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• Archiv 02-14

Project archive 2002 - 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

  
  
  

• 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/

• 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