Publications

Articles in Refereed Journals

  • D. Peschka, S. Haefner, L. Marquant, K. Jacobs, A. Münch, B. Wagner, Signatures of slip in dewetting polymer films, Proceedings of the National Academy of Sciences of the United States of America, 116 (2019), pp. 9275--9284, DOI 10.1073/pnas.1820487116 .

  • L. Adam, M. Hintermüller, D. Peschka, Th.M. Surowiec, Optimization of a multiphysics problem in semiconductor laser design, SIAM Journal on Applied Mathematics, 79 (2019), pp. 257--283, DOI 10.1137/18M1179183 .
    Abstract
    A multimaterial topology optimization framework is suggested for the simultaneous optimization of mechanical and optical properties to be used in the development of optoelectronic devices. Based on the physical aspects of the underlying device, a nonlinear multiphysics model for the elastic and optical properties is proposed. Rigorous proofs are provided for the sensitivity of the fundamental mode of the device with respect to the changes in the underlying topology. After proving existence and optimality results, numerical experiments leading to an optimal material distribution for maximizing the strain in a Ge-on-Si microbridge are given. The highly favorable electronic properties of this design are demonstrated by steady-state simulations of the corresponding van Roosbroeck (drift-diffusion) system.

  • P. Farrell, D. Peschka, Challenges for drift-diffusion simulations of semiconductors: A comparative study of different discretization philosophies, Computers & Mathematics with Applications. An International Journal, published online on 18.06.2019, DOI 10.1016/j.camwa.2019.06.007 .
    Abstract
    We analyze and benchmark the error and the convergence order of finite difference, finite-element as well as Voronoi finite-volume discretization schemes for the drift-diffusion equations describing charge transport in bulk semiconductor devices. Three common challenges, that can corrupt the precision of numerical solutions, will be discussed: boundary layers at Ohmic contacts, discontinuties in the doping profile, and corner singularities in L-shaped domains. The influence on the order of convergence is assessed for each computational challenge and the different discretization schemes. Additionally, we provide an analysis of the inner boundary layer asymptotics near Ohmic contacts to support our observations.

  • D. Peschka, N. Rotundo, M. Thomas, Doping optimization for optoelectronic devices, Optical and Quantum Electronics, 50 (2018), pp. 125/1--125/9, DOI 10.1007/s11082-018-1393-4 .
    Abstract
    We present a mathematical and numerical framework for the optimal design of doping profiles for optoelectronic devices using methods from mathematical optimization. With the goal to maximize light emission and reduce the threshold of an edge-emitting laser, we consider a drift-diffusion model for charge transport and include modal gain and total current into a cost functional, which we optimize in cross sections of the emitter. We present 1D and 2D results for exemplary setups that point out possible routes for device improvement.

  • D. Peschka, Variational approach to dynamic contact angles for thin films, Physics of Fluids, 30 (2018), pp. 082115/1--082115/11, DOI 10.1063/1.5040985 .
    Abstract
    This paper investigates a variational approach to viscous flows with contact line dynamics based on energy-dissipation modeling. The corresponding model is reduced to a thin-film equation and its variational structure is also constructed and discussed. Feasibility of this modeling approach is shown by constructing a numerical scheme in 1D and by computing numerical solutions for the problem of gravity driven droplets. Some implications of the contact line model are highlighted in this setting.

  • S. Bommer, R. Seemann, S. Jachalski, D. Peschka, B. Wagner, Impact of energy dissipation on interface shapes and on rates for dewetting from liquid substrates, Scientific Reports, 8 (2018), pp. 13295/1--13295/11, DOI 10.1038/s41598-018-31418-1 .
    Abstract
    The dependence of the dissipation on the local details of the flow field of a liquid polymer film dewetting from a liquid polymer substrate is shown, solving the free boundary problem for a two-layer liquid system. As a key result we show that the dewetting rates of such a liquid bi-layer system can not be described by a single power law but shows transient behaviour of the rates, changing from increasing to decreasing behaviour. The theoretical predictions on the evolution of morphology and rates of the free surfaces and free interfaces are compared to measurements of the evolution of the polystyrene(PS)-air, the polymethyl methacrylate (PMMA)-air and the PS-PMMA interfaces using in situ atomic force microscopy (AFM), and they show excellent agreement.

  • G. Lazzaroni, R. Rossi, M. Thomas, R. Toader, Rate-independent damage in thermo-viscoelastic materials with inertia, Journal of Dynamics and Differential Equations, 30 (2018), pp. 1311--1364, DOI 10.1007/s10884-018-9666-y .
    Abstract
    We present a model for rate-independent, unidirectional, partial damage in visco-elastic materials with inertia and thermal effects. The damage process is modeled by means of an internal variable, governed by a rate-independent flow rule. The heat equation and the momentum balance for the displacements are coupled in a highly nonlinear way. Our assumptions on the corresponding energy functional also comprise the case of the Ambrosio-Tortorelli phase-field model (without passage to the brittle limit). We discuss a suitable weak formulation and prove an existence theorem obtained with the aid of a (partially) decoupled time-discrete scheme and variational convergence methods. We also carry out the asymptotic analysis for vanishing viscosity and inertia and obtain a fully rate-independent limit model for displacements and damage, which is independent of temperature.

  • M. Thomas, C. Bilgen, K. Weinberg, Phase-field fracture at finite strains based on modified invariants: A note on its analysis and simulations, GAMM-Mitteilungen, 40 (2018), pp. 207--237, DOI 10.1002/gamm.201730004 .
    Abstract
    Phase-field models have already been proven to predict complex fracture patterns in two and three dimensions for brittle fracture at small strains. In this paper we discuss a model for phase-field fracture at finite deformations in more detail. Among the identification of crack location and projection of crack growth the numerical stability is one of the main challenges in solid mechanics. We here present a phase-field model at finite strains, which takes into account the anisotropy of damage by applying an anisotropic split and the modified invariants of the right Cauchy-Green strain tensor. We introduce a suitable weak notion of solution that also allows for a spatial and temporal discretization of the model. In this framework we study the existence of solutions %Second the mathematical background of the approach is examined and and we show that the time-discrete solutions converge in a weak sense to a solution of the time-continuous formulation of the model. Numerical examples in two and three space dimensions are carried out in the range of validity of the analytical results.

Contributions to Collected Editions

  • R. Rossi, M. Thomas, From nonlinear to linear elasticity in a coupled rate-dependent/independent system for brittle delamination, in: Proceedings of the INdAM-ISIMM Workshop on Trends on Applications of Mathematics to Mechanics, Rome, Italy, September 2016, E. Rocca, U. Stefanelli, L. Truskinovsky, A. Visintin, eds., 27 of Springer INdAM Series, Springer International Publishing, Cham, 2018, pp. 127--157, DOI 10.1007/978-3-319-75940-1_7 .
    Abstract
    We revisit the weak, energetic-type existence results obtained in [Rossi/Thomas-ESAIM-COCV-21(1):1-59,2015] for a system for rate-independent, brittle delamination between two visco-elastic, physically nonlinear bulk materials and explain how to rigorously extend such results to the case of visco-elastic, linearly elastic bulk materials. Our approximation result is essentially based on deducing the Mosco-convergence of the functionals involved in the energetic formulation of the system. We apply this approximation result in two different situations: Firstly, to pass from a nonlinearly elastic to a linearly elastic, brittle model on the time-continuous level, and secondly, to pass from a time-discrete to a time-continuous model using an adhesive contact approximation of the brittle model, in combination with a vanishing, super-quadratic regularization of the bulk energy. The latter approach is beneficial if the model also accounts for the evolution of temperature.

  • S. Bartels, M. Milicevic, M. Thomas, Numerical approach to a model for quasistatic damage with spatial $BV$-regularization, in: Proceedings of the INdAM-ISIMM Workshop on Trends on Applications of Mathematics to Mechanics, Rome, Italy, September 2016, E. Rocca, U. Stefanelli, L. Truskinovsky, A. Visintin, eds., 27 of Springer INdAM Series, Springer International Publishing, Cham, 2018, pp. 179--203, DOI 10.1007/978-3-319-75940-1_9 .
    Abstract
    We address a model for rate-independent, partial, isotropic damage in quasistatic small strain linear elasticity, featuring a damage variable with spatial BV-regularization. Discrete solutions are obtained using an alternate time-discrete scheme and the Variable-ADMM algorithm to solve the constrained nonsmooth optimization problem that determines the damage variable at each time step. We prove convergence of the method and show that discrete solutions approximate a semistable energetic solution of the rate-independent system. Moreover, we present our numerical results for two benchmark problems.

  • M. Thomas, A comparison of delamination models: Modeling, properties, and applications, in: Mathematical Analysis of Continuum Mechanics and Industrial Applications II, Proceedings of the International Conference CoMFoS16, P. VAN Meurs, M. Kimura, H. Notsu, eds., 30 of Mathematics for Industry, Springer Nature, Singapore, 2018, pp. 27--38, DOI 10.1007/978-981-10-6283-4_3 .
    Abstract
    This contribution presents recent results in the modeling and the analysis of delamination problems. It addresses adhesive contact, brittle, and cohesive zone models both in a quasistatic and a viscous, dynamic setting for the bulk part. Also different evolution laws for the delaminating surface are discussed.

Preprints, Reports, Technical Reports

  • M.H. Farshbaf Shaker, M. Gugat, H. Heitsch, R. Henrion, Optimal Neumann boundary control of a vibrating string with uncertain initial data and probabilistic terminal constraints, Preprint no. 2626, WIAS, Berlin, 2019, DOI 10.20347/WIAS.PREPRINT.2626 .
    Abstract, PDF (424 kByte)
    In optimal control problems, often initial data are required that are not known exactly in practice. In order to take into account this uncertainty, we consider optimal control problems for a system with an uncertain initial state. A finite terminal time is given. On account of the uncertainty of the initial state, it is not possible to prescribe an exact terminal state. Instead, we are looking for controls that steer the system into a given neighborhood of the desired terminal state with sufficiently high probability. This neighborhood is described in terms of an inequality for the terminal energy. The probabilistic constraint in the considered optimal control problem leads to optimal controls that are robust against the inevitable uncertainties of the initial state. We show the existence of such optimal controls. Numerical examples with optimal Neumann control of the wave equation are presented.

  • R. Rossi, U. Stefanelli, M. Thomas, Rate-independent evolution of sets, Preprint no. 2578, WIAS, Berlin, 2019, DOI 10.20347/WIAS.PREPRINT.2578 .
    Abstract, PDF (475 kByte)
    The goal of this work is to analyze a model for the rate-independent evolution of sets with finite perimeter. The evolution of the admissible sets is driven by that of a given time-dependent set, which has to include the admissible sets and hence is to be understood as an external loading. The process is driven by the competition between perimeter minimization and minimization of volume changes. In the mathematical modeling of this process, we distinguish the adhesive case, in which the constraint that the (complement of) the `external load' contains the evolving sets is penalized by a term contributing to the driving energy functional, from the brittle case, enforcing this constraint. The existence of Energetic solutions for the adhesive system is proved by passing to the limit in the associated time-incremental minimization scheme. In the brittle case, this time-discretization procedure gives rise to evolving sets satisfying the stability condition, but it remains an open problem to additionally deduce energy-dissipation balance in the time-continuous limit. This can be obtained under some suitable quantification of data. The properties of the brittle evolution law are illustrated by numerical examples in two space dimensions.

  • D. Peschka, M. Thomas, T. Ahnert, A. Münch, B. Wagner, Gradient structures for flows of concentrated suspensions, Preprint no. 2543, WIAS, Berlin, 2018, DOI 10.20347/WIAS.PREPRINT.2543 .
    Abstract, PDF (6456 kByte)
    In this work we investigate a two-phase model for concentrated suspensions. We construct a PDE formulation using a gradient flow structure featuring dissipative coupling between fluid and solid phase as well as different driving forces. Our construction is based on the concept of flow maps that also allows it to account for flows in moving domains with free boundaries. The major difference compared to similar existing approaches is the incorporation of a non-smooth two-homogeneous term to the dissipation potential, which creates a normal pressure even for pure shear flows

Talks, Poster

  • D. Peschka, Dynamic contact angles via generalized gradient flows, ``Modelling of Thin Liquid Films - Asymptotic Approach vs. Gradient Dynamics", April 28 - May 3, 2019, Banff International Research Station for Mathematical Information and Discovery, Canada, April 30, 2019.

  • D. Peschka, Dynamic contact angles via gradient flows, 694. WE-Heraeus-Seminar ``Wetting on Soft or Microstructured Surfaces", Bad Honnef, April 10 - 13, 2019.

  • D. Peschka, Gradient formulations with flow maps - mathematical and numerical approaches to free boundary problems, Kolloquium des Graduiertenkollegs, May 24, 2019, Universität Regensburg, May 24, 2019.

  • D. Peschka, Gradient structures for flows of concentrated suspensions - jamming and free boundaries, 90th Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM 2019), Section S11 ``Interfacial Flows", February 18 - 22, 2019, Technische Universität Wien, Austria, February 20, 2019.

  • D. Peschka, Mathematical modeling and simulation of substrate-flow interaction using generalized gradient flow, Begutachtungskolloquium für die Anträge des SPP 2171 ``Dynamische Benetzung flexibler, adaptiver und schaltbarer Oberflächen", Mainz, February 7 - 8, 2019.

  • D. Peschka, Mathematical modeling of fluid flows using gradient systems, Seminar in PDE and Applications, May 27 - 29, 2019, Delft University of Technology, Netherlands, May 28, 2019.

  • D. Peschka, Steering pattern formation of viscous flows, DMV-Jahrestagung 2019, September 23 - 26, 2019, KIT - Karlsruher Institut für Technologie, September 23, 2019.

  • D. Peschka, ``Numerical methods for charge transport in semiconductors: FEM vs FV", 9th International Congress on Industrial and Applied Mathematics (ICIAM 2019), July 15 - 19, 2019, Valencia, Spain, July 17, 2019.

  • S. Tornquist, Variational problems involving Caccioppoli partitions, 90th Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM 2019), Section S14 ``Applied Analysis", February 18 - 22, 2019, Technische Universität Wien, Austria, February 19, 2019.

  • A. Zafferi, An approach to multi-phase flows in geosciences, MURPHYS-HSFS 2019 Summer School on Multi-Rate Processes, Slow-Fast Systems and Hysteresis, Turin, Italy, June 17 - 21, 2019.

  • A. Zafferi, Dynamics of rock dehydration on multiple scales, SCCS Days 2019 of the Collaborative Research Center - CRC 1114, May 20 - 22, 2019.

  • A. Zafferi, Some regularity results for a non-isothermal Cahn-Hilliard model, 90th Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM 2019), Section S14 ``Applied Analysis'', February 18 - 22, 2019, Technische Universität Wien, Austria, February 20, 2019.

  • M. Thomas, Analysis for the discrete approximation of gradient-regularized damage models, Mathematics Seminar Brescia, March 11 - 14, 2019, Università degli Studi di Brescia, Italy, March 13, 2019.

  • M. Thomas, Analysis for the discrete approximation of gradient-regularized damage models, PDE Afternoon, Universität Wien, Austria, April 10, 2019.

  • M. Thomas, Analytical and numerical aspects of rate-independent gradient-regularized damage models, ``Dynamics, Equations and Applications" (DEA), September 16 - 20, 2019, AGH University of Science and Technology, Kraków, Poland, September 19, 2019.

  • M. Thomas, Convergence of a numerical method for quasistatic, rate-independent damage evolution, ECCOMAS Thematic Conference ``Modern Finite Element Technologies 2019", July 1 - 3, 2019, Physikzentrum Bad Honnef, July 2, 2019.

  • M. Thomas, Coupling of rate-independent and rate-dependent systems, MURPHYS-HSFS 2019 Summer School on Multi-Rate Processes, Slow-Fast Systems and Hysteresis, June 17 - 19, 2019, Politecnico di Torino, Turin, Italy.

  • M. Thomas, Coupling of rate-independent and rate-dependent systems with application to delamination processes in solids, Mathematics for Mechanics, October 29 - November 1, 2019, Czech Academy of Sciences, Prague, Czech Republic, October 31, 2019.

  • M. Thomas, Coupling of rate-independent and rate-dependent systems with application to delamination processes in solids, Seminar ``Applied and Computational Analysis", University of Cambridge, UK, October 10, 2019.

  • M. Thomas, Dynamics of rock dehydration on multiple scales, SCCS Days 2019 of the Collaborative Research Center - CRC 1114, May 20 - 22, 2019, Freie Universität Berlin, Zeuthen, May 21, 2019.

  • M. Thomas, GENERIC structures with bulk-interface interaction, SFB 910 Symposium ``Energy based modeling, simulation and control", October 25, 2019, Technische Universität Berlin, October 25, 2019.

  • M. Thomas, Rate-independent evolution of sets and application to fracture processes, 90th Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM 2019), Section S14 ``Applied Analysis", February 18 - 22, 2019, Technische Universität Wien, Austria, February 20, 2019.

  • M. Thomas, ``Analytical and numerical aspects for the approximation of gradient-regularized damage models", Thematic Minisymposium MS A3-2-26 ``Phase-Field Models in Simulation and Optimization", ``9th International Congress on Industrial and Applied Mathematics" (ICIAM 2019), July 15 - 19, 2019, Universitat de València, Spain, July 17, 2019.

  • M. Thomas, ``Gradient structures for flows of concentrated suspensions", Thematic Minisymposium MS ME-0-75 ``Recent advances in understanding suspensions and granular media flow", ``9th International Congress on Industrial and Applied Mathematics" (ICIAM 2019), July 15 - 19, 2019, Universitat de València, Spain, July 17, 2019.

  • S. Tornquist, Towards the analysis of dynamic phase-field fracture, ``Spring School on Variational Analysis 2019", Paseky, Czech Republic, May 19 - 25, 2019.

  • S. Tornquist, Towards the analysis of dynamic phase-field fracture, MURPHYS-HSFS 2019 Summer School on Multi-Rate Processes, Slow-Fast Systems and Hysteresis, Turin, Italy, June 17 - 21, 2019.

  • D. Peschka, Droplet and satellite droplet shedding in dewetting polymer films, 89th Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM 2018), Section S11 ``Interfacial Flows'', March 19 - 23, 2018, Technische Universität München, March 21, 2018.

  • D. Peschka, Steering pattern formation during dewetting with interface and contact lines properties, The 20th European Conference on Mathematics for Industry (ECMI 2018), Minisymposium 38 ``ECMI Special Interest Group: Material Design and Performance in Sustainable Energies'', June 18 - 22, 2018, Budapest, Hungary, June 21, 2018.

  • D. Peschka, Topics for the SPP 2171: Variational modeling for fluid flows on substrates with dissipation, Dynamic Wetting of Flexible Adaptive and Switchable Surfaces, May 17 - 18, 2018, University of Münster, Center for Nonlinear Science, May 17, 2018.

  • S. Tornquist, Towards the analysis of dynamic phase-field fracture, 3rd Berlin Dresden Prague Würzburg Workshop ``Mathematics of Continuum Mechanics'', Würzburg, November 29 - 30, 2018.

  • A. Zafferi, Flows of concentrated suspensions in geosciences, 3rd Berlin Dresden Prague Würzburg Workshop ``Mathematics of Continuum Mechanics'', Würzburg, November 29 - 30, 2018.

  • A. Zafferi, Regularity results for a thermodynamically consistent non-isothermal Cahn--Hilliard model, Summer School ``Dissipative Dynamical Systems and Applications'', September 3 - 7, 2018, University of Modena, Department of Physics, Informatics and Mathematics, Italy, September 6, 2018.

  • P. Farrell, D. Peschka, Challenges for drift-diffusion simulations of semiconductors: A comparative study of different discretization philosophies, Applied Mathematics and Simulation for Semiconductors (AMaSiS 2018), WIAS Berlin, October 8 - 10, 2018.

  • M. Thomas, D. Peschka, B. Wagner, V. Mehrmann, M. Rosenau, Modeling and analysis of suspension flows, MATH+ Center Days 2018, October 31 - November 2, 2018, Zuse-Institut Berlin (ZIB), Berlin, October 31, 2018.

  • M. Thomas, Analysis and simulation for a phase-field fracture model at finite strains based on modified invariants, 89th Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM 2018), Section DFG Priority Programmes PP1748 ``Reliable Simulation Techniques in Solid Mechanics. Development of Non-standard Discretization Methods, Mechanical and Mathematical Analysis'', March 19 - 23, 2018, Technische Universität München, March 20, 2018.

  • M. Thomas, Analysis and simulation for a phase-field fracture model at finite strains based on modified invariants, Workshop ``Special Materials and Complex Systems'' (SMACS 2018), June 18 - 22, 2018, University of Milan/University of Pavia, Gargnano, Italy, June 18, 2018.

  • M. Thomas, Analysis and simulation for a phase-field fracture model at finite strains based on modified invariants, Analysis Seminar, University of Brescia, Department of Mathematics, Italy, May 10, 2018.

  • M. Thomas, Analysis for the discrete approximation of damage and fracture, Applied Analysis Day, June 28 - 29, 2018, Technische Universität Dresden, Chair of Partial Differential Equations, June 29, 2018.

  • M. Thomas, Analysis for the discrete approximation of gradient-regularized damage models, Workshop ``Women in Mathematical Materials Science'', November 5 - 6, 2018, Universität Regensburg, Fakultät für Mathematik, November 6, 2018.

  • M. Thomas, Analytical and numerical approach to a class of damage models, The 12th AIMS Conference on Dynamical Systems, Differential Equations and Applications, Special Session 75 ``Mathematics and Materials: Models and Applications'', July 5 - 9, 2018, National Taiwan University, Taipeh, Taiwan, Province Of China, July 6, 2018.

  • M. Thomas, Analytical and numerical aspects of damage models, Berlin Dresden Prague Würzburg Workshop ``Mathematics of Continuum Mechanics'', November 29 - 30, 2018, Technische Universität Würzburg, Institut für Mathematik, November 30, 2018.

  • M. Thomas, Dynamics of rock dehydration on multiple scales, Begutachtung SFB 1114: Scaling Cascades in Complex Systems, Freie Universität Berlin, February 27 - 28, 2018.

  • M. Thomas, Gradient structures for flows of concentrated suspensions, The 12th AIMS Conference on Dynamical Systems, Differential Equations and Applications, Special Session 18 ``Emergence and Dynamics of Patterns in Nonlinear Partial Differential Equations and Related Fields'', July 5 - 9, 2018, National Taiwan University, Taipeh, Taiwan, Province Of China, July 7, 2018.

  • M. Thomas, Optimization of the radiative emission for mechanically strained optoelectronic semiconductor devices, 9th International Conference ``Inverse Problems: Modeling and Simulation'' (IPMS 2018), Minisymposium M16 ``Inverse and Control Problems in Mechanics'', May 21 - 25, 2018, The Eurasian Association on Inverse Problems, Malta, May 24, 2018.

  • M. Thomas, Rate-independent evolution of sets & applications to damage and delamination, PDEs Friends, June 21 - 22, 2018, Politecnico di Torino, Dipartimento di Scienze Matematiche ``Giuseppe Luigi Lagrange'', Italy, June 22, 2018.

  • M. Thomas, Reliable error estimates for phase-field models of brittle fracture, MATH+ Center Days 2018, October 31 - November 2, 2018, Zuse-Institut Berlin (ZIB), Berlin, October 31, 2018.