) and optically active nanostructures like quantum layers and quantum dots. A proper modelling of such structures has to describe simultaneously electrical charge transport, light generation, light propagation and scattering. Moreover, optical active nanostructures have to be described by quantum mechanics.

    In spite of the achievements of electronic/optoelectronic device and circuit simulation obtained so far, new nanotechnologies create new challenging tasks for mathematical modeling and numerical simulation in this field.

    Topics:
    • shape memory alloys in airfoils
    • production of semiconductor crystals
    • methanole fuel cell optimization
    • online production planning metamaterials


    http://www.math.hu-berlin.de/~monica/projectD7.html
  • D8

    Nonlinear dynamical effects in integrated optoelectronic structures

    Project heads: -
    Project members: -
    Duration: 06/02-05/14
    Status: completed

    Description

    The technical progress of the last decades has been enormously stimulated by two technological revolutions: the invention of the transistor in 1947 (Nobel prize 1956) and the invention of the laser in 1958 (Nobel prize 1964). The impact of both inventions on modern life is an evident fact.

    Already in 1950, a system of partial differential equations was published that models adequately the essential charge transport processes in semiconductor devices. On the basis of this drift-diffusion model the first bipolar transistor was successfully simulated in 1964. Just in that time the first integrated circuits containing a few transistors became commercially available. Since then, the electronics industry has achieved a phenomenal growth, mainly due to the rapid advances in integration technologies, large-scale systems design and numerical simulation. The number of applications of integrated circuits in high-performance computing, telecommunications, and consumer electronics has been rising steadily, and at a very fast pace. As microelectronic research moves into the nanometer scale device regime with GHz or higher operating speeds, the physics of electron flow through devices becomes more complicated, and physical effects, which previously could be safely ignored, become significant. Consequently, models of a higher abstraction level are needed. Conversely, faster simulation is typically required, which places a constraint on the model refinement if conventional simulation techniques are applied.

    Like the invention of the transistor triggered research in circuit simulation, the invention of the laser had a major impact on optical technologies. Classical optics turned into photonics. In todays telecommunication technologies, photons have already become the main carrier of information, regardless of the fact that even today most of the applied optical devices are based on conventional optical fibers and low index-contrast waveguides. Recently, a number of pioneering developments - all based on nanotechnologies - opened up the door to completely new working principles, hence to new classes of optoelectronic devices. Among them are nanostructured periodic materials (photonic crystals) and optically active nanostructures like quantum layers and quantum dots. A proper modelling of such structures has to describe simultaneously electrical charge transport, light generation, light propagation and scattering. Moreover, optical active nanostructures have to be described by quantum mechanics.

    In spite of the achievements of electronic/optoelectronic device and circuit simulation obtained so far, new nanotechnologies create new challenging tasks for mathematical modeling and numerical simulation in this field.

    Topics:
    • shape memory alloys in airfoils
    • production of semiconductor crystals
    • methanole fuel cell optimization
    • online production planning metamaterials


    http://www.wias-berlin.de/projects/Matheon-d8/project_d8.jsp
  • D9

    Design of nano-photonic devices

    Project heads: -
    Project members: -
    Duration: 01/03-05/10
    Status: completed

    Description

    The technical progress of the last decades has been enormously stimulated by two technological revolutions: the invention of the transistor in 1947 (Nobel prize 1956) and the invention of the laser in 1958 (Nobel prize 1964). The impact of both inventions on modern life is an evident fact.

    Already in 1950, a system of partial differential equations was published that models adequately the essential charge transport processes in semiconductor devices. On the basis of this drift-diffusion model the first bipolar transistor was successfully simulated in 1964. Just in that time the first integrated circuits containing a few transistors became commercially available. Since then, the electronics industry has achieved a phenomenal growth, mainly due to the rapid advances in integration technologies, large-scale systems design and numerical simulation. The number of applications of integrated circuits in high-performance computing, telecommunications, and consumer electronics has been rising steadily, and at a very fast pace. As microelectronic research moves into the nanometer scale device regime with GHz or higher operating speeds, the physics of electron flow through devices becomes more complicated, and physical effects, which previously could be safely ignored, become significant. Consequently, models of a higher abstraction level are needed. Conversely, faster simulation is typically required, which places a constraint on the model refinement if conventional simulation techniques are applied.

    Like the invention of the transistor triggered research in circuit simulation, the invention of the laser had a major impact on optical technologies. Classical optics turned into photonics. In todays telecommunication technologies, photons have already become the main carrier of information, regardless of the fact that even today most of the applied optical devices are based on conventional optical fibers and low index-contrast waveguides. Recently, a number of pioneering developments - all based on nanotechnologies - opened up the door to completely new working principles, hence to new classes of optoelectronic devices. Among them are nanostructured periodic materials (photonic crystals) and optically active nanostructures like quantum layers and quantum dots. A proper modelling of such structures has to describe simultaneously electrical charge transport, light generation, light propagation and scattering. Moreover, optical active nanostructures have to be described by quantum mechanics.

    In spite of the achievements of electronic/optoelectronic device and circuit simulation obtained so far, new nanotechnologies create new challenging tasks for mathematical modeling and numerical simulation in this field.

    Topics:
    • shape memory alloys in airfoils
    • production of semiconductor crystals
    • methanole fuel cell optimization
    • online production planning metamaterials


    http://www.zib.de/en/numerik/computational-nano-optics/projects/archive-projects-short-details/article/Matheon-d9-photonic-devices.html
  • D10

    Entropy decay and shape design for nonlinear drift diffusion systems

    Project heads: -
    Project members: -
    Duration: 05/03-01/05
    Status: completed

    Description

    The technical progress of the last decades has been enormously stimulated by two technological revolutions: the invention of the transistor in 1947 (Nobel prize 1956) and the invention of the laser in 1958 (Nobel prize 1964). The impact of both inventions on modern life is an evident fact.

    Already in 1950, a system of partial differential equations was published that models adequately the essential charge transport processes in semiconductor devices. On the basis of this drift-diffusion model the first bipolar transistor was successfully simulated in 1964. Just in that time the first integrated circuits containing a few transistors became commercially available. Since then, the electronics industry has achieved a phenomenal growth, mainly due to the rapid advances in integration technologies, large-scale systems design and numerical simulation. The number of applications of integrated circuits in high-performance computing, telecommunications, and consumer electronics has been rising steadily, and at a very fast pace. As microelectronic research moves into the nanometer scale device regime with GHz or higher operating speeds, the physics of electron flow through devices becomes more complicated, and physical effects, which previously could be safely ignored, become significant. Consequently, models of a higher abstraction level are needed. Conversely, faster simulation is typically required, which places a constraint on the model refinement if conventional simulation techniques are applied.

    Like the invention of the transistor triggered research in circuit simulation, the invention of the laser had a major impact on optical technologies. Classical optics turned into photonics. In todays telecommunication technologies, photons have already become the main carrier of information, regardless of the fact that even today most of the applied optical devices are based on conventional optical fibers and low index-contrast waveguides. Recently, a number of pioneering developments - all based on nanotechnologies - opened up the door to completely new working principles, hence to new classes of optoelectronic devices. Among them are nanostructured periodic materials (photonic crystals) and optically active nanostructures like quantum layers and quantum dots. A proper modelling of such structures has to describe simultaneously electrical charge transport, light generation, light propagation and scattering. Moreover, optical active nanostructures have to be described by quantum mechanics.

    In spite of the achievements of electronic/optoelectronic device and circuit simulation obtained so far, new nanotechnologies create new challenging tasks for mathematical modeling and numerical simulation in this field.

    Topics:
    • shape memory alloys in airfoils
    • production of semiconductor crystals
    • methanole fuel cell optimization
    • online production planning metamaterials


    http://www.math.tu-berlin.de/~plato/dfg.html
  • D11

    Numerical Treatment of PDEs on unbounded Domains

    Project heads: -
    Project members: -
    Duration: 11/02-05/06
    Status: completed

    Description

    The technical progress of the last decades has been enormously stimulated by two technological revolutions: the invention of the transistor in 1947 (Nobel prize 1956) and the invention of the laser in 1958 (Nobel prize 1964). The impact of both inventions on modern life is an evident fact.

    Already in 1950, a system of partial differential equations was published that models adequately the essential charge transport processes in semiconductor devices. On the basis of this drift-diffusion model the first bipolar transistor was successfully simulated in 1964. Just in that time the first integrated circuits containing a few transistors became commercially available. Since then, the electronics industry has achieved a phenomenal growth, mainly due to the rapid advances in integration technologies, large-scale systems design and numerical simulation. The number of applications of integrated circuits in high-performance computing, telecommunications, and consumer electronics has been rising steadily, and at a very fast pace. As microelectronic research moves into the nanometer scale device regime with GHz or higher operating speeds, the physics of electron flow through devices becomes more complicated, and physical effects, which previously could be safely ignored, become significant. Consequently, models of a higher abstraction level are needed. Conversely, faster simulation is typically required, which places a constraint on the model refinement if conventional simulation techniques are applied.

    Like the invention of the transistor triggered research in circuit simulation, the invention of the laser had a major impact on optical technologies. Classical optics turned into photonics. In todays telecommunication technologies, photons have already become the main carrier of information, regardless of the fact that even today most of the applied optical devices are based on conventional optical fibers and low index-contrast waveguides. Recently, a number of pioneering developments - all based on nanotechnologies - opened up the door to completely new working principles, hence to new classes of optoelectronic devices. Among them are nanostructured periodic materials (photonic crystals) and optically active nanostructures like quantum layers and quantum dots. A proper modelling of such structures has to describe simultaneously electrical charge transport, light generation, light propagation and scattering. Moreover, optical active nanostructures have to be described by quantum mechanics.

    In spite of the achievements of electronic/optoelectronic device and circuit simulation obtained so far, new nanotechnologies create new challenging tasks for mathematical modeling and numerical simulation in this field.

    Topics:
    • shape memory alloys in airfoils
    • production of semiconductor crystals
    • methanole fuel cell optimization
    • online production planning metamaterials


    http://www.math.tu-berlin.de/~ehrhardt/Projects/dfg.html
  • D12

    General linear methods for integrated circuit design

    Project heads: -
    Project members: -
    Duration: 12/02-05/06
    Status: completed

    Description

    The technical progress of the last decades has been enormously stimulated by two technological revolutions: the invention of the transistor in 1947 (Nobel prize 1956) and the invention of the laser in 1958 (Nobel prize 1964). The impact of both inventions on modern life is an evident fact.

    Already in 1950, a system of partial differential equations was published that models adequately the essential charge transport processes in semiconductor devices. On the basis of this drift-diffusion model the first bipolar transistor was successfully simulated in 1964. Just in that time the first integrated circuits containing a few transistors became commercially available. Since then, the electronics industry has achieved a phenomenal growth, mainly due to the rapid advances in integration technologies, large-scale systems design and numerical simulation. The number of applications of integrated circuits in high-performance computing, telecommunications, and consumer electronics has been rising steadily, and at a very fast pace. As microelectronic research moves into the nanometer scale device regime with GHz or higher operating speeds, the physics of electron flow through devices becomes more complicated, and physical effects, which previously could be safely ignored, become significant. Consequently, models of a higher abstraction level are needed. Conversely, faster simulation is typically required, which places a constraint on the model refinement if conventional simulation techniques are applied.

    Like the invention of the transistor triggered research in circuit simulation, the invention of the laser had a major impact on optical technologies. Classical optics turned into photonics. In todays telecommunication technologies, photons have already become the main carrier of information, regardless of the fact that even today most of the applied optical devices are based on conventional optical fibers and low index-contrast waveguides. Recently, a number of pioneering developments - all based on nanotechnologies - opened up the door to completely new working principles, hence to new classes of optoelectronic devices. Among them are nanostructured periodic materials (photonic crystals) and optically active nanostructures like quantum layers and quantum dots. A proper modelling of such structures has to describe simultaneously electrical charge transport, light generation, light propagation and scattering. Moreover, optical active nanostructures have to be described by quantum mechanics.

    In spite of the achievements of electronic/optoelectronic device and circuit simulation obtained so far, new nanotechnologies create new challenging tasks for mathematical modeling and numerical simulation in this field.

    Topics:
    • shape memory alloys in airfoils
    • production of semiconductor crystals
    • methanole fuel cell optimization
    • online production planning metamaterials


    http://www.math.hu-berlin.de/~steffen/d12_project.htm
  • D13

    Control and numerical methods for coupled systems

    Project heads: -
    Project members: -
    Duration: 09/03-05/10
    Status: completed

    Description

    The technical progress of the last decades has been enormously stimulated by two technological revolutions: the invention of the transistor in 1947 (Nobel prize 1956) and the invention of the laser in 1958 (Nobel prize 1964). The impact of both inventions on modern life is an evident fact.

    Already in 1950, a system of partial differential equations was published that models adequately the essential charge transport processes in semiconductor devices. On the basis of this drift-diffusion model the first bipolar transistor was successfully simulated in 1964. Just in that time the first integrated circuits containing a few transistors became commercially available. Since then, the electronics industry has achieved a phenomenal growth, mainly due to the rapid advances in integration technologies, large-scale systems design and numerical simulation. The number of applications of integrated circuits in high-performance computing, telecommunications, and consumer electronics has been rising steadily, and at a very fast pace. As microelectronic research moves into the nanometer scale device regime with GHz or higher operating speeds, the physics of electron flow through devices becomes more complicated, and physical effects, which previously could be safely ignored, become significant. Consequently, models of a higher abstraction level are needed. Conversely, faster simulation is typically required, which places a constraint on the model refinement if conventional simulation techniques are applied.

    Like the invention of the transistor triggered research in circuit simulation, the invention of the laser had a major impact on optical technologies. Classical optics turned into photonics. In todays telecommunication technologies, photons have already become the main carrier of information, regardless of the fact that even today most of the applied optical devices are based on conventional optical fibers and low index-contrast waveguides. Recently, a number of pioneering developments - all based on nanotechnologies - opened up the door to completely new working principles, hence to new classes of optoelectronic devices. Among them are nanostructured periodic materials (photonic crystals) and optically active nanostructures like quantum layers and quantum dots. A proper modelling of such structures has to describe simultaneously electrical charge transport, light generation, light propagation and scattering. Moreover, optical active nanostructures have to be described by quantum mechanics.

    In spite of the achievements of electronic/optoelectronic device and circuit simulation obtained so far, new nanotechnologies create new challenging tasks for mathematical modeling and numerical simulation in this field.

    Topics:
    • shape memory alloys in airfoils
    • production of semiconductor crystals
    • methanole fuel cell optimization
    • online production planning metamaterials


    http://www.math.tu-berlin.de/~stykel/Research/ProjectD13/
  • E1

    Microscopic modelling of complex financial assets

    Project heads: -
    Project members: -
    Duration: 06/02-05/10
    Status: completed

    Description

    Mathematics has become highly visible as a key technology in the area of finance and insurance. Increasingly, advanced probabilistic and statistical methods are being applied to the analysis of financial risk in its various forms. Their impact is not only felt on a computational level. To a surprising extent, concepts of stochastic analysis are shaping the discourse of the field, both in academia and in the financial industry. Conversely, finance has become a significant source of new research problems in mathematical modelling, simulation and optimization.

    Such problems arise typically beyond the idealized context of a complete financial market model without frictions, where derivatives admit a perfect hedge and hence can be priced by arbitrage. As one moves on to more realistic models, the Black-Scholes paradigm of a perfect hedge breaks down. Instead, one is confronted with an incomplete financial market model where derivatives carry an intrinsic risk which cannot be hedged away. In an incomplete model, the challenge is to construct hedging strategies which are optimal in terms of some criterion of risk minimization. Considerable progress has been made over the last years in understanding the mathematical structure of such strategies, and Berlin has played a leading role in this development.

    At the same time, demand by the financial industry for advanced mathematical methods of assessing and hedging financial risk has increased dramatically. One major factor is the growing pressure of supervising agencies on banks to improve their internal models for quantifying risk exposure, triggered by the 1995 guidelines of the Basel Committee on Banking Supervision and their ongoing improvements. Banks are now competing not only in the innovation of financial products but also in the development of new methods of risk management. Another important factor is the breakdown of traditional boundaries between the financial and the insurance industry, in particular the growing trend towards financial securitization of insurance risks. This leads to the design of new products which combine very different sources of risk and pose new valuation and hedging problems.

    Topics:
    • measurement and hedging of risks
    • interaction models for asset price fluctuation


    http://www.wias-berlin.de/projects/Matheon-e1/
  • E2

    Securitization: assessment of external risk factors

    Project heads: -
    Project members: -
    Duration: 06/02-05/14
    Status: completed

    Description

    Mathematics has become highly visible as a key technology in the area of finance and insurance. Increasingly, advanced probabilistic and statistical methods are being applied to the analysis of financial risk in its various forms. Their impact is not only felt on a computational level. To a surprising extent, concepts of stochastic analysis are shaping the discourse of the field, both in academia and in the financial industry. Conversely, finance has become a significant source of new research problems in mathematical modelling, simulation and optimization.

    Such problems arise typically beyond the idealized context of a complete financial market model without frictions, where derivatives admit a perfect hedge and hence can be priced by arbitrage. As one moves on to more realistic models, the Black-Scholes paradigm of a perfect hedge breaks down. Instead, one is confronted with an incomplete financial market model where derivatives carry an intrinsic risk which cannot be hedged away. In an incomplete model, the challenge is to construct hedging strategies which are optimal in terms of some criterion of risk minimization. Considerable progress has been made over the last years in understanding the mathematical structure of such strategies, and Berlin has played a leading role in this development.

    At the same time, demand by the financial industry for advanced mathematical methods of assessing and hedging financial risk has increased dramatically. One major factor is the growing pressure of supervising agencies on banks to improve their internal models for quantifying risk exposure, triggered by the 1995 guidelines of the Basel Committee on Banking Supervision and their ongoing improvements. Banks are now competing not only in the innovation of financial products but also in the development of new methods of risk management. Another important factor is the breakdown of traditional boundaries between the financial and the insurance industry, in particular the growing trend towards financial securitization of insurance risks. This leads to the design of new products which combine very different sources of risk and pose new valuation and hedging problems.

    Topics:
    • measurement and hedging of risks
    • interaction models for asset price fluctuation


  • E3

    Probabilistic interaction models for the microstructure of asset price fluctuation

    Project heads: -
    Project members: -
    Duration: 06/02-05/06
    Status: completed

    Description

    Mathematics has become highly visible as a key technology in the area of finance and insurance. Increasingly, advanced probabilistic and statistical methods are being applied to the analysis of financial risk in its various forms. Their impact is not only felt on a computational level. To a surprising extent, concepts of stochastic analysis are shaping the discourse of the field, both in academia and in the financial industry. Conversely, finance has become a significant source of new research problems in mathematical modelling, simulation and optimization.

    Such problems arise typically beyond the idealized context of a complete financial market model without frictions, where derivatives admit a perfect hedge and hence can be priced by arbitrage. As one moves on to more realistic models, the Black-Scholes paradigm of a perfect hedge breaks down. Instead, one is confronted with an incomplete financial market model where derivatives carry an intrinsic risk which cannot be hedged away. In an incomplete model, the challenge is to construct hedging strategies which are optimal in terms of some criterion of risk minimization. Considerable progress has been made over the last years in understanding the mathematical structure of such strategies, and Berlin has played a leading role in this development.

    At the same time, demand by the financial industry for advanced mathematical methods of assessing and hedging financial risk has increased dramatically. One major factor is the growing pressure of supervising agencies on banks to improve their internal models for quantifying risk exposure, triggered by the 1995 guidelines of the Basel Committee on Banking Supervision and their ongoing improvements. Banks are now competing not only in the innovation of financial products but also in the development of new methods of risk management. Another important factor is the breakdown of traditional boundaries between the financial and the insurance industry, in particular the growing trend towards financial securitization of insurance risks. This leads to the design of new products which combine very different sources of risk and pose new valuation and hedging problems.

    Topics:
    • measurement and hedging of risks
    • interaction models for asset price fluctuation


    http://wws.mathematik.hu-berlin.de/~foellmer
  • E4

    Beyond value at risk: Quantifying and hedging the downside risk

    Project heads: -
    Project members: -
    Duration: 06/02-04/08
    Status: completed

    Description

    Mathematics has become highly visible as a key technology in the area of finance and insurance. Increasingly, advanced probabilistic and statistical methods are being applied to the analysis of financial risk in its various forms. Their impact is not only felt on a computational level. To a surprising extent, concepts of stochastic analysis are shaping the discourse of the field, both in academia and in the financial industry. Conversely, finance has become a significant source of new research problems in mathematical modelling, simulation and optimization.

    Such problems arise typically beyond the idealized context of a complete financial market model without frictions, where derivatives admit a perfect hedge and hence can be priced by arbitrage. As one moves on to more realistic models, the Black-Scholes paradigm of a perfect hedge breaks down. Instead, one is confronted with an incomplete financial market model where derivatives carry an intrinsic risk which cannot be hedged away. In an incomplete model, the challenge is to construct hedging strategies which are optimal in terms of some criterion of risk minimization. Considerable progress has been made over the last years in understanding the mathematical structure of such strategies, and Berlin has played a leading role in this development.

    At the same time, demand by the financial industry for advanced mathematical methods of assessing and hedging financial risk has increased dramatically. One major factor is the growing pressure of supervising agencies on banks to improve their internal models for quantifying risk exposure, triggered by the 1995 guidelines of the Basel Committee on Banking Supervision and their ongoing improvements. Banks are now competing not only in the innovation of financial products but also in the development of new methods of risk management. Another important factor is the breakdown of traditional boundaries between the financial and the insurance industry, in particular the growing trend towards financial securitization of insurance risks. This leads to the design of new products which combine very different sources of risk and pose new valuation and hedging problems.

    Topics:
    • measurement and hedging of risks
    • interaction models for asset price fluctuation


    http://page.math.tu-berlin.de/~bank
  • E5

    Statistical and numerical methods in modelling of financial derivatives and valuation of risk

    Project heads: -
    Project members: -
    Duration: 06/02-05/14
    Status: completed

    Description

    Mathematics has become highly visible as a key technology in the area of finance and insurance. Increasingly, advanced probabilistic and statistical methods are being applied to the analysis of financial risk in its various forms. Their impact is not only felt on a computational level. To a surprising extent, concepts of stochastic analysis are shaping the discourse of the field, both in academia and in the financial industry. Conversely, finance has become a significant source of new research problems in mathematical modelling, simulation and optimization.

    Such problems arise typically beyond the idealized context of a complete financial market model without frictions, where derivatives admit a perfect hedge and hence can be priced by arbitrage. As one moves on to more realistic models, the Black-Scholes paradigm of a perfect hedge breaks down. Instead, one is confronted with an incomplete financial market model where derivatives carry an intrinsic risk which cannot be hedged away. In an incomplete model, the challenge is to construct hedging strategies which are optimal in terms of some criterion of risk minimization. Considerable progress has been made over the last years in understanding the mathematical structure of such strategies, and Berlin has played a leading role in this development.

    At the same time, demand by the financial industry for advanced mathematical methods of assessing and hedging financial risk has increased dramatically. One major factor is the growing pressure of supervising agencies on banks to improve their internal models for quantifying risk exposure, triggered by the 1995 guidelines of the Basel Committee on Banking Supervision and their ongoing improvements. Banks are now competing not only in the innovation of financial products but also in the development of new methods of risk management. Another important factor is the breakdown of traditional boundaries between the financial and the insurance industry, in particular the growing trend towards financial securitization of insurance risks. This leads to the design of new products which combine very different sources of risk and pose new valuation and hedging problems.

    Topics:
    • measurement and hedging of risks
    • interaction models for asset price fluctuation


    http://www.wias-berlin.de/research/ats/calibration/E5poster-2010.pdf
  • E6

    Adaptive FE Algorithm for Option Evaluation

    Project heads: -
    Project members: -
    Duration: 02/04-05/05
    Status: completed

    Description

    Mathematics has become highly visible as a key technology in the area of finance and insurance. Increasingly, advanced probabilistic and statistical methods are being applied to the analysis of financial risk in its various forms. Their impact is not only felt on a computational level. To a surprising extent, concepts of stochastic analysis are shaping the discourse of the field, both in academia and in the financial industry. Conversely, finance has become a significant source of new research problems in mathematical modelling, simulation and optimization.

    Such problems arise typically beyond the idealized context of a complete financial market model without frictions, where derivatives admit a perfect hedge and hence can be priced by arbitrage. As one moves on to more realistic models, the Black-Scholes paradigm of a perfect hedge breaks down. Instead, one is confronted with an incomplete financial market model where derivatives carry an intrinsic risk which cannot be hedged away. In an incomplete model, the challenge is to construct hedging strategies which are optimal in terms of some criterion of risk minimization. Considerable progress has been made over the last years in understanding the mathematical structure of such strategies, and Berlin has played a leading role in this development.

    At the same time, demand by the financial industry for advanced mathematical methods of assessing and hedging financial risk has increased dramatically. One major factor is the growing pressure of supervising agencies on banks to improve their internal models for quantifying risk exposure, triggered by the 1995 guidelines of the Basel Committee on Banking Supervision and their ongoing improvements. Banks are now competing not only in the innovation of financial products but also in the development of new methods of risk management. Another important factor is the breakdown of traditional boundaries between the financial and the insurance industry, in particular the growing trend towards financial securitization of insurance risks. This leads to the design of new products which combine very different sources of risk and pose new valuation and hedging problems.

    Topics:
    • measurement and hedging of risks
    • interaction models for asset price fluctuation


    http://www.math.hu-berlin.de/~cc/english/research/dfg_project_e6.html
  • E7

    Adaptive monotone multigrid methods for option pricing

    Project heads: -
    Project members: -
    Duration: 01/05-05/06
    Status: completed

    Description

    Mathematics has become highly visible as a key technology in the area of finance and insurance. Increasingly, advanced probabilistic and statistical methods are being applied to the analysis of financial risk in its various forms. Their impact is not only felt on a computational level. To a surprising extent, concepts of stochastic analysis are shaping the discourse of the field, both in academia and in the financial industry. Conversely, finance has become a significant source of new research problems in mathematical modelling, simulation and optimization.

    Such problems arise typically beyond the idealized context of a complete financial market model without frictions, where derivatives admit a perfect hedge and hence can be priced by arbitrage. As one moves on to more realistic models, the Black-Scholes paradigm of a perfect hedge breaks down. Instead, one is confronted with an incomplete financial market model where derivatives carry an intrinsic risk which cannot be hedged away. In an incomplete model, the challenge is to construct hedging strategies which are optimal in terms of some criterion of risk minimization. Considerable progress has been made over the last years in understanding the mathematical structure of such strategies, and Berlin has played a leading role in this development.

    At the same time, demand by the financial industry for advanced mathematical methods of assessing and hedging financial risk has increased dramatically. One major factor is the growing pressure of supervising agencies on banks to improve their internal models for quantifying risk exposure, triggered by the 1995 guidelines of the Basel Committee on Banking Supervision and their ongoing improvements. Banks are now competing not only in the innovation of financial products but also in the development of new methods of risk management. Another important factor is the breakdown of traditional boundaries between the financial and the insurance industry, in particular the growing trend towards financial securitization of insurance risks. This leads to the design of new products which combine very different sources of risk and pose new valuation and hedging problems.

    Topics:
    • measurement and hedging of risks
    • interaction models for asset price fluctuation


    http://numerik.mi.fu-berlin.de/Matheon-E7/index.php
  • F1

    Discrete surface parametrization

    Project heads: -
    Project members: -
    Duration: 06/02-05/14
    Status: completed

    Description

    Visualization has the task to create insight from given data. Image analysis is to extract information from data and to make it explicit in the form of a geometric model. The two areas have tight relations on both the methodical and the application level. Prominent examples are image-based rendering and visual analysis of 3D image data, e.g. in tomography or confocal microscopy.

    In recent years we have seen a rapid development of fundamentally new techniques for the visualization of complex physical phenomena as well as for imaging applications. At the very heart of these new technologies we encounter fundamentally new data structures and algorithms, all with a quest for a new level of abstraction. Here is where mathematics enters the scene.

    Especially in visualization, it is still a challenge to give the underlying objects a solid mathematical description. Here the research field of mathematical visualization faces the challenge to develop precise abstractions which eventually enables the development of new algorithms and visualization tools. Efforts in this direction can build on broad mathematical foundations, laid among others in the fields of discrete geometry, computational geometry, discrete differential geometry, and combinatorial topology. Results of this development are not only needed in research, where scientifically correct visualization is essential, but also meant to provide a solid basis for applications, for example, in computer graphics as well as in mathematics education projects.

    Even more so, the fields of visualization and image processing are key technologies for very current fields of research, among them many of the natural sciences (physics, chemistry, climate research), the life sciences (medicine, biochemistry, biotechnology, pharmacy), but also for various problems of engineering and production. Due to the multiple applications, but also due to technological reasons such as the availability of new imaging devices and display technology, imaging and visualization have been - and will be - areas of impressive growth.

    Topics:
    • discrete differential geometry
    • geometry processing
    • image processing
    • virtual reality PORTAL


    http://www3.math.tu-berlin.de/geometrie/ddg/
  • F2

    Atlas-based 3d image segmentation

    Project heads: -
    Project members: -
    Duration: 06/02-05/14
    Status: completed

    Description

    Visualization has the task to create insight from given data. Image analysis is to extract information from data and to make it explicit in the form of a geometric model. The two areas have tight relations on both the methodical and the application level. Prominent examples are image-based rendering and visual analysis of 3D image data, e.g. in tomography or confocal microscopy.

    In recent years we have seen a rapid development of fundamentally new techniques for the visualization of complex physical phenomena as well as for imaging applications. At the very heart of these new technologies we encounter fundamentally new data structures and algorithms, all with a quest for a new level of abstraction. Here is where mathematics enters the scene.

    Especially in visualization, it is still a challenge to give the underlying objects a solid mathematical description. Here the research field of mathematical visualization faces the challenge to develop precise abstractions which eventually enables the development of new algorithms and visualization tools. Efforts in this direction can build on broad mathematical foundations, laid among others in the fields of discrete geometry, computational geometry, discrete differential geometry, and combinatorial topology. Results of this development are not only needed in research, where scientifically correct visualization is essential, but also meant to provide a solid basis for applications, for example, in computer graphics as well as in mathematics education projects.

    Even more so, the fields of visualization and image processing are key technologies for very current fields of research, among them many of the natural sciences (physics, chemistry, climate research), the life sciences (medicine, biochemistry, biotechnology, pharmacy), but also for various problems of engineering and production. Due to the multiple applications, but also due to technological reasons such as the availability of new imaging devices and display technology, imaging and visualization have been - and will be - areas of impressive growth.

    Topics:
    • discrete differential geometry
    • geometry processing
    • image processing
    • virtual reality PORTAL


    http://www.zib.de/en/numerik/projects/details/article/Matheon-f2-1.html
  • F3

    Visualization of Algorithms

    Project heads: -
    Project members: -
    Duration: 06/02-12/03
    Status: completed

    Description

    Visualization has the task to create insight from given data. Image analysis is to extract information from data and to make it explicit in the form of a geometric model. The two areas have tight relations on both the methodical and the application level. Prominent examples are image-based rendering and visual analysis of 3D image data, e.g. in tomography or confocal microscopy.

    In recent years we have seen a rapid development of fundamentally new techniques for the visualization of complex physical phenomena as well as for imaging applications. At the very heart of these new technologies we encounter fundamentally new data structures and algorithms, all with a quest for a new level of abstraction. Here is where mathematics enters the scene.

    Especially in visualization, it is still a challenge to give the underlying objects a solid mathematical description. Here the research field of mathematical visualization faces the challenge to develop precise abstractions which eventually enables the development of new algorithms and visualization tools. Efforts in this direction can build on broad mathematical foundations, laid among others in the fields of discrete geometry, computational geometry, discrete differential geometry, and combinatorial topology. Results of this development are not only needed in research, where scientifically correct visualization is essential, but also meant to provide a solid basis for applications, for example, in computer graphics as well as in mathematics education projects.

    Even more so, the fields of visualization and image processing are key technologies for very current fields of research, among them many of the natural sciences (physics, chemistry, climate research), the life sciences (medicine, biochemistry, biotechnology, pharmacy), but also for various problems of engineering and production. Due to the multiple applications, but also due to technological reasons such as the availability of new imaging devices and display technology, imaging and visualization have been - and will be - areas of impressive growth.

    Topics:
    • discrete differential geometry
    • geometry processing
    • image processing
    • virtual reality PORTAL


    http://www3.math.tu-berlin.de/Matheon/projects/F3/tiki-index.php?page=Matheon+F3
  • F4

    Geometric shape optimization

    Project heads: -
    Project members: -
    Duration: 06/02-05/14
    Status: completed

    Description

    Visualization has the task to create insight from given data. Image analysis is to extract information from data and to make it explicit in the form of a geometric model. The two areas have tight relations on both the methodical and the application level. Prominent examples are image-based rendering and visual analysis of 3D image data, e.g. in tomography or confocal microscopy.

    In recent years we have seen a rapid development of fundamentally new techniques for the visualization of complex physical phenomena as well as for imaging applications. At the very heart of these new technologies we encounter fundamentally new data structures and algorithms, all with a quest for a new level of abstraction. Here is where mathematics enters the scene.

    Especially in visualization, it is still a challenge to give the underlying objects a solid mathematical description. Here the research field of mathematical visualization faces the challenge to develop precise abstractions which eventually enables the development of new algorithms and visualization tools. Efforts in this direction can build on broad mathematical foundations, laid among others in the fields of discrete geometry, computational geometry, discrete differential geometry, and combinatorial topology. Results of this development are not only needed in research, where scientifically correct visualization is essential, but also meant to provide a solid basis for applications, for example, in computer graphics as well as in mathematics education projects.

    Even more so, the fields of visualization and image processing are key technologies for very current fields of research, among them many of the natural sciences (physics, chemistry, climate research), the life sciences (medicine, biochemistry, biotechnology, pharmacy), but also for various problems of engineering and production. Due to the multiple applications, but also due to technological reasons such as the availability of new imaging devices and display technology, imaging and visualization have been - and will be - areas of impressive growth.

    Topics:
    • discrete differential geometry
    • geometry processing
    • image processing
    • virtual reality PORTAL


    http://geom.mi.fu-berlin.de/projects/Matheon/f4/index.html
  • F5

    Mathematics in Virtual Reality

    Project heads: -
    Project members: -
    Duration: 01/05-05/10
    Status: completed

    Description

    Visualization has the task to create insight from given data. Image analysis is to extract information from data and to make it explicit in the form of a geometric model. The two areas have tight relations on both the methodical and the application level. Prominent examples are image-based rendering and visual analysis of 3D image data, e.g. in tomography or confocal microscopy.

    In recent years we have seen a rapid development of fundamentally new techniques for the visualization of complex physical phenomena as well as for imaging applications. At the very heart of these new technologies we encounter fundamentally new data structures and algorithms, all with a quest for a new level of abstraction. Here is where mathematics enters the scene.

    Especially in visualization, it is still a challenge to give the underlying objects a solid mathematical description. Here the research field of mathematical visualization faces the challenge to develop precise abstractions which eventually enables the development of new algorithms and visualization tools. Efforts in this direction can build on broad mathematical foundations, laid among others in the fields of discrete geometry, computational geometry, discrete differential geometry, and combinatorial topology. Results of this development are not only needed in research, where scientifically correct visualization is essential, but also meant to provide a solid basis for applications, for example, in computer graphics as well as in mathematics education projects.

    Even more so, the fields of visualization and image processing are key technologies for very current fields of research, among them many of the natural sciences (physics, chemistry, climate research), the life sciences (medicine, biochemistry, biotechnology, pharmacy), but also for various problems of engineering and production. Due to the multiple applications, but also due to technological reasons such as the availability of new imaging devices and display technology, imaging and visualization have been - and will be - areas of impressive growth.

    Topics:
    • discrete differential geometry
    • geometry processing
    • image processing
    • virtual reality PORTAL


    http://www3.math.tu-berlin.de/Matheon/projects/f5/
  • G1

    Combinatorial optimization at work

    Project heads: -
    Project members: -
    Duration: 09/04-05/06
    Status: completed

    Description

    The recent TIMSS studies have displayed and highlighted considerable deficits in the mathematical education in Germany, in particular on the gymnasium level. According to the study, in general, German pupils seem to be able to master calculations in a satisfactory way, but their abilities to solve application oriented problems are below average. Moreover, the mathematics taught at schools is not experienced as something interesting and attractive, so pupils are not well-motivated. This in turn leads to the fact that the mathematical knowledge acquired by the pupils is not sufficient for their orientation in the real-world. In particular, we observe corresponding problems in our mathematical education of students at the university. Such deficits were also stressed in the influential lecture Drawbridge Up by the noted German poet and essayist H. M. Enzensberger.

    There are a number of reasons for the unfavourable situation. Among others, we mention first that the sensitivity for mathematics in the German public is rather low, despite the fact that mathematics is more and more present in everyday life: most of the public many acknowledge that mathematics is difficult and impressive, but they do not view it as something interesting, or as a genuine part of culture. Secondly, the mathematics taught at schools often misses a certain amount of attractivity: very little of what the pupils see or learn is new, and there are typically very few references to any current mathematical developments; it does not become clear that there are new mathematical discoveries made every day, that there is recent and current progress on many different questions. A third reason is a deficit in the practice orientation of the mathematics taught at high schools: pupils do not see that mathematics is relevant and important in the real-world, that there are lots of interesting applications and developments.

    To improve the situation the following measures seem promising. The very experts have to give more emphasis to the popularization of current mathematics. Moreover, the teaching of mathematics, including the corresponding mathematics curricula, at schools and universities has to be made more attractive and problem-solving-oriented. Last but not least, the teacher students education has to obtain a more practice-oriented component.

    The basis to attack and solve the problems that we have described lies in greater educational activity of university mathematicians, and in a much closer cooperation between schools and universities than the present one.

    Projects

    http://www.zib.de/Optimization/Projects/education/Matheon-G1/
  • Z1.1

    Current mathematics at schools

    Project heads: -
    Project members: -
    Duration: 11/02-05/10
    Status: completed

    Description

    The recent TIMSS studies have displayed and highlighted considerable deficits in the mathematical education in Germany, in particular on the gymnasium level. According to the study, in general, German pupils seem to be able to master calculations in a satisfactory way, but their abilities to solve application oriented problems are below average. Moreover, the mathematics taught at schools is not experienced as something interesting and attractive, so pupils are not well-motivated. This in turn leads to the fact that the mathematical knowledge acquired by the pupils is not sufficient for their orientation in the real-world. In particular, we observe corresponding problems in our mathematical education of students at the university. Such deficits were also stressed in the influential lecture Drawbridge Up by the noted German poet and essayist H. M. Enzensberger.

    There are a number of reasons for the unfavourable situation. Among others, we mention first that the sensitivity for mathematics in the German public is rather low, despite the fact that mathematics is more and more present in everyday life: most of the public many acknowledge that mathematics is difficult and impressive, but they do not view it as something interesting, or as a genuine part of culture. Secondly, the mathematics taught at schools often misses a certain amount of attractivity: very little of what the pupils see or learn is new, and there are typically very few references to any current mathematical developments; it does not become clear that there are new mathematical discoveries made every day, that there is recent and current progress on many different questions. A third reason is a deficit in the practice orientation of the mathematics taught at high schools: pupils do not see that mathematics is relevant and important in the real-world, that there are lots of interesting applications and developments.

    To improve the situation the following measures seem promising. The very experts have to give more emphasis to the popularization of current mathematics. Moreover, the teaching of mathematics, including the corresponding mathematics curricula, at schools and universities has to be made more attractive and problem-solving-oriented. Last but not least, the teacher students education has to obtain a more practice-oriented component.

    The basis to attack and solve the problems that we have described lies in greater educational activity of university mathematicians, and in a much closer cooperation between schools and universities than the present one.

    Topics:
    • modern mathematics at school
    • school teachers at universities
    • network of math-science oriented schools
    • public awareness of mathematics
    • media presence


    http://www.mathematik.hu-berlin.de/~kramer/dfgfz/g2.html
  • Z1.2

    Teachers at universities

    Project heads: -
    Project members: -
    Duration: 09/02-05/10
    Status: completed

    Description

    The recent TIMSS studies have displayed and highlighted considerable deficits in the mathematical education in Germany, in particular on the gymnasium level. According to the study, in general, German pupils seem to be able to master calculations in a satisfactory way, but their abilities to solve application oriented problems are below average. Moreover, the mathematics taught at schools is not experienced as something interesting and attractive, so pupils are not well-motivated. This in turn leads to the fact that the mathematical knowledge acquired by the pupils is not sufficient for their orientation in the real-world. In particular, we observe corresponding problems in our mathematical education of students at the university. Such deficits were also stressed in the influential lecture Drawbridge Up by the noted German poet and essayist H. M. Enzensberger.

    There are a number of reasons for the unfavourable situation. Among others, we mention first that the sensitivity for mathematics in the German public is rather low, despite the fact that mathematics is more and more present in everyday life: most of the public many acknowledge that mathematics is difficult and impressive, but they do not view it as something interesting, or as a genuine part of culture. Secondly, the mathematics taught at schools often misses a certain amount of attractivity: very little of what the pupils see or learn is new, and there are typically very few references to any current mathematical developments; it does not become clear that there are new mathematical discoveries made every day, that there is recent and current progress on many different questions. A third reason is a deficit in the practice orientation of the mathematics taught at high schools: pupils do not see that mathematics is relevant and important in the real-world, that there are lots of interesting applications and developments.

    To improve the situation the following measures seem promising. The very experts have to give more emphasis to the popularization of current mathematics. Moreover, the teaching of mathematics, including the corresponding mathematics curricula, at schools and universities has to be made more attractive and problem-solving-oriented. Last but not least, the teacher students education has to obtain a more practice-oriented component.

    The basis to attack and solve the problems that we have described lies in greater educational activity of university mathematicians, and in a much closer cooperation between schools and universities than the present one.

    Topics:
    • modern mathematics at school
    • school teachers at universities
    • network of math-science oriented schools
    • public awareness of mathematics
    • media presence


    http://didaktik.mathematik.hu-berlin.de/index.php?article_id=49&clang=0
  • G4

    Virtual math-science lab

    Project heads: -
    Project members: -
    Duration: 06/02-05/06
    Status: completed

    Description

    The recent TIMSS studies have displayed and highlighted considerable deficits in the mathematical education in Germany, in particular on the gymnasium level. According to the study, in general, German pupils seem to be able to master calculations in a satisfactory way, but their abilities to solve application oriented problems are below average. Moreover, the mathematics taught at schools is not experienced as something interesting and attractive, so pupils are not well-motivated. This in turn leads to the fact that the mathematical knowledge acquired by the pupils is not sufficient for their orientation in the real-world. In particular, we observe corresponding problems in our mathematical education of students at the university. Such deficits were also stressed in the influential lecture Drawbridge Up by the noted German poet and essayist H. M. Enzensberger.

    There are a number of reasons for the unfavourable situation. Among others, we mention first that the sensitivity for mathematics in the German public is rather low, despite the fact that mathematics is more and more present in everyday life: most of the public many acknowledge that mathematics is difficult and impressive, but they do not view it as something interesting, or as a genuine part of culture. Secondly, the mathematics taught at schools often misses a certain amount of attractivity: very little of what the pupils see or learn is new, and there are typically very few references to any current mathematical developments; it does not become clear that there are new mathematical discoveries made every day, that there is recent and current progress on many different questions. A third reason is a deficit in the practice orientation of the mathematics taught at high schools: pupils do not see that mathematics is relevant and important in the real-world, that there are lots of interesting applications and developments.

    To improve the situation the following measures seem promising. The very experts have to give more emphasis to the popularization of current mathematics. Moreover, the teaching of mathematics, including the corresponding mathematics curricula, at schools and universities has to be made more attractive and problem-solving-oriented. Last but not least, the teacher students education has to obtain a more practice-oriented component.

    The basis to attack and solve the problems that we have described lies in greater educational activity of university mathematicians, and in a much closer cooperation between schools and universities than the present one.

    Projects

    http://www.math.tu-berlin.de/~thor/videoeasel/
  • G5

    (*) Discrete Mathematics for Highschool Education

    Project heads: -
    Project members: -
    Duration: 04/04-04/06
    Status: completed

    Description

    The recent TIMSS studies have displayed and highlighted considerable deficits in the mathematical education in Germany, in particular on the gymnasium level. According to the study, in general, German pupils seem to be able to master calculations in a satisfactory way, but their abilities to solve application oriented problems are below average. Moreover, the mathematics taught at schools is not experienced as something interesting and attractive, so pupils are not well-motivated. This in turn leads to the fact that the mathematical knowledge acquired by the pupils is not sufficient for their orientation in the real-world. In particular, we observe corresponding problems in our mathematical education of students at the university. Such deficits were also stressed in the influential lecture Drawbridge Up by the noted German poet and essayist H. M. Enzensberger.

    There are a number of reasons for the unfavourable situation. Among others, we mention first that the sensitivity for mathematics in the German public is rather low, despite the fact that mathematics is more and more present in everyday life: most of the public many acknowledge that mathematics is difficult and impressive, but they do not view it as something interesting, or as a genuine part of culture. Secondly, the mathematics taught at schools often misses a certain amount of attractivity: very little of what the pupils see or learn is new, and there are typically very few references to any current mathematical developments; it does not become clear that there are new mathematical discoveries made every day, that there is recent and current progress on many different questions. A third reason is a deficit in the practice orientation of the mathematics taught at high schools: pupils do not see that mathematics is relevant and important in the real-world, that there are lots of interesting applications and developments.

    To improve the situation the following measures seem promising. The very experts have to give more emphasis to the popularization of current mathematics. Moreover, the teaching of mathematics, including the corresponding mathematics curricula, at schools and universities has to be made more attractive and problem-solving-oriented. Last but not least, the teacher students education has to obtain a more practice-oriented component.

    The basis to attack and solve the problems that we have described lies in greater educational activity of university mathematicians, and in a much closer cooperation between schools and universities than the present one.

    Projects

    http://www.math.tu-berlin.de/~westphal/projekt/
  • Z1.3

    Visualization of Algorithms

    Project heads: -
    Project members: -
    Duration: 06/04-05/08
    Status: completed

    Description

    The recent TIMSS studies have displayed and highlighted considerable deficits in the mathematical education in Germany, in particular on the gymnasium level. According to the study, in general, German pupils seem to be able to master calculations in a satisfactory way, but their abilities to solve application oriented problems are below average. Moreover, the mathematics taught at schools is not experienced as something interesting and attractive, so pupils are not well-motivated. This in turn leads to the fact that the mathematical knowledge acquired by the pupils is not sufficient for their orientation in the real-world. In particular, we observe corresponding problems in our mathematical education of students at the university. Such deficits were also stressed in the influential lecture Drawbridge Up by the noted German poet and essayist H. M. Enzensberger.

    There are a number of reasons for the unfavourable situation. Among others, we mention first that the sensitivity for mathematics in the German public is rather low, despite the fact that mathematics is more and more present in everyday life: most of the public many acknowledge that mathematics is difficult and impressive, but they do not view it as something interesting, or as a genuine part of culture. Secondly, the mathematics taught at schools often misses a certain amount of attractivity: very little of what the pupils see or learn is new, and there are typically very few references to any current mathematical developments; it does not become clear that there are new mathematical discoveries made every day, that there is recent and current progress on many different questions. A third reason is a deficit in the practice orientation of the mathematics taught at high schools: pupils do not see that mathematics is relevant and important in the real-world, that there are lots of interesting applications and developments.

    To improve the situation the following measures seem promising. The very experts have to give more emphasis to the popularization of current mathematics. Moreover, the teaching of mathematics, including the corresponding mathematics curricula, at schools and universities has to be made more attractive and problem-solving-oriented. Last but not least, the teacher students education has to obtain a more practice-oriented component.

    The basis to attack and solve the problems that we have described lies in greater educational activity of university mathematicians, and in a much closer cooperation between schools and universities than the present one.

    Topics:
    • modern mathematics at school
    • school teachers at universities
    • network of math-science oriented schools
    • public awareness of mathematics
    • media presence


    http://cermat.org/visage/
  • C16

    Simulation of phase field models and geometric evolution problems

    Project heads: -
    Project members: -
    Duration: 08/05-12/08
    Status: completed

    Description

    Production is one of the most important parts of the economy and at the very heart of the creation of value. Due to the central importance of production, big efforts have been made to improve production processes ever since the beginning of the industrial revolution. Nowadays, many production processes are highly automated. Computer programs based on numerical algorithms monitor the processes, improve efficiency and robustness, and guarantee high quality products. Consequently, mathematics is playing a steadily increasing role in this field. The possibilities of applying mathematical methods in production are wide-ranging. The Application Area cannot cover their full scale. For that reason, the projects concentrate on the development of new mathematical methods for special topics in manufacturing and production planning, two central aspects of production, in which the participating groups have longstanding expertise in mathematical modeling, simulation and optimization.

    In the field of manufacturing, we focus on innovative technologies having a big impact on technological progress: growth and processing of semiconductor bulk single crystals, phase transitions in modern steels and solder alloys, modeling of active and passive behavior of functional materials like shape-memory materials, growth of thin films. In the projects devoted to production planning, the main aim is the effective control of the whole production flow. Among the subjects to be studied, there is also electricity portfolio management.

    Topics:
    • phase transitions in steels and solder alloys
    • production of semiconductor crystals
    • modeling of active and passive behavior of functional materials
    • online production planning
    • growth of thin films


    http://bartels.ins.uni-bonn.de/research/projects/c16/index.html?noframe
  • D14

    Nonlocal and nonlinear effects in fiber optics

    Project heads: -
    Project members: -
    Duration: 05/05-05/14
    Status: completed

    Description

    The technical progress of the last decades has been enormously stimulated by two technological revolutions: the invention of the transistor in 1947 (Nobel prize 1956) and the invention of the laser in 1958 (Nobel prize 1964). The impact of both inventions on modern life is an evident fact.

    Already in 1950, a system of partial differential equations was published that models adequately the essential charge transport processes in semiconductor devices. On the basis of this drift-diffusion model the first bipolar transistor was successfully simulated in 1964. Just in that time the first integrated circuits containing a few transistors became commercially available. Since then, the electronics industry has achieved a phenomenal growth, mainly due to the rapid advances in integration technologies, large-scale systems design and numerical simulation. The number of applications of integrated circuits in high-performance computing, telecommunications, and consumer electronics has been rising steadily, and at a very fast pace. As microelectronic research moves into the nanometer scale device regime with GHz or higher operating speeds, the physics of electron flow through devices becomes more complicated, and physical effects, which previously could be safely ignored, become significant. Consequently, models of a higher abstraction level are needed. Conversely, faster simulation is typically required, which places a constraint on the model refinement if conventional simulation techniques are applied.

    Like the invention of the transistor triggered research in circuit simulation, the invention of the laser had a major impact on optical technologies. Classical optics turned into photonics. In todays telecommunication technologies, photons have already become the main carrier of information, regardless of the fact that even today most of the applied optical devices are based on conventional optical fibers and low index-contrast waveguides. Recently, a number of pioneering developments - all based on nanotechnologies - opened up the door to completely new working principles, hence to new classes of optoelectronic devices. Among them are nanostructured periodic materials (photonic crystals) and optically active nanostructures like quantum layers and quantum dots. A proper modelling of such structures has to describe simultaneously electrical charge transport, light generation, light propagation and scattering. Moreover, optical active nanostructures have to be described by quantum mechanics.

    In spite of the achievements of electronic/optoelectronic device and circuit simulation obtained so far, new nanotechnologies create new challenging tasks for mathematical modeling and numerical simulation in this field.

    Topics:
    • shape memory alloys in airfoils
    • production of semiconductor crystals
    • methanole fuel cell optimization
    • online production planning metamaterials


    http://www.wias-berlin.de/projects/Matheon-d14/project_d14.jsp
  • G8

    Computer Oriented Mathematics

    Project heads: -
    Project members: -
    Duration: 10/04-12/05
    Status: completed

    Description

    The recent TIMSS studies have displayed and highlighted considerable deficits in the mathematical education in Germany, in particular on the gymnasium level. According to the study, in general, German pupils seem to be able to master calculations in a satisfactory way, but their abilities to solve application oriented problems are below average. Moreover, the mathematics taught at schools is not experienced as something interesting and attractive, so pupils are not well-motivated. This in turn leads to the fact that the mathematical knowledge acquired by the pupils is not sufficient for their orientation in the real-world. In particular, we observe corresponding problems in our mathematical education of students at the university. Such deficits were also stressed in the influential lecture Drawbridge Up by the noted German poet and essayist H. M. Enzensberger.

    There are a number of reasons for the unfavourable situation. Among others, we mention first that the sensitivity for mathematics in the German public is rather low, despite the fact that mathematics is more and more present in everyday life: most of the public many acknowledge that mathematics is difficult and impressive, but they do not view it as something interesting, or as a genuine part of culture. Secondly, the mathematics taught at schools often misses a certain amount of attractivity: very little of what the pupils see or learn is new, and there are typically very few references to any current mathematical developments; it does not become clear that there are new mathematical discoveries made every day, that there is recent and current progress on many different questions. A third reason is a deficit in the practice orientation of the mathematics taught at high schools: pupils do not see that mathematics is relevant and important in the real-world, that there are lots of interesting applications and developments.

    To improve the situation the following measures seem promising. The very experts have to give more emphasis to the popularization of current mathematics. Moreover, the teaching of mathematics, including the corresponding mathematics curricula, at schools and universities has to be made more attractive and problem-solving-oriented. Last but not least, the teacher students education has to obtain a more practice-oriented component.

    The basis to attack and solve the problems that we have described lies in greater educational activity of university mathematicians, and in a much closer cooperation between schools and universities than the present one.

    Projects

    http://numerik.mi.fu-berlin.de/Matheon-G8/index.php
  • A10

    Automatic model reduction for complex dynamical systems

    Project heads: -
    Project members: -
    Duration: 06/05-12/07
    Status: completed

    Description

    "Life sciences" describe a wide research area with enormous technological and social impact. However, there exist specific areas where mathematics has just begun to take on an active role.

    In medicine, the already traditional role of mathematics in medical imaging (e.g., computer tomography) has been successfully extended. Mathematical progress has proved to directly influence medical progress towards the design of patient-specific therapies - e.g., in the cancer therapy hyperthermia. As another example, computer-assisted surgery planning allows the comparison of various operation options before the actual operation on the basis of a simulation of more and more realistic models describing soft tissue, bone, or typical human gaits such as stair climbing. Further mathematization of the field is expected to open entirely new perspectives for the optimal design of joint prostheses adapted to individual anatomy.

    In biotechnology, the present situation is clearly dominated by the generation of huge datasets about biomolecular, genetic, metabolic or other bio-processes. Algorithms from discrete mathematics or computer science (e.g., in multiple alignment) already play a publicly visible role in the decoding of the human and other genomes. In contrast to that, the mathematical treatment of the dynamics of bio-processes is still rather limited - even though this aspect seems to be crucial for the detailed understanding of virus diseases or the design of narrow band drugs. Therefore, beyond the well-established core areas of bioinformatics, numerical biocomputing has recently become more and more accepted as one of the keys to data-based reliable prediction, control and design of real-life bio-processes: As it turns out, a significant increase in our ability in a reliable quantitative simulation of the dynamics of large biomolecules is essential for a detailed understanding of, e.g., the enzymatic mechanisms of prion diseases (like the mad cow disease or its human counterpart, the Creutzfeldt-Jacob syndrome).

    Topics:
    • computer-assisted surgery
    • patient-specific therapy planning
    • protein data base analysis
    • protein conformation dynamics
    • systems biology
    • pharmacokinetics


    http://www.math.fu-berlin.de/groups/biocomputing/projects/projekt_A10/index.html
  • A9

    Simulation and control of positive descriptor systems

    Project heads: -
    Project members: -
    Duration: 03/05-05/10
    Status: completed

    Description

    "Life sciences" describe a wide research area with enormous technological and social impact. However, there exist specific areas where mathematics has just begun to take on an active role.

    In medicine, the already traditional role of mathematics in medical imaging (e.g., computer tomography) has been successfully extended. Mathematical progress has proved to directly influence medical progress towards the design of patient-specific therapies - e.g., in the cancer therapy hyperthermia. As another example, computer-assisted surgery planning allows the comparison of various operation options before the actual operation on the basis of a simulation of more and more realistic models describing soft tissue, bone, or typical human gaits such as stair climbing. Further mathematization of the field is expected to open entirely new perspectives for the optimal design of joint prostheses adapted to individual anatomy.

    In biotechnology, the present situation is clearly dominated by the generation of huge datasets about biomolecular, genetic, metabolic or other bio-processes. Algorithms from discrete mathematics or computer science (e.g., in multiple alignment) already play a publicly visible role in the decoding of the human and other genomes. In contrast to that, the mathematical treatment of the dynamics of bio-processes is still rather limited - even though this aspect seems to be crucial for the detailed understanding of virus diseases or the design of narrow band drugs. Therefore, beyond the well-established core areas of bioinformatics, numerical biocomputing has recently become more and more accepted as one of the keys to data-based reliable prediction, control and design of real-life bio-processes: As it turns out, a significant increase in our ability in a reliable quantitative simulation of the dynamics of large biomolecules is essential for a detailed understanding of, e.g., the enzymatic mechanisms of prion diseases (like the mad cow disease or its human counterpart, the Creutzfeldt-Jacob syndrome).

    Topics:
    • computer-assisted surgery
    • patient-specific therapy planning
    • protein data base analysis
    • protein conformation dynamics
    • systems biology
    • pharmacokinetics


    http://www3.math.tu-berlin.de//Matheon/projects/A9
  • C17

    Adaptive multigrid methods for local and nonlocal phase-field models of solder alloys

    Project heads: -
    Project members: -
    Duration: 12/05-05/14
    Status: completed

    Description

    Production is one of the most important parts of the economy and at the very heart of the creation of value. Due to the central importance of production, big efforts have been made to improve production processes ever since the beginning of the industrial revolution. Nowadays, many production processes are highly automated. Computer programs based on numerical algorithms monitor the processes, improve efficiency and robustness, and guarantee high quality products. Consequently, mathematics is playing a steadily increasing role in this field. The possibilities of applying mathematical methods in production are wide-ranging. The Application Area cannot cover their full scale. For that reason, the projects concentrate on the development of new mathematical methods for special topics in manufacturing and production planning, two central aspects of production, in which the participating groups have longstanding expertise in mathematical modeling, simulation and optimization.

    In the field of manufacturing, we focus on innovative technologies having a big impact on technological progress: growth and processing of semiconductor bulk single crystals, phase transitions in modern steels and solder alloys, modeling of active and passive behavior of functional materials like shape-memory materials, growth of thin films. In the projects devoted to production planning, the main aim is the effective control of the whole production flow. Among the subjects to be studied, there is also electricity portfolio management.

    Topics:
    • phase transitions in steels and solder alloys
    • production of semiconductor crystals
    • modeling of active and passive behavior of functional materials
    • online production planning
    • growth of thin films


    http://numerik.mi.fu-berlin.de/Matheon-C17/
  • A8

    Constraint-based modeling in systems biology

    Project heads: -
    Project members: -
    Duration: 04/05-05/10
    Status: completed

    Description

    "Life sciences" describe a wide research area with enormous technological and social impact. However, there exist specific areas where mathematics has just begun to take on an active role.

    In medicine, the already traditional role of mathematics in medical imaging (e.g., computer tomography) has been successfully extended. Mathematical progress has proved to directly influence medical progress towards the design of patient-specific therapies - e.g., in the cancer therapy hyperthermia. As another example, computer-assisted surgery planning allows the comparison of various operation options before the actual operation on the basis of a simulation of more and more realistic models describing soft tissue, bone, or typical human gaits such as stair climbing. Further mathematization of the field is expected to open entirely new perspectives for the optimal design of joint prostheses adapted to individual anatomy.

    In biotechnology, the present situation is clearly dominated by the generation of huge datasets about biomolecular, genetic, metabolic or other bio-processes. Algorithms from discrete mathematics or computer science (e.g., in multiple alignment) already play a publicly visible role in the decoding of the human and other genomes. In contrast to that, the mathematical treatment of the dynamics of bio-processes is still rather limited - even though this aspect seems to be crucial for the detailed understanding of virus diseases or the design of narrow band drugs. Therefore, beyond the well-established core areas of bioinformatics, numerical biocomputing has recently become more and more accepted as one of the keys to data-based reliable prediction, control and design of real-life bio-processes: As it turns out, a significant increase in our ability in a reliable quantitative simulation of the dynamics of large biomolecules is essential for a detailed understanding of, e.g., the enzymatic mechanisms of prion diseases (like the mad cow disease or its human counterpart, the Creutzfeldt-Jacob syndrome).

    Topics:
    • computer-assisted surgery
    • patient-specific therapy planning
    • protein data base analysis
    • protein conformation dynamics
    • systems biology
    • pharmacokinetics


    http://www.math.fu-berlin.de/en/groups/mathlife/projects/A8.html
  • D16

    Adapted linear algebra for TR1 updates

    Project heads: -
    Project members: -
    Duration: 06/05-05/06
    Status: completed

    Description

    The technical progress of the last decades has been enormously stimulated by two technological revolutions: the invention of the transistor in 1947 (Nobel prize 1956) and the invention of the laser in 1958 (Nobel prize 1964). The impact of both inventions on modern life is an evident fact.

    Already in 1950, a system of partial differential equations was published that models adequately the essential charge transport processes in semiconductor devices. On the basis of this drift-diffusion model the first bipolar transistor was successfully simulated in 1964. Just in that time the first integrated circuits containing a few transistors became commercially available. Since then, the electronics industry has achieved a phenomenal growth, mainly due to the rapid advances in integration technologies, large-scale systems design and numerical simulation. The number of applications of integrated circuits in high-performance computing, telecommunications, and consumer electronics has been rising steadily, and at a very fast pace. As microelectronic research moves into the nanometer scale device regime with GHz or higher operating speeds, the physics of electron flow through devices becomes more complicated, and physical effects, which previously could be safely ignored, become significant. Consequently, models of a higher abstraction level are needed. Conversely, faster simulation is typically required, which places a constraint on the model refinement if conventional simulation techniques are applied.

    Like the invention of the transistor triggered research in circuit simulation, the invention of the laser had a major impact on optical technologies. Classical optics turned into photonics. In todays telecommunication technologies, photons have already become the main carrier of information, regardless of the fact that even today most of the applied optical devices are based on conventional optical fibers and low index-contrast waveguides. Recently, a number of pioneering developments - all based on nanotechnologies - opened up the door to completely new working principles, hence to new classes of optoelectronic devices. Among them are nanostructured periodic materials (photonic crystals) and optically active nanostructures like quantum layers and quantum dots. A proper modelling of such structures has to describe simultaneously electrical charge transport, light generation, light propagation and scattering. Moreover, optical active nanostructures have to be described by quantum mechanics.

    In spite of the achievements of electronic/optoelectronic device and circuit simulation obtained so far, new nanotechnologies create new challenging tasks for mathematical modeling and numerical simulation in this field.

    Topics:
    • shape memory alloys in airfoils
    • production of semiconductor crystals
    • methanole fuel cell optimization
    • online production planning metamaterials


    http://www.math.tu-berlin.de/~stange/d16.html
  • Z1.4

    Innovations in Mathematics Education for the Engineering science

    Project heads: -
    Project members: -
    Duration: 06/06-05/10
    Status: completed

    Description

    The recent TIMSS studies have displayed and highlighted considerable deficits in the mathematical education in Germany, in particular on the gymnasium level. According to the study, in general, German pupils seem to be able to master calculations in a satisfactory way, but their abilities to solve application oriented problems are below average. Moreover, the mathematics taught at schools is not experienced as something interesting and attractive, so pupils are not well-motivated. This in turn leads to the fact that the mathematical knowledge acquired by the pupils is not sufficient for their orientation in the real-world. In particular, we observe corresponding problems in our mathematical education of students at the university. Such deficits were also stressed in the influential lecture Drawbridge Up by the noted German poet and essayist H. M. Enzensberger.

    There are a number of reasons for the unfavourable situation. Among others, we mention first that the sensitivity for mathematics in the German public is rather low, despite the fact that mathematics is more and more present in everyday life: most of the public many acknowledge that mathematics is difficult and impressive, but they do not view it as something interesting, or as a genuine part of culture. Secondly, the mathematics taught at schools often misses a certain amount of attractivity: very little of what the pupils see or learn is new, and there are typically very few references to any current mathematical developments; it does not become clear that there are new mathematical discoveries made every day, that there is recent and current progress on many different questions. A third reason is a deficit in the practice orientation of the mathematics taught at high schools: pupils do not see that mathematics is relevant and important in the real-world, that there are lots of interesting applications and developments.

    To improve the situation the following measures seem promising. The very experts have to give more emphasis to the popularization of current mathematics. Moreover, the teaching of mathematics, including the corresponding mathematics curricula, at schools and universities has to be made more attractive and problem-solving-oriented. Last but not least, the teacher students education has to obtain a more practice-oriented component.

    The basis to attack and solve the problems that we have described lies in greater educational activity of university mathematicians, and in a much closer cooperation between schools and universities than the present one.

    Topics:
    • modern mathematics at school
    • school teachers at universities
    • network of math-science oriented schools
    • public awareness of mathematics
    • media presence


    http://www.math.tu-berlin.de/MatheonZ1.4/
  • F6

    Multilevel Methods on Manifold Meshes

    Project heads: -
    Project members: -
    Duration: 05/05-05/14
    Status: completed

    Description

    Visualization has the task to create insight from given data. Image analysis is to extract information from data and to make it explicit in the form of a geometric model. The two areas have tight relations on both the methodical and the application level. Prominent examples are image-based rendering and visual analysis of 3D image data, e.g. in tomography or confocal microscopy.

    In recent years we have seen a rapid development of fundamentally new techniques for the visualization of complex physical phenomena as well as for imaging applications. At the very heart of these new technologies we encounter fundamentally new data structures and algorithms, all with a quest for a new level of abstraction. Here is where mathematics enters the scene.

    Especially in visualization, it is still a challenge to give the underlying objects a solid mathematical description. Here the research field of mathematical visualization faces the challenge to develop precise abstractions which eventually enables the development of new algorithms and visualization tools. Efforts in this direction can build on broad mathematical foundations, laid among others in the fields of discrete geometry, computational geometry, discrete differential geometry, and combinatorial topology. Results of this development are not only needed in research, where scientifically correct visualization is essential, but also meant to provide a solid basis for applications, for example, in computer graphics as well as in mathematics education projects.

    Even more so, the fields of visualization and image processing are key technologies for very current fields of research, among them many of the natural sciences (physics, chemistry, climate research), the life sciences (medicine, biochemistry, biotechnology, pharmacy), but also for various problems of engineering and production. Due to the multiple applications, but also due to technological reasons such as the availability of new imaging devices and display technology, imaging and visualization have been - and will be - areas of impressive growth.

    Topics:
    • discrete differential geometry
    • geometry processing
    • image processing
    • virtual reality PORTAL


    http://geom.mi.fu-berlin.de/projects/Matheon/f6/index.html
  • C18

    Analysis and numerics of multidimensional models for elastic phase transformations in shape-memory alloys

    Project heads: -
    Project members: -
    Duration: 06/06-05/14
    Status: completed

    Description

    Production is one of the most important parts of the economy and at the very heart of the creation of value. Due to the central importance of production, big efforts have been made to improve production processes ever since the beginning of the industrial revolution. Nowadays, many production processes are highly automated. Computer programs based on numerical algorithms monitor the processes, improve efficiency and robustness, and guarantee high quality products. Consequently, mathematics is playing a steadily increasing role in this field. The possibilities of applying mathematical methods in production are wide-ranging. The Application Area cannot cover their full scale. For that reason, the projects concentrate on the development of new mathematical methods for special topics in manufacturing and production planning, two central aspects of production, in which the participating groups have longstanding expertise in mathematical modeling, simulation and optimization.

    In the field of manufacturing, we focus on innovative technologies having a big impact on technological progress: growth and processing of semiconductor bulk single crystals, phase transitions in modern steels and solder alloys, modeling of active and passive behavior of functional materials like shape-memory materials, growth of thin films. In the projects devoted to production planning, the main aim is the effective control of the whole production flow. Among the subjects to be studied, there is also electricity portfolio management.

    Topics:
    • phase transitions in steels and solder alloys
    • production of semiconductor crystals
    • modeling of active and passive behavior of functional materials
    • online production planning
    • growth of thin films


    http://www.wias-berlin.de/projects/Matheon-c18/index.jsp
  • B13

    Optimization under uncertainty in logistics and scheduling

    Project heads: -
    Project members: -
    Duration: 06/06 - 05/10
    Status: completed

    Description

    Networks, such as telephone networks, the internet, airline, railway, and bus networks are omnipresent and play a fundamental role for communication and mobility in our society. We almost take their permanent availability, reliability, and quality at low cost for granted. However, traffic jams, ill-designed train schedules, canceled flights, break-downs of telephone and computing networks, and slow internet access are reminders that networks are not automatically good networks.

    In fact, designing and operating communication and traffic networks are extremely complex tasks that lead directly to mathematical problems. A good example is the design of telecommunication networks. They were implemented with simple low-cost tree topologies until 15 years ago. Then, in 1988, a telco hub broke down in Chicago. This brought O Hare airport to a stand-still and caused an estimated business loss of billions of US dollars. Disasters of this kind made it clear that more sophisticated designs were needed. Nowadays, telecommunication companies use mathematically designed networks with built-in failure safety and rerouting capacities. Similar developments are expected in road traffic. We are now facing the installation of the first generation of load measuring, signalling, pricing, and route finding devices. These will soon integrate into a network-wide telematic system based on mathematical methods of traffic prediction, simulation, and control.

    Network design and operation tasks of this type are traditionally handled under the responsibility of various engineering disciplines (electrical engineering, traffic management and logistics, industrial engineering). While these disciplines can contribute to the improvement of the engineering components of such networks, todays demand on global optimization of the entire system poses problems where qualitative progress has to come from a better theoretical understanding of the structural aspects of the networks.

    This is where mathematics must come into play. The appearance of the word "network" in all the systems described above is not accidental, but hints at a common feature that has deep mathematical roots: networks are fundamental structures of graph theory and combinatorial optimization. Their study has become a prosperous subject in recent years, with impressive successes in many applications. The groups in Berlin are among the driving forces in this development.

    Nowadays, mathematical optimization techniques are used to locate switches and hubs in a phone system, to schedule buses and bus drivers in metropolitan transportation systems, etc. These tasks are individual steps in a hierarchical and sequential network planning process. In public transport, for example, this sequential process encompasses line planning, finding a periodic time table, assigning buses to lines, and creating individual bus driver schedules.

    Topics:
    • planning of optical, multilayer, and UMTS telecommunication networks
    • line planning, periodic timetabling, and revenue management in public transport networks
    • optimization in logistics, scheduling and material flows
    • optimization under uncertainty
    • symmetries in integer programming
    • game theoretic methods in network design


    http://www3.math.tu-berlin.de/Matheon/projects/B13/
  • B12

    Symmetries in integer programming

    Project heads: -
    Project members: -
    Duration: 06/06-04/09
    Status: completed

    Description

    Networks, such as telephone networks, the internet, airline, railway, and bus networks are omnipresent and play a fundamental role for communication and mobility in our society. We almost take their permanent availability, reliability, and quality at low cost for granted. However, traffic jams, ill-designed train schedules, canceled flights, break-downs of telephone and computing networks, and slow internet access are reminders that networks are not automatically good networks.

    In fact, designing and operating communication and traffic networks are extremely complex tasks that lead directly to mathematical problems. A good example is the design of telecommunication networks. They were implemented with simple low-cost tree topologies until 15 years ago. Then, in 1988, a telco hub broke down in Chicago. This brought O Hare airport to a stand-still and caused an estimated business loss of billions of US dollars. Disasters of this kind made it clear that more sophisticated designs were needed. Nowadays, telecommunication companies use mathematically designed networks with built-in failure safety and rerouting capacities. Similar developments are expected in road traffic. We are now facing the installation of the first generation of load measuring, signalling, pricing, and route finding devices. These will soon integrate into a network-wide telematic system based on mathematical methods of traffic prediction, simulation, and control.

    Network design and operation tasks of this type are traditionally handled under the responsibility of various engineering disciplines (electrical engineering, traffic management and logistics, industrial engineering). While these disciplines can contribute to the improvement of the engineering components of such networks, todays demand on global optimization of the entire system poses problems where qualitative progress has to come from a better theoretical understanding of the structural aspects of the networks.

    This is where mathematics must come into play. The appearance of the word "network" in all the systems described above is not accidental, but hints at a common feature that has deep mathematical roots: networks are fundamental structures of graph theory and combinatorial optimization. Their study has become a prosperous subject in recent years, with impressive successes in many applications. The groups in Berlin are among the driving forces in this development.

    Nowadays, mathematical optimization techniques are used to locate switches and hubs in a phone system, to schedule buses and bus drivers in metropolitan transportation systems, etc. These tasks are individual steps in a hierarchical and sequential network planning process. In public transport, for example, this sequential process encompasses line planning, finding a periodic time table, assigning buses to lines, and creating individual bus driver schedules.

    Topics:
    • planning of optical, multilayer, and UMTS telecommunication networks
    • line planning, periodic timetabling, and revenue management in public transport networks
    • optimization in logistics, scheduling and material flows
    • optimization under uncertainty
    • symmetries in integer programming
    • game theoretic methods in network design


    http://www.zib.de/Optimization/Projects/MIP/Matheon-B12/index.en.html
  • D17

    Chip design verification with constraint integer programming

    Project heads: -
    Project members: -
    Duration: 06/06-04/09
    Status: completed

    Description

    The technical progress of the last decades has been enormously stimulated by two technological revolutions: the invention of the transistor in 1947 (Nobel prize 1956) and the invention of the laser in 1958 (Nobel prize 1964). The impact of both inventions on modern life is an evident fact.

    Already in 1950, a system of partial differential equations was published that models adequately the essential charge transport processes in semiconductor devices. On the basis of this drift-diffusion model the first bipolar transistor was successfully simulated in 1964. Just in that time the first integrated circuits containing a few transistors became commercially available. Since then, the electronics industry has achieved a phenomenal growth, mainly due to the rapid advances in integration technologies, large-scale systems design and numerical simulation. The number of applications of integrated circuits in high-performance computing, telecommunications, and consumer electronics has been rising steadily, and at a very fast pace. As microelectronic research moves into the nanometer scale device regime with GHz or higher operating speeds, the physics of electron flow through devices becomes more complicated, and physical effects, which previously could be safely ignored, become significant. Consequently, models of a higher abstraction level are needed. Conversely, faster simulation is typically required, which places a constraint on the model refinement if conventional simulation techniques are applied.

    Like the invention of the transistor triggered research in circuit simulation, the invention of the laser had a major impact on optical technologies. Classical optics turned into photonics. In todays telecommunication technologies, photons have already become the main carrier of information, regardless of the fact that even today most of the applied optical devices are based on conventional optical fibers and low index-contrast waveguides. Recently, a number of pioneering developments - all based on nanotechnologies - opened up the door to completely new working principles, hence to new classes of optoelectronic devices. Among them are nanostructured periodic materials (photonic crystals) and optically active nanostructures like quantum layers and quantum dots. A proper modelling of such structures has to describe simultaneously electrical charge transport, light generation, light propagation and scattering. Moreover, optical active nanostructures have to be described by quantum mechanics.

    In spite of the achievements of electronic/optoelectronic device and circuit simulation obtained so far, new nanotechnologies create new challenging tasks for mathematical modeling and numerical simulation in this field.

    Topics:
    • shape memory alloys in airfoils
    • production of semiconductor crystals
    • methanole fuel cell optimization
    • online production planning metamaterials


    http://www.zib.de/Optimization/Projects/Verification/Matheon-D17/index.en.html
  • B15

    Service design in public transport

    Project heads: -
    Project members: -
    Duration: 06/06-05/14
    Status: completed

    Description

    Networks, such as telephone networks, the internet, airline, railway, and bus networks are omnipresent and play a fundamental role for communication and mobility in our society. We almost take their permanent availability, reliability, and quality at low cost for granted. However, traffic jams, ill-designed train schedules, canceled flights, break-downs of telephone and computing networks, and slow internet access are reminders that networks are not automatically good networks.

    In fact, designing and operating communication and traffic networks are extremely complex tasks that lead directly to mathematical problems. A good example is the design of telecommunication networks. They were implemented with simple low-cost tree topologies until 15 years ago. Then, in 1988, a telco hub broke down in Chicago. This brought O Hare airport to a stand-still and caused an estimated business loss of billions of US dollars. Disasters of this kind made it clear that more sophisticated designs were needed. Nowadays, telecommunication companies use mathematically designed networks with built-in failure safety and rerouting capacities. Similar developments are expected in road traffic. We are now facing the installation of the first generation of load measuring, signalling, pricing, and route finding devices. These will soon integrate into a network-wide telematic system based on mathematical methods of traffic prediction, simulation, and control.

    Network design and operation tasks of this type are traditionally handled under the responsibility of various engineering disciplines (electrical engineering, traffic management and logistics, industrial engineering). While these disciplines can contribute to the improvement of the engineering components of such networks, todays demand on global optimization of the entire system poses problems where qualitative progress has to come from a better theoretical understanding of the structural aspects of the networks.

    This is where mathematics must come into play. The appearance of the word "network" in all the systems described above is not accidental, but hints at a common feature that has deep mathematical roots: networks are fundamental structures of graph theory and combinatorial optimization. Their study has become a prosperous subject in recent years, with impressive successes in many applications. The groups in Berlin are among the driving forces in this development.

    Nowadays, mathematical optimization techniques are used to locate switches and hubs in a phone system, to schedule buses and bus drivers in metropolitan transportation systems, etc. These tasks are individual steps in a hierarchical and sequential network planning process. In public transport, for example, this sequential process encompasses line planning, finding a periodic time table, assigning buses to lines, and creating individual bus driver schedules.

    Topics:
    • planning of optical, multilayer, and UMTS telecommunication networks
    • line planning, periodic timetabling, and revenue management in public transport networks
    • optimization in logistics, scheduling and material flows
    • optimization under uncertainty
    • symmetries in integer programming
    • game theoretic methods in network design


    http://www.zib.de/en/optimization/traffic/projects-long/Matheon-b15-service-design-in-public-transport.html
  • B14

    Combinatorial aspects of logistics

    Project heads: -
    Project members: -
    Duration: 06/06-05/10
    Status: completed

    Description

    Networks, such as telephone networks, the internet, airline, railway, and bus networks are omnipresent and play a fundamental role for communication and mobility in our society. We almost take their permanent availability, reliability, and quality at low cost for granted. However, traffic jams, ill-designed train schedules, canceled flights, break-downs of telephone and computing networks, and slow internet access are reminders that networks are not automatically good networks.

    In fact, designing and operating communication and traffic networks are extremely complex tasks that lead directly to mathematical problems. A good example is the design of telecommunication networks. They were implemented with simple low-cost tree topologies until 15 years ago. Then, in 1988, a telco hub broke down in Chicago. This brought O Hare airport to a stand-still and caused an estimated business loss of billions of US dollars. Disasters of this kind made it clear that more sophisticated designs were needed. Nowadays, telecommunication companies use mathematically designed networks with built-in failure safety and rerouting capacities. Similar developments are expected in road traffic. We are now facing the installation of the first generation of load measuring, signalling, pricing, and route finding devices. These will soon integrate into a network-wide telematic system based on mathematical methods of traffic prediction, simulation, and control.

    Network design and operation tasks of this type are traditionally handled under the responsibility of various engineering disciplines (electrical engineering, traffic management and logistics, industrial engineering). While these disciplines can contribute to the improvement of the engineering components of such networks, todays demand on global optimization of the entire system poses problems where qualitative progress has to come from a better theoretical understanding of the structural aspects of the networks.

    This is where mathematics must come into play. The appearance of the word "network" in all the systems described above is not accidental, but hints at a common feature that has deep mathematical roots: networks are fundamental structures of graph theory and combinatorial optimization. Their study has become a prosperous subject in recent years, with impressive successes in many applications. The groups in Berlin are among the driving forces in this development.

    Nowadays, mathematical optimization techniques are used to locate switches and hubs in a phone system, to schedule buses and bus drivers in metropolitan transportation systems, etc. These tasks are individual steps in a hierarchical and sequential network planning process. In public transport, for example, this sequential process encompasses line planning, finding a periodic time table, assigning buses to lines, and creating individual bus driver schedules.

    Topics:
    • planning of optical, multilayer, and UMTS telecommunication networks
    • line planning, periodic timetabling, and revenue management in public transport networks
    • optimization in logistics, scheduling and material flows
    • optimization under uncertainty
    • symmetries in integer programming
    • game theoretic methods in network design


    http://www.zib.de/Optimization/Projects/TrafficLogistic/Matheon-B14/index.en.html
  • D15

    Functional nano-structures

    Project heads: -
    Project members: -
    Duration: 04/05-05/10
    Status: completed

    Description

    The technical progress of the last decades has been enormously stimulated by two technological revolutions: the invention of the transistor in 1947 (Nobel prize 1956) and the invention of the laser in 1958 (Nobel prize 1964). The impact of both inventions on modern life is an evident fact.

    Already in 1950, a system of partial differential equations was published that models adequately the essential charge transport processes in semiconductor devices. On the basis of this drift-diffusion model the first bipolar transistor was successfully simulated in 1964. Just in that time the first integrated circuits containing a few transistors became commercially available. Since then, the electronics industry has achieved a phenomenal growth, mainly due to the rapid advances in integration technologies, large-scale systems design and numerical simulation. The number of applications of integrated circuits in high-performance computing, telecommunications, and consumer electronics has been rising steadily, and at a very fast pace. As microelectronic research moves into the nanometer scale device regime with GHz or higher operating speeds, the physics of electron flow through devices becomes more complicated, and physical effects, which previously could be safely ignored, become significant. Consequently, models of a higher abstraction level are needed. Conversely, faster simulation is typically required, which places a constraint on the model refinement if conventional simulation techniques are applied.

    Like the invention of the transistor triggered research in circuit simulation, the invention of the laser had a major impact on optical technologies. Classical optics turned into photonics. In todays telecommunication technologies, photons have already become the main carrier of information, regardless of the fact that even today most of the applied optical devices are based on conventional optical fibers and low index-contrast waveguides. Recently, a number of pioneering developments - all based on nanotechnologies - opened up the door to completely new working principles, hence to new classes of optoelectronic devices. Among them are nanostructured periodic materials (photonic crystals) and optically active nanostructures like quantum layers and quantum dots. A proper modelling of such structures has to describe simultaneously electrical charge transport, light generation, light propagation and scattering. Moreover, optical active nanostructures have to be described by quantum mechanics.

    In spite of the achievements of electronic/optoelectronic device and circuit simulation obtained so far, new nanotechnologies create new challenging tasks for mathematical modeling and numerical simulation in this field.

    Topics:
    • shape memory alloys in airfoils
    • production of semiconductor crystals
    • methanole fuel cell optimization
    • online production planning metamaterials


    http://www.zib.de/en/numerik/computational-nano-optics/projects/archive-projects-short-details/article/Matheon-d15-functional-nano-structures.html
  • G7

    (*) Vivid Mathematics

    Project heads: -
    Project members: -
    Duration: 10/04-05/06
    Status: completed

    Description

    The recent TIMSS studies have displayed and highlighted considerable deficits in the mathematical education in Germany, in particular on the gymnasium level. According to the study, in general, German pupils seem to be able to master calculations in a satisfactory way, but their abilities to solve application oriented problems are below average. Moreover, the mathematics taught at schools is not experienced as something interesting and attractive, so pupils are not well-motivated. This in turn leads to the fact that the mathematical knowledge acquired by the pupils is not sufficient for their orientation in the real-world. In particular, we observe corresponding problems in our mathematical education of students at the university. Such deficits were also stressed in the influential lecture Drawbridge Up by the noted German poet and essayist H. M. Enzensberger.

    There are a number of reasons for the unfavourable situation. Among others, we mention first that the sensitivity for mathematics in the German public is rather low, despite the fact that mathematics is more and more present in everyday life: most of the public many acknowledge that mathematics is difficult and impressive, but they do not view it as something interesting, or as a genuine part of culture. Secondly, the mathematics taught at schools often misses a certain amount of attractivity: very little of what the pupils see or learn is new, and there are typically very few references to any current mathematical developments; it does not become clear that there are new mathematical discoveries made every day, that there is recent and current progress on many different questions. A third reason is a deficit in the practice orientation of the mathematics taught at high schools: pupils do not see that mathematics is relevant and important in the real-world, that there are lots of interesting applications and developments.

    To improve the situation the following measures seem promising. The very experts have to give more emphasis to the popularization of current mathematics. Moreover, the teaching of mathematics, including the corresponding mathematics curricula, at schools and universities has to be made more attractive and problem-solving-oriented. Last but not least, the teacher students education has to obtain a more practice-oriented component.

    The basis to attack and solve the problems that we have described lies in greater educational activity of university mathematicians, and in a much closer cooperation between schools and universities than the present one.

    Projects

  • A11

    Non-adiabatic effects in molecular dynamics

    Project heads: -
    Project members: -
    Duration: 09/05-05/10
    Status: completed

    Description

    "Life sciences" describe a wide research area with enormous technological and social impact. However, there exist specific areas where mathematics has just begun to take on an active role.

    In medicine, the already traditional role of mathematics in medical imaging (e.g., computer tomography) has been successfully extended. Mathematical progress has proved to directly influence medical progress towards the design of patient-specific therapies - e.g., in the cancer therapy hyperthermia. As another example, computer-assisted surgery planning allows the comparison of various operation options before the actual operation on the basis of a simulation of more and more realistic models describing soft tissue, bone, or typical human gaits such as stair climbing. Further mathematization of the field is expected to open entirely new perspectives for the optimal design of joint prostheses adapted to individual anatomy.

    In biotechnology, the present situation is clearly dominated by the generation of huge datasets about biomolecular, genetic, metabolic or other bio-processes. Algorithms from discrete mathematics or computer science (e.g., in multiple alignment) already play a publicly visible role in the decoding of the human and other genomes. In contrast to that, the mathematical treatment of the dynamics of bio-processes is still rather limited - even though this aspect seems to be crucial for the detailed understanding of virus diseases or the design of narrow band drugs. Therefore, beyond the well-established core areas of bioinformatics, numerical biocomputing has recently become more and more accepted as one of the keys to data-based reliable prediction, control and design of real-life bio-processes: As it turns out, a significant increase in our ability in a reliable quantitative simulation of the dynamics of large biomolecules is essential for a detailed understanding of, e.g., the enzymatic mechanisms of prion diseases (like the mad cow disease or its human counterpart, the Creutzfeldt-Jacob syndrome).

    Topics:
    • computer-assisted surgery
    • patient-specific therapy planning
    • protein data base analysis
    • protein conformation dynamics
    • systems biology
    • pharmacokinetics


    http://page.mi.fu-berlin.de/lasser/A11.html
  • B16

    Mechanisms for Network Design Problems

    Project heads: -
    Project members: -
    Duration: 09/05-05/10
    Status: completed

    Description

    Networks, such as telephone networks, the internet, airline, railway, and bus networks are omnipresent and play a fundamental role for communication and mobility in our society. We almost take their permanent availability, reliability, and quality at low cost for granted. However, traffic jams, ill-designed train schedules, canceled flights, break-downs of telephone and computing networks, and slow internet access are reminders that networks are not automatically good networks.

    In fact, designing and operating communication and traffic networks are extremely complex tasks that lead directly to mathematical problems. A good example is the design of telecommunication networks. They were implemented with simple low-cost tree topologies until 15 years ago. Then, in 1988, a telco hub broke down in Chicago. This brought O Hare airport to a stand-still and caused an estimated business loss of billions of US dollars. Disasters of this kind made it clear that more sophisticated designs were needed. Nowadays, telecommunication companies use mathematically designed networks with built-in failure safety and rerouting capacities. Similar developments are expected in road traffic. We are now facing the installation of the first generation of load measuring, signalling, pricing, and route finding devices. These will soon integrate into a network-wide telematic system based on mathematical methods of traffic prediction, simulation, and control.

    Network design and operation tasks of this type are traditionally handled under the responsibility of various engineering disciplines (electrical engineering, traffic management and logistics, industrial engineering). While these disciplines can contribute to the improvement of the engineering components of such networks, todays demand on global optimization of the entire system poses problems where qualitative progress has to come from a better theoretical understanding of the structural aspects of the networks.

    This is where mathematics must come into play. The appearance of the word "network" in all the systems described above is not accidental, but hints at a common feature that has deep mathematical roots: networks are fundamental structures of graph theory and combinatorial optimization. Their study has become a prosperous subject in recent years, with impressive successes in many applications. The groups in Berlin are among the driving forces in this development.

    Nowadays, mathematical optimization techniques are used to locate switches and hubs in a phone system, to schedule buses and bus drivers in metropolitan transportation systems, etc. These tasks are individual steps in a hierarchical and sequential network planning process. In public transport, for example, this sequential process encompasses line planning, finding a periodic time table, assigning buses to lines, and creating individual bus driver schedules.

    Topics:
    • planning of optical, multilayer, and UMTS telecommunication networks
    • line planning, periodic timetabling, and revenue management in public transport networks
    • optimization in logistics, scheduling and material flows
    • optimization under uncertainty
    • symmetries in integer programming
    • game theoretic methods in network design


    http://www3.math.tu-berlin.de/Matheon/projects/B16/
  • B17

    Improvement of the linear algebra kernel of Simplex-based LP- and MIP-solvers

    Project heads: -
    Project members: -
    Duration: 08/06-01/07
    Status: completed

    Description

    Networks, such as telephone networks, the internet, airline, railway, and bus networks are omnipresent and play a fundamental role for communication and mobility in our society. We almost take their permanent availability, reliability, and quality at low cost for granted. However, traffic jams, ill-designed train schedules, canceled flights, break-downs of telephone and computing networks, and slow internet access are reminders that networks are not automatically good networks.

    In fact, designing and operating communication and traffic networks are extremely complex tasks that lead directly to mathematical problems. A good example is the design of telecommunication networks. They were implemented with simple low-cost tree topologies until 15 years ago. Then, in 1988, a telco hub broke down in Chicago. This brought O Hare airport to a stand-still and caused an estimated business loss of billions of US dollars. Disasters of this kind made it clear that more sophisticated designs were needed. Nowadays, telecommunication companies use mathematically designed networks with built-in failure safety and rerouting capacities. Similar developments are expected in road traffic. We are now facing the installation of the first generation of load measuring, signalling, pricing, and route finding devices. These will soon integrate into a network-wide telematic system based on mathematical methods of traffic prediction, simulation, and control.

    Network design and operation tasks of this type are traditionally handled under the responsibility of various engineering disciplines (electrical engineering, traffic management and logistics, industrial engineering). While these disciplines can contribute to the improvement of the engineering components of such networks, todays demand on global optimization of the entire system poses problems where qualitative progress has to come from a better theoretical understanding of the structural aspects of the networks.

    This is where mathematics must come into play. The appearance of the word "network" in all the systems described above is not accidental, but hints at a common feature that has deep mathematical roots: networks are fundamental structures of graph theory and combinatorial optimization. Their study has become a prosperous subject in recent years, with impressive successes in many applications. The groups in Berlin are among the driving forces in this development.

    Nowadays, mathematical optimization techniques are used to locate switches and hubs in a phone system, to schedule buses and bus drivers in metropolitan transportation systems, etc. These tasks are individual steps in a hierarchical and sequential network planning process. In public transport, for example, this sequential process encompasses line planning, finding a periodic time table, assigning buses to lines, and creating individual bus driver schedules.

    Topics:
    • planning of optical, multilayer, and UMTS telecommunication networks
    • line planning, periodic timetabling, and revenue management in public transport networks
    • optimization in logistics, scheduling and material flows
    • optimization under uncertainty
    • symmetries in integer programming
    • game theoretic methods in network design


    http://www.math.tu-berlin.de/~luce/B17
  • C19

    (*) Analysis and numerics of the peridynamic equation

    Project heads: -
    Project members: -
    Duration: 06/06-02/07
    Status: completed

    Description

    Production is one of the most important parts of the economy and at the very heart of the creation of value. Due to the central importance of production, big efforts have been made to improve production processes ever since the beginning of the industrial revolution. Nowadays, many production processes are highly automated. Computer programs based on numerical algorithms monitor the processes, improve efficiency and robustness, and guarantee high quality products. Consequently, mathematics is playing a steadily increasing role in this field. The possibilities of applying mathematical methods in production are wide-ranging. The Application Area cannot cover their full scale. For that reason, the projects concentrate on the development of new mathematical methods for special topics in manufacturing and production planning, two central aspects of production, in which the participating groups have longstanding expertise in mathematical modeling, simulation and optimization.

    In the field of manufacturing, we focus on innovative technologies having a big impact on technological progress: growth and processing of semiconductor bulk single crystals, phase transitions in modern steels and solder alloys, modeling of active and passive behavior of functional materials like shape-memory materials, growth of thin films. In the projects devoted to production planning, the main aim is the effective control of the whole production flow. Among the subjects to be studied, there is also electricity portfolio management.

    Topics:
    • phase transitions in steels and solder alloys
    • production of semiconductor crystals
    • modeling of active and passive behavior of functional materials
    • online production planning
    • growth of thin films


    http://www.math.tu-berlin.de/~emmrich/project.htm
  • C20

    Car frame structure optimization - Design to Cost

    Project heads: -
    Project members: -
    Duration: 06/06-09/06
    Status: completed

    Description

    Production is one of the most important parts of the economy and at the very heart of the creation of value. Due to the central importance of production, big efforts have been made to improve production processes ever since the beginning of the industrial revolution. Nowadays, many production processes are highly automated. Computer programs based on numerical algorithms monitor the processes, improve efficiency and robustness, and guarantee high quality products. Consequently, mathematics is playing a steadily increasing role in this field. The possibilities of applying mathematical methods in production are wide-ranging. The Application Area cannot cover their full scale. For that reason, the projects concentrate on the development of new mathematical methods for special topics in manufacturing and production planning, two central aspects of production, in which the participating groups have longstanding expertise in mathematical modeling, simulation and optimization.

    In the field of manufacturing, we focus on innovative technologies having a big impact on technological progress: growth and processing of semiconductor bulk single crystals, phase transitions in modern steels and solder alloys, modeling of active and passive behavior of functional materials like shape-memory materials, growth of thin films. In the projects devoted to production planning, the main aim is the effective control of the whole production flow. Among the subjects to be studied, there is also electricity portfolio management.

    Topics:
    • phase transitions in steels and solder alloys
    • production of semiconductor crystals
    • modeling of active and passive behavior of functional materials
    • online production planning
    • growth of thin films


    http://www.math.hu-berlin.de/~griewank/#VW
  • A12

    Biomolecular Transition as Shortest Paths in Incompletely Explored Transition Networks

    Project heads: -
    Project members: -
    Duration: 09/06-12/08
    Status: completed

    Description

    "Life sciences" describe a wide research area with enormous technological and social impact. However, there exist specific areas where mathematics has just begun to take on an active role.

    In medicine, the already traditional role of mathematics in medical imaging (e.g., computer tomography) has been successfully extended. Mathematical progress has proved to directly influence medical progress towards the design of patient-specific therapies - e.g., in the cancer therapy hyperthermia. As another example, computer-assisted surgery planning allows the comparison of various operation options before the actual operation on the basis of a simulation of more and more realistic models describing soft tissue, bone, or typical human gaits such as stair climbing. Further mathematization of the field is expected to open entirely new perspectives for the optimal design of joint prostheses adapted to individual anatomy.

    In biotechnology, the present situation is clearly dominated by the generation of huge datasets about biomolecular, genetic, metabolic or other bio-processes. Algorithms from discrete mathematics or computer science (e.g., in multiple alignment) already play a publicly visible role in the decoding of the human and other genomes. In contrast to that, the mathematical treatment of the dynamics of bio-processes is still rather limited - even though this aspect seems to be crucial for the detailed understanding of virus diseases or the design of narrow band drugs. Therefore, beyond the well-established core areas of bioinformatics, numerical biocomputing has recently become more and more accepted as one of the keys to data-based reliable prediction, control and design of real-life bio-processes: As it turns out, a significant increase in our ability in a reliable quantitative simulation of the dynamics of large biomolecules is essential for a detailed understanding of, e.g., the enzymatic mechanisms of prion diseases (like the mad cow disease or its human counterpart, the Creutzfeldt-Jacob syndrome).

    Topics:
    • computer-assisted surgery
    • patient-specific therapy planning
    • protein data base analysis
    • protein conformation dynamics
    • systems biology
    • pharmacokinetics


  • F7

    Visualization of Quantum molecular Systems

    Project heads: -
    Project members: -
    Duration: 09/06-09/08
    Status: completed

    Description

    Visualization has the task to create insight from given data. Image analysis is to extract information from data and to make it explicit in the form of a geometric model. The two areas have tight relations on both the methodical and the application level. Prominent examples are image-based rendering and visual analysis of 3D image data, e.g. in tomography or confocal microscopy.

    In recent years we have seen a rapid development of fundamentally new techniques for the visualization of complex physical phenomena as well as for imaging applications. At the very heart of these new technologies we encounter fundamentally new data structures and algorithms, all with a quest for a new level of abstraction. Here is where mathematics enters the scene.

    Especially in visualization, it is still a challenge to give the underlying objects a solid mathematical description. Here the research field of mathematical visualization faces the challenge to develop precise abstractions which eventually enables the development of new algorithms and visualization tools. Efforts in this direction can build on broad mathematical foundations, laid among others in the fields of discrete geometry, computational geometry, discrete differential geometry, and combinatorial topology. Results of this development are not only needed in research, where scientifically correct visualization is essential, but also meant to provide a solid basis for applications, for example, in computer graphics as well as in mathematics education projects.

    Even more so, the fields of visualization and image processing are key technologies for very current fields of research, among them many of the natural sciences (physics, chemistry, climate research), the life sciences (medicine, biochemistry, biotechnology, pharmacy), but also for various problems of engineering and production. Due to the multiple applications, but also due to technological reasons such as the availability of new imaging devices and display technology, imaging and visualization have been - and will be - areas of impressive growth.

    Topics:
    • discrete differential geometry
    • geometry processing
    • image processing
    • virtual reality PORTAL


    http://www.zib.de/visual/projects/molqm/
  • D18

    Sparse representation of solutions of differential equations

    Project heads: -
    Project members: -
    Duration: 11/06-04/08
    Status: completed

    Description

    The technical progress of the last decades has been enormously stimulated by two technological revolutions: the invention of the transistor in 1947 (Nobel prize 1956) and the invention of the laser in 1958 (Nobel prize 1964). The impact of both inventions on modern life is an evident fact.

    Already in 1950, a system of partial differential equations was published that models adequately the essential charge transport processes in semiconductor devices. On the basis of this drift-diffusion model the first bipolar transistor was successfully simulated in 1964. Just in that time the first integrated circuits containing a few transistors became commercially available. Since then, the electronics industry has achieved a phenomenal growth, mainly due to the rapid advances in integration technologies, large-scale systems design and numerical simulation. The number of applications of integrated circuits in high-performance computing, telecommunications, and consumer electronics has been rising steadily, and at a very fast pace. As microelectronic research moves into the nanometer scale device regime with GHz or higher operating speeds, the physics of electron flow through devices becomes more complicated, and physical effects, which previously could be safely ignored, become significant. Consequently, models of a higher abstraction level are needed. Conversely, faster simulation is typically required, which places a constraint on the model refinement if conventional simulation techniques are applied.

    Like the invention of the transistor triggered research in circuit simulation, the invention of the laser had a major impact on optical technologies. Classical optics turned into photonics. In todays telecommunication technologies, photons have already become the main carrier of information, regardless of the fact that even today most of the applied optical devices are based on conventional optical fibers and low index-contrast waveguides. Recently, a number of pioneering developments - all based on nanotechnologies - opened up the door to completely new working principles, hence to new classes of optoelectronic devices. Among them are nanostructured periodic materials (photonic crystals) and optically active nanostructures like quantum layers and quantum dots. A proper modelling of such structures has to describe simultaneously electrical charge transport, light generation, light propagation and scattering. Moreover, optical active nanostructures have to be described by quantum mechanics.

    In spite of the achievements of electronic/optoelectronic device and circuit simulation obtained so far, new nanotechnologies create new challenging tasks for mathematical modeling and numerical simulation in this field.

    Topics:
    • shape memory alloys in airfoils
    • production of semiconductor crystals
    • methanole fuel cell optimization
    • online production planning metamaterials


    http://www.math.tu-berlin.de/~jokar/D18
  • C21

    Reduced-order modelling and optimal control of robot guided laser material treatments

    Project heads: -
    Project members: -
    Duration: 10/06 - 09/08
    Status: completed

    Description

    Production is one of the most important parts of the economy and at the very heart of the creation of value. Due to the central importance of production, big efforts have been made to improve production processes ever since the beginning of the industrial revolution. Nowadays, many production processes are highly automated. Computer programs based on numerical algorithms monitor the processes, improve efficiency and robustness, and guarantee high quality products. Consequently, mathematics is playing a steadily increasing role in this field. The possibilities of applying mathematical methods in production are wide-ranging. The Application Area cannot cover their full scale. For that reason, the projects concentrate on the development of new mathematical methods for special topics in manufacturing and production planning, two central aspects of production, in which the participating groups have longstanding expertise in mathematical modeling, simulation and optimization.

    In the field of manufacturing, we focus on innovative technologies having a big impact on technological progress: growth and processing of semiconductor bulk single crystals, phase transitions in modern steels and solder alloys, modeling of active and passive behavior of functional materials like shape-memory materials, growth of thin films. In the projects devoted to production planning, the main aim is the effective control of the whole production flow. Among the subjects to be studied, there is also electricity portfolio management.

    Topics:
    • phase transitions in steels and solder alloys
    • production of semiconductor crystals
    • modeling of active and passive behavior of functional materials
    • online production planning
    • growth of thin films


    http://www.wias-berlin.de/people/anst/Forschung/Optcontr/intro.shtml