Laufende Projekte

ECMath finanziert

  • SE1

    Reduced order modeling for data assimilation

    Prof. Dr. Volker Mehrmann / Dr. Christian Schröder

    Projektleiter: Prof. Dr. Volker Mehrmann / Dr. Christian Schröder
    Projekt Mitglieder: Matthias Voigt
    Laufzeit: -
    Status: laufend
    Standort: Technische Universität Berlin

    Beschreibung

    One of the bottlenecks of current procedures for the generation and distribution of green (wind or solar) energy is the accurate and timely simulation of processes in the ocean and atmosphere that can be used in short term planning and real time control of energy systems. A particular difficulty is the real time construction of physically plausible model initializations and 'controls/inputs' to bring simulations into coherence with available observations when observation locations and observations are coming in at variable times and locations.

    The currently best approach for fixed observation times and locations are variational data assimilation techniques. These methods use a four dimensional model that is adapted to the incoming observations using a combination of different filtering techniques and numerical integration of the dynamical system. In order to make these methods efficient in real time data assimilation they have to be combined with appropriate model order reduction methods. A major difficulty in these techniques is the combination of approximate transfer functions and approximate initial and boundary conditions as well as the construction of guaranteed error estimates and the capturing of essential features of the original model. The so-called representer approach formulates the data assimilation problem as the numerical solution of a large-scale nonlinear optimal control problem and incorporates the assimilation of the model to the observations, via an extended ensemble Kalman filter, and the adaptation of the initial data in one approach. Adding further assumptions and linearization this optimization problem usually reduces to a linear quadratic optimal control problem which is solved via the solution of a boundary value problem with Hamiltonian structure.

    http://www3.math.tu-berlin.de/numerik/NumMat/ECMath/SE1/
  • SE2

    Electrothermal modeling of large-area OLEDs

    PD Dr. Annegret Glitzky / Prof. Dr. Alexander Mielke

    Projektleiter: PD Dr. Annegret Glitzky / Prof. Dr. Alexander Mielke
    Projekt Mitglieder: Dr. Matthias Liero
    Laufzeit: -
    Status: laufend
    Standort: Weierstraß-Institut

    Beschreibung

    The aim of the project D-SE2 is to find adequate spatially resolved PDE models for the electrothermal description of organic semiconductor devices describing self-heating and thermal switching phenomena. Moreover, the project intends to investigate their analytical properties, derive suitable numerical approximation schemes, and provide simulation results which can help to optimize large-area organic light emitting diodes.
    Click here for more information

    http://www.wias-berlin.de/projects/ECMath-SE2/index.html
  • SE3

    Stability analysis of power networks and power network models

    Prof. Dr. Christian Mehl / Prof. Dr. Volker Mehrmann / Prof. Dr. Caren Tischendorf

    Projektleiter: Prof. Dr. Christian Mehl / Prof. Dr. Volker Mehrmann / Prof. Dr. Caren Tischendorf
    Projekt Mitglieder: Dr. Jan Philipp Pade / Dr. Andreas Steinbrecher
    Laufzeit: -
    Status: laufend
    Standort: Humboldt Universität Berlin / Technische Universität Berlin

    Beschreibung

    In the project the stability of power networks and power network models is analyzed. The classical way of modeling a power network is via a large differential-algebraic system of network equations (DAE). Modifications of the power network by adding extra power lines into the network grid or by removing some power lines can be interpreted as low rank perturbations of matrices and matrix pencils that linearize the DAE system mentioned above. In the project, the influence of these perturbation on the stability of the network is analyzed.

    http://www.math.hu-berlin.de/~numteam1/projects/SE3.php
  • SE4

    Mathematical modeling, analysis and novel numerical concepts for anisotropic nanostructured materials

    Dr. Christiane Kraus / Prof. Dr. Gitta Kutyniok / Prof. Dr. Barbara Wagner

    Projektleiter: Dr. Christiane Kraus / Prof. Dr. Gitta Kutyniok / Prof. Dr. Barbara Wagner
    Projekt Mitglieder: Esteban Meca Álvarez / Dr. Arne Roggensack
    Laufzeit: -
    Status: laufend
    Standort: Technische Universität Berlin / Weierstraß-Institut

    Beschreibung

    The project SE4 aims to develop and study mathematical models in order to understand, functionalize and optimize modern nanostructured materials. Such materials are fundamental for the design of next generation thin-film solar cells as well as batteries for the production and storage of sustainable energy, respectively. Besides the mathematical modeling, the main goals of this research project are the analysis of the developed phase field systems and the construction of numerical algorithms that efficiently capture the material properties and, in particular, their anisotropic nature. More information...

    http://www.wias-berlin.de/people/roggensa/se4/
  • SE5

    Optimal design and control of optofluidic solar steerers and concentrators

    Prof. Dr. Michael Hintermüller

    Projektleiter: Prof. Dr. Michael Hintermüller
    Projekt Mitglieder: Soheil Hajian / Tobias Keil
    Laufzeit: -
    Status: laufend
    Standort: Humboldt Universität Berlin

    Beschreibung

    Solar energy is mostly harvested by means of photovoltaic (PV) or concentrating photovoltaic (CPV) solar cells. The efficiency of CPV is higher (at least twice) than the traditional PV but significantly more expensive. To reduce costs, optical condensers (e.g., a Fresnel lens) to concentrate solar light on each CPV cell are used. Moreover, since the energy production is maximized when the panels are perpendicular to the light beam, mechanical tracking systems that move the array of solar panels based on the position of the sun. But these tracking system increases costs, requires power and are error-prone. The goal of this project is the optimal design and control of steerers and concentrators for PV or CPV using electrowetting (EW) and electrowetting-on-dielectric (EWOD).

    https://www.math.hu-berlin.de/~hp_hint/SE5/index.html
  • SE6

    Plasmonic concepts for solar fuel generation

    Prof. Dr. Rupert Klein / Prof. Dr. Frank Schmidt

    Projektleiter: Prof. Dr. Rupert Klein / Prof. Dr. Frank Schmidt
    Projekt Mitglieder: Dr. Sven Burger / Dr. Martin Hammerschmidt
    Laufzeit: -
    Status: laufend
    Standort: Konrad-Zuse-Zentrum für Informationstechnik Berlin

    Beschreibung

    Artificial photosynthesis and water splitting, i.e. the sustainable production of chemical fuels like hydrogen and carbohydrates from water and carbon dioxide, has the potential to store the abundance of solar energy that reaches the earth in chemical bonds. Fundamental in this process is the conversion of electromagnetic energy. In photoelectrochemical water splitting semiconductor materials are employed to generate electron hole pairs with sufficient energy to drive the electrochemical reactions. In this project we investigate the use of metallic nanoparticles to excite plasmonic resonances by means of numerical simulations. These resonances localize electromagnetic nearfields which is beneficial for the electrochemical reactions. We develop electromagnetic models and numerical methods to facilite in depth analysis of these processes in close contact with our collaboration partners within the ECMath and the joint lab ``Berlin Joint Lab for Optical Simulation for renewable Energy research'' (BerOSE) between the ZIB, FU and HZB.

    http://www.zib.de/projects/plasmonic-concepts-solar-fuel-generation
  • SE7

    Optimizing strategies in energy and storage markets

    PD Dr. John Schoenmakers / Prof. Dr. Vladimir Spokoiny

    Projektleiter: PD Dr. John Schoenmakers / Prof. Dr. Vladimir Spokoiny
    Projekt Mitglieder: Roland Hildebrand
    Laufzeit: -
    Status: laufend
    Standort: Weierstraß-Institut

    Beschreibung

    The project aims at developing numerical methods for the solution of complex optimal control problems arising in energy production, storage, and trading on energy markets. As a first step, we implement a Monte-Carlo approach to a hydro-electricity production and storage problem coupled with a stochastic model of the electricity market. Further we develop algorithms for pricing of complex energy derivatives based on the dual martingale approach.

    http://www.wias-berlin.de/projects/ECMath-SE7/
  • SE8

    Stochastic methods for the analysis of lithium-ion batteries

    Prof. Dr. Wolfgang Dreyer / Prof. Dr. Peter Karl Friz

    Projektleiter: Prof. Dr. Wolfgang Dreyer / Prof. Dr. Peter Karl Friz
    Projekt Mitglieder: Paul Gajewski / Dr Mario Maurelli
    Laufzeit: -
    Status: laufend
    Standort: Weierstraß-Institut

    Beschreibung

    The aim of the project is to better understand and to give simulations for a successful model for the charging and discharging of lithium-ion batteries, which are currently the most promising storage devices to store and convert chemical energy into electrical energy and vice versa. The model exhibits phase transition under different small parameter regimes and gives rise to hysteresis. We study these phenomena using the interpretation of the model as a stochastic particle system, with the goal of providing stability bounds, fast simulations, improvement of the model itself and optimization of the device. More information...

    http://www.wias-berlin.de/projects/ECMath-SE8/
  • SE9

    Optimal control of evolution Maxwell equations and low rank approximation

    Prof. Dr. Reinhold Schneider / Prof. Dr. Fredi Tröltzsch

    Projektleiter: Prof. Dr. Reinhold Schneider / Prof. Dr. Fredi Tröltzsch
    Projekt Mitglieder: Benjamin Huber
    Laufzeit: -
    Status: laufend
    Standort: Technische Universität Berlin

    Beschreibung

    The project D-SE9 focuses on the analysis and efficient numerical solution of optimal control problems for nonlinear evolution equations with Maxwell's evolution equations as a challenging benchmark example. In particular, we aim at developing low rank approximation techniques for the solution of forward-backward optimality systems that arise whenever optimal control problems for evolution equations are considered. In this project, we thus merge existing expertise in optimal control and low rank matrix and tensor approximation.

    http://www.d-se9.de
  • SE10

    Low rank tensor recovery

    Prof. Dr. Reinhold Schneider

    Projektleiter: Prof. Dr. Reinhold Schneider
    Projekt Mitglieder: Sebastian Wolf
    Laufzeit: -
    Status: laufend
    Standort: Technische Universität Berlin

    Beschreibung

    In the project D-SE10 we aspire to recover higher order tensors from a relatively small number of measurements using low rank assumptions. As straight forward generalizations of the matrix recovery techniques to the problem of tensor recovery are often either infeasible or impossible, the focus of this project is twofold. First, to investigate those generalizations that might still be feasible in a tensor setting in particular Riemannian methods on low rank tensor manifolds, and second, to apply and specialize existing techniques from tensor product approximation like the ALS to the tensor recovery and completion settings.

    http://d-se10.de
  • SE11

    Model order reduction for light-controlled nanocatalysis

    Prof. Dr. Carsten Hartmann

    Projektleiter: Prof. Dr. Carsten Hartmann
    Projekt Mitglieder: PD Dr. Burkhard Schmidt
    Laufzeit: -
    Status: laufend
    Standort: Freie Universität Berlin

    Beschreibung

    Photocatalysis is a key application in the field of femtochemistry where chemical reaction dynamics is controlled by temporally shaped femtosecond laser pulses, with the target to promote specific product channels while suppressing competing undesired channels, e.g. pollutants. The optimal shaping of the laser pulse requires a detailed insight into the underlying reaction mechanisms at the atomic or molec- ular level that can often only be obtained by theoretical modelling and computer simulations of the quantum mechanical equations of motion. For catalytic system, this boils down to the iterated integration of the dissipative Liouville–von–Neumann (LvN) equation for reduced quantum mechanical density matrices, which represents the computational bottleneck for theoretical modelling, as the size of the matrices grows quadratically with the number of quantum states involved. The aim of this project is to study model order reduction (MOR) of LvN-based models to beat the curse of dimensionality in the simulation and (optimal) control of photocatalytic processes. In the setting of first-order perturbation theory, the laser field in these models is linearly coupled to the density matrix, which leads to a time- inhomogeneous bilinear system of equations of motion. MOR of bilinear systems has recently been a field of intense research. The downside of many available methods is their lack of structure preservation, most importantly, asymptotic stability of fixed points. An alternative that is in the focus of this project is MOR based on balancing the controllable and observable subspace of the system. Even though the identification of the essential subspace requires the solution of large-scale Lyapunov equations, which limits the applicability of the method to systems of moderate size (up to 100,000 DOFs), it has proven powerful for linear control systems in terms of computable error bounds and structure preservation. Whether these results carry over to the bilinear case is still open.

    https://sites.google.com/site/ecmathse11/
  • SE12

    Fast solvers for heterogeneous saddle point problems

    Prof. Dr. Carsten Gräser

    Projektleiter: Prof. Dr. Carsten Gräser
    Projekt Mitglieder: Pawan Kumar
    Laufzeit: -
    Status: laufend
    Standort: Freie Universität Berlin

    Beschreibung

    The aim of this project is to develop fast linear solvers for heterogeneous saddle point problems as appearing during the iterative solution of non-smooth optimization problems, e.g., in the context of phase field models. While the development of nonlinear solvers for phase field models has reached a certain maturity, the existing solvers for the linear subproblems are still unsatisfactory. As a first step, we focus on two-phase models. Later, we plan to extend these solvers for multiphase systems.

    Matheon-C-SE12.php">http://numerik.mi.fu-berlin.de/wiki/Projects/Matheon-C-SE12.php
  • SE13

    Topology optimization of wind turbines under uncertainties

    Dr. Martin Eigel / PD Dr. René Henrion / Prof. Dr. Dietmar Hömberg / Prof. Dr. Reinhold Schneider

    Projektleiter: Dr. Martin Eigel / PD Dr. René Henrion / Prof. Dr. Dietmar Hömberg / Prof. Dr. Reinhold Schneider
    Projekt Mitglieder: Dr. Johannes Neumann / Dr. Thomas Petzold
    Laufzeit: -
    Status: laufend
    Standort: Technische Universität Berlin / Weierstraß-Institut

    Beschreibung

    The application focus of this project is the topology optimization of the main frame of wind turbines. This is the central assembly platform at the tower head accommodating the drive train, the generator carrier, the azimuth bearing and drives and a lot of small components. Topology optimization should not be mistaken for legally mandated structural analysis computations. For the latter, it is standard to solicit a number of single load scenarios based on available time series data. While this approach is questionable already for stress analysis, it is prohibitive for topology optimization. Disregarding the multivariate distribution of the random loads would not provide any probabilistic certificate for bounding stresses. Moreover, the natural way to choose weights is to derive a stochastic load from available time series data. The main frame is made of cast iron which is prone to a number of material impurities like shrink holes, dross, and chunky graphite. This motivates the additional consideration of randomness for the material stiffness. Structures resulting from topology optimization often exhibit unacceptably high stresses necessitating costly subsequent shape design works. To avoid this already during the optimization, state constraints have to be included in the optimization problem. The main novelty of this project is that it combines a phase field relaxed topology optimisation problem not only with uncertain loading and material data but also with chance state constraints. Even in the finite-dimensional case, the derivation of optimality conditions including gradient formulas is completely open. In the long run, including an appropriate damage model as additional state equation will be a further task of great practical importance.

    http://www.wias-berlin.de/projects/ECMath-SE13/
  • SE14

    Error-aware analysis of multi-scale reactivity models for photochemical surface reactions

    Dr. Sebastian Matera

    Projektleiter: Dr. Sebastian Matera
    Projekt Mitglieder: Sandra Doepking
    Laufzeit: -
    Status: laufend
    Standort: Freie Universität Berlin

    Beschreibung

    On the route to a more efficient exploitation of energy and materials, the design of new heterogenous catalysts is a central aspect, be it for the production of fine chemicals or the conversion of solar energy to fuels. Ideally, such a design is based on an atomistic understanding of the origin of catalytic activity. In order to enable this detailed undestanding, first-principles kinetic Monte Carlo approaches have been established during the last decade. Despite their success, these still have some some limitations. On the one hand, the electronic structure methods, employed to determine required rate parameters, introduce a non-negligible error into the later. On the other hand, the need for stochastic simulation and the typically large dimension of the parameter space hampers the determination of the rate determining steps by sensitivity analysis, i.e. the most interesting input for a rational catalyst design.

    http://www.mi.fu-berlin.de/math/groups/ag-photo/forschung/EC-Math-SE14/index.html
  • SE15

    Optimal Network Sensor Placement for Energy Efficiency

    Dr. Carlos Rautenberg

    Projektleiter: Dr. Carlos Rautenberg
    Projekt Mitglieder: Simon Rösel
    Laufzeit: -
    Status: laufend
    Standort: Humboldt Universität Berlin

    Beschreibung

    The optimal sensor placement problem for the estimation of the temperature distribution in buildings is a highly nonlinear and multi-scale problem where stochastic perturbations are usually present. The main goal here is to properly locate sensors in order to reliably estimate the temperature distribution in certain areas. Since feedback controllers are usually in use, a proper estimation of the state is of utmost importance in order to reduce energy consumption of such controllers.

    http://www2.mathematik.hu-berlin.de/~rautenca/SE15.htm




Anders finanziert

  • SE-AP2

    Pattern formation in systems with multiple scales

    Prof. Dr. Alexander Mielke

    Projektleiter: Prof. Dr. Alexander Mielke
    Projekt Mitglieder: -
    Laufzeit: 01.01.2011 - 31.12.2018
    Status: laufend
    Standort: Technische Universität Berlin

    Beschreibung

    Pattern formation in nonlinear partial differential equations depends on nontrivial interactions between different internal length scales and nonlinearities of the system as well as on the size and geometry of the underlying domain. The challenge is to understand how effects on the small scales generate effective pattern formation on the larger scales. Using well-chosen model problems reflecting the focus applications of the CRC, we will investigate the mathematical foundations of the derivation of effective models for pattern formation in multiscale problems. Controls for the effective models will be used to construct controls for the original system.

    http://www.itp.tu-berlin.de/collaborative_research_center_910/sonderforschungsbereich_910/project_groups/a_theoretical_methods/tp_a5/
  • SE-AP7

    Understanding of microstructure evolution in copper indium selenide (CISe) and copper gallium indium selenide (CGSe)

    Prof. Dr. Ralf Kornhuber

    Projektleiter: Prof. Dr. Ralf Kornhuber
    Projekt Mitglieder: -
    Laufzeit: 01.11.2012 - 31.10.2017
    Status: laufend
    Standort: Freie Universität Berlin

    Beschreibung

    Photovoltaic devices, which operate by directly converting solar energy into electricity, have become rapidly one of the most important “clean” energy sources. The optimization of thin-film solar cells for such use has been mainly a trial-and-error process. A detailed understanding of the relationships between growth processes, structural defects, strain, and electrical properties would benefit the development of these devices considerably. In the Virtual Institute "Microstructure control for thin-film solar cells", the formation of structural defects and related strain during the growth of thin film solar cells is investigated by combining various experimental as well as simulation approaches. The goal of this subproject is to derive vector-valued phase field models describing CISe (CIGSe) systems (Wagner, TU Berlin) together with fast, robust, and reliable numerical solution techniques (Kornhuber, FU Berlin). Suitable free energies will be determined by density functional theory (Albe, TU Darmstadt).

  • SE-AP8

    Entwicklung eines reduzierten Modells eines Pulsed Detonation Combustors

    Prof. Dr. Volker Mehrmann

    Projektleiter: Prof. Dr. Volker Mehrmann
    Projekt Mitglieder: -
    Laufzeit: 01.07.2012 - 30.06.2020
    Status: laufend
    Standort: Technische Universität Berlin

    Beschreibung

    In this project a model reduction of reactive flows is developed. Model reduction aims to replace complex, high-dimensional models by models of much smaller dimension. Goal of this project is to improve the existing techniques for systems where transport phenomena are dominant. To this end an appropriate error estimator is developed and combined with a model reduction. The small model can then be adaptively improved by adding physically motivated ansatz-functions. By this approach a low order model of a pulsed combustion is derived. This is used for control and design of a pulsed detonation combustor.

    The reduced order models shall not only describe the process of the combustion but also show the changes due to specific manipulation. The controllability in the context of mathematical fluid dynamics is determined via adjoint equations. For this the adjoint equations for reactive flows have to be differentiated and implemented.

    The reduced models are then used to design the combustor and to control the combustion process.

    https://www.sfb1029.tu-berlin.de/menue/teilprojekte/a02/parameter/en/
  • SE-AP11

    Multiscale tensor decomposition methods for partial differential equations

    Prof. Dr. Rupert Klein / Prof. Dr. Reinhold Schneider / Prof. Dr. Harry Yserentant

    Projektleiter: Prof. Dr. Rupert Klein / Prof. Dr. Reinhold Schneider / Prof. Dr. Harry Yserentant
    Projekt Mitglieder: -
    Laufzeit: 01.10.2014 - 30.09.2018
    Status: laufend
    Standort: Freie Universität Berlin / Technische Universität Berlin

    Beschreibung

    Novel hierarchical tensor product methods currently emerge as an important tool in numerical analysis and scienti.c computing. One reason is that these methods often enable one to attack high-dimensional problems successfully, another that they allow very compact representations of large data sets. These representations are in some sense optimal and by construction at least as good as approximations by classical function systems like polynomials, trigonometric polynomials, or wavelets. Moreover, the new tensor-product methods are by construction able to detect and to take advantage of self-similarities in the data sets. They should therefore be ideally suited to represent solutions of partial differential equations that exhibit certain types of multiscale behavior.
    The aim of this project is both to develop methods and algorithms that utilize these properties and to check their applicability to concrete problems as they arise in the collobarative research centre. We plan to attack this task from two sides. On the one hand we will try to decompose solutions that are known from experiments, e.g., on Earthquake fault behavior, or large scale computations, such as turbulent flow fields. The question here is whether the new tensor product methods can support the devel­opment of improved understanding of the multiscale behavior and whether they are an improved starting point in the development of compact storage schemes for solutions of such problems relative to linear ansatz spaces.
    On the other hand, we plan to apply such tensor product approximations in the frame­work of Galerkin methods, aiming at the reinterpretation of existing schemes and at the development of new approaches to the ef.cient approximation of partial differential equations involving multiple spatial scales. The basis functions in this setting are not taken from a given library, but are themselves generated and adapted in the course of the solution process.
    One mid-to long-term goal of the project that combines the results from the two tracks of research described above is the construction of a self-consistent closure for Large Eddy Simulations (LES) of turbulent flows that explicitly exploits the tensorproduct approach’s capability of capturing self-similar structures. If this proves successful, we plan to transfer the developed concepts also to Earthquake modelling in joint work with partner project B01.

    http://sfb1114.imp.fu-berlin.de/research/index.php?option=com_projectlog&view=project&id=8
  • SE-AP14

    Foundation and application of generalized mixed FEM towards nonlinear problems in solid mechanics

    Prof. Dr. Carsten Carstensen

    Projektleiter: Prof. Dr. Carsten Carstensen
    Projekt Mitglieder: Philipp Bringmann / Friederike Hellwig
    Laufzeit: 01.09.2014 - 31.08.2017
    Status: laufend
    Standort: Humboldt Universität Berlin

    Beschreibung

    Despite the practical success in computational engineering and a few partial mathematical convergence proofs, many fundamental questions on the reliable and effective computer simulation in nonlinear mechanics are still open. The success of mixed FEMs in the linear elasticity with focus on the accuracy of the stress variable motivated the research of novel discretization schemes in the SPP1748. This and recent surprising advantages of related nonconforming finite element methods in nonlinear partial differential equations with guaranteed lower eigenvalue bounds or lower energy bounds in convex minimization problems suggests the investigation of mixed and simpler generalized mixed finite element methods such as discontinuous Petrov-Galerkin schemes for linear or linearized elasticity and nonlinear elasticity with polyconvex energy densities in this project. The practical applications in computational engineering will be the focus of the Workgroup LUH with all 3D simulations to provide numerical insight in the feasibility and robustness of the novel simulation tools, while the Workgroup HU will provide mathematical foundation of the novel schemes with rigorous a priori and a posteriori error estimates. The synergy effects of the two workgroups will be visible in that problems with a known rigorous mathematical analysis or the Lavrentiev gap phenomenon or cavitation will be investigated by engineers for the first time and, vice versa, more practical relevant models in nonlinear mechanics will be looked at from a mathematical viewpoint with arguments from the calculus of variations and the implicit function theorem combined with recent arguments for a posteriori error analysis and adaptive mesh-refining. A combination of ideas in least-squares finite element methods with those of hybridized methods recently led to discontinuous Petrov Galerkin (dPG) FEMs. They minimize a residual inherited from a piecewise ultra weak formulation in a nonstandard localized dual norm. This innovative ansatz will be generalized from Hilbert to Banach spaces to allow the numerical approximation of linearized problems in nonlinear mechanics which leads to some global inf-sup condition on the continuous and on the discrete level for stability of the novel ultra weak formulations. The joint interest is the design of adaptive algorithms for effective mesh-design and the understanding of the weak or penalized coupling of the nonlinear stress-strain relations. A key difficulty arises from the global or localized and then numerical inversion of the nonlinear stress-strain relation in some overall Hu-Washizu-type mixed formulation. While convex energy densities allow a formal inversion of the stress-strain relation via a duality in convex analysis, it contradicts the frame indifference in continuum mechanics. The extension for polyconvex energy densities is only possible for special cases in closed form but has, in general, to be localized and approximated.

    https://www.uni-due.de/spp1748/generalized_mixed_nonlinear_fem.php
  • SE-AP15

    Structure Formation in Thin Liquid-Liquid Films

    Dr. Dirk Peschka / Prof. Dr. Barbara Wagner

    Projektleiter: Dr. Dirk Peschka / Prof. Dr. Barbara Wagner
    Projekt Mitglieder: -
    Laufzeit: 01.04.2011 - 30.09.2017
    Status: laufend
    Standort: Weierstraß-Institut

    Beschreibung

    The main topic of this tandem proposal is the direct comparison of results from mathematical modeling, analysis and experimental investigations of rupture,dewetting dynamics and equilibrium patterns of a thin liquid-liquid system. The experimental system uses a PS (polystyrene)/ PMMA (polymethylmethacrylate) thin bilayer of a few hundred nanometer, whose liquid properties can be tuned from Newtonian to visoelastic rheological flow behavior by varying the length of the polymer chains. On these small scales, apart from capillary forces and viscous dissipation, intermolecular forces will play an important role in the dynamics and morphology of the interfaces. The mathematical analysis and numerical simulation of adequate thin film models that will be derived from the underlying fluid mechanical equations, will be used through direct comparisons with experiments. Thus, we aim at clarifying also fundamental properties, such as equilibrium contact angles, singularity formation or dewetting rates. This shall form the basis for more complex situations involving evaporation, surfactant monolayers, and slippage, to yield the understanding crucial for many important nanofluidic problems in nature and technology ranging from rupture of the human tear film to the interface dynamics of donor/acceptor polymer solutions used in organic solar cells.

    http://www.dfg-spp1506.de/project-seemann-wagner-peschka
  • SE-AP16

    Phase field modeling for multi-phase systems applied to the growth of Cu(In,Ga)Se2 thin films

    Prof. Dr. Barbara Wagner

    Projektleiter: Prof. Dr. Barbara Wagner
    Projekt Mitglieder: -
    Laufzeit: 01.04.2013 - 30.09.2018
    Status: laufend
    Standort: Weierstraß-Institut

    Beschreibung

    • phase field models involving surface diffusion, temperature, and elasticity for growing poly-Si film; • mathematical modeling of the evolution of In and Ga distributions during the growth of CIGSe thin films. Numerical simulations (in cooperation with PhD-6); • advanced phase field models for grain growth in ternary (CISe and CGSe) as well as for quaternary (CIGSe) thin films

    http://www.helmholtz-berlin.de/projects/hvi/microstructure/phd-projects_en.html
  • SE-AP20

    Analysis, numerical solution and control of delay differential-algebraic equations

    Prof. Dr. Volker Mehrmann

    Projektleiter: Prof. Dr. Volker Mehrmann
    Projekt Mitglieder: -
    Laufzeit: 01.01.2011 - 31.12.2018
    Status: laufend
    Standort: Technische Universität Berlin

    Beschreibung

    Delay differential-algebraic equations (DDAEs) arise in a variety of applications including flow control, biological systems and electronic networks. We will study existence and uniqueness as well as the development of numerical methods for general nonlinear DDAEs. For this, regularization techniques need to be performed that prepare the DDAE for numerical simulation and control. We will derive such techniques for DDAEs on the basis of a combination of time-differentiations and time-shifts, in particular for systems with multiple delays. We also plan to extend the spectral stability theory, i.e. the concepts of Lyapunov, Bohl and Sacker-Sell spectra, to DDAEs. We will also develop numerical methods for the computation of these spectra using semi-explicit integration methods. Another goal is to study the solution of algebraically constrained partial delay-differential equations arising in flow control and to derive discretization as well as optimal control methods in space and time.

    http://www.itp.tu-berlin.de/collaborative_research_center_910/sonderforschungsbereich_910/project_groups/a_theoretical_methods/tp_a2/
  • SE-AP21

    Numerische Lösungsverfahren für gekoppelte Populationsbilanzsysteme zur dynamischen Simulation multivariater Feststoffprozesse am Beispiel der formselektiven Kristallisation

    Prof. Dr. Volker John

    Projektleiter: Prof. Dr. Volker John
    Projekt Mitglieder: -
    Laufzeit: 01.10.2013 - 30.09.2017
    Status: laufend
    Standort: Weierstraß-Institut

    Beschreibung

    Feststoffprozesse in der Verfahrenstechnik lassen sich durch Populationsbilanzsysteme beschreiben. Hierbei handelt es sich um ein gekoppeltes System von partiellen Differentialgleichungen zur Charakterisierung der kontinuierlichen Phase, sowie einer Populationsbilanzgleichung zur Beschreibung der Feststoffphase. Die Lösung dieser Populationsbilanzgleichung, die Partikelverteilungsdichte f(t,r,x), beschreibt die Partikelverteilung zum Zeitpunkt t in den Ortskoordinaten r und in einer bzw. mehreren Eigenschaftskoordinaten x.

    Ziel des Projektes ist der Vergleich und die Weiterentwicklung von numerischen Verfahren zur Lösung von Populationsbilanzsystemen. Dies soll am Beispiel der formselektiven Kristallisation von ausgewählten Modellsubstanzen, die sich über eine bzw. mehrere Eigenschaftskoordinaten beschreiben lassen, geschehen. Weiterhin sollen im Rahmen dieses Projektes optimale statistisch geplante wachstums- bzw. agglomerationsdominierte Benchmarkexperimente durchgeführt werden. Diese dienen sowohl zur Bestimmung von kinetischen Parametern wie Nukleations- und Wachstumsraten oder Agglomerationskernen, als auch zur Abschätzung der numerischen Fehler der zur Simulation verwendeten Lösungsverfahren. Abschließend sollen die entwickelten Methoden, sowie die ermittelten Prozesskinetiken zur Auslegung und Optimierung eines Gesamtprozesses zur kontinuierlichen und formselektiven Kristallisation verwendet werden.

    http://www.dynsim-fp.de/projekte/c-algorithmen/gekoppelte-populationsbilanzsysteme.html
  • SE-AP25

    Optimizing metabolic regulation in yeast production strains for dynamic conditions

    Prof. Dr. Alexander Bockmayr

    Projektleiter: Prof. Dr. Alexander Bockmayr
    Projekt Mitglieder: Alexandra-M. Reimers
    Laufzeit: 01.12.2015 - 30.11.2018
    Status: laufend
    Standort: Freie Universität Berlin

    Beschreibung

    Microbial strains used in biotechnological industry need to produce their biotechnological products at high yield and at the same time they are desired to be robust to the intrinsic nutrient dynamics of large-scale bioreactors, most noticeably to transient limitations of carbon sources and oxygen. The engineering principles for robustness of metabolism to nutrient dynamics are however not yet well understood. The ROBUSTYEAST project aims to reveal these principles for microbial strain improvement in biotechnological applications using a systems biology approach. This will contribute to establishing evolutionary optimization protocols for making microbial production strains robust against dynamic nutrient conditions. The consortium will study the robustness of Saccharomyces cerevisiae in experiments during the dynamics associated with two cyclic nutrient transitions that are each of major relevance to industry: repeated cycles of glucose and ethanol growth and of aerobic and anaerobic growth. We shall monitor the physiological changes during the evolutionary adaptation of yeast to those transitions, using laboratory-evolution in lab-scale bioreactors (chemostat mode). By combining this data with computational modelling we shall identify the metabolic features that make yeast robust to these industrially relevant condition cycles. The theoretical and computational approaches that the consortium will develop involve optimisation methods applicable to metabolism transiting from one steady state to the next via dynamic regulation. We shall iterate experiments and modelling to improve our models given experimental data, to identify new measurements critical to improve our understanding, and to finally identify key regulatory mechanisms for a robust metabolism of S. cerevisiae, given changes in glucose, ethanol and oxygen concentrations. The robustness of metabolic regulation under dynamic conditions will be evaluated from the kinetic models, and the regulatory interactions that confer such robustness will be determined.

    https://www.erasysapp.eu/calls/2nd-call/robustyeast