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. 92759284, 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. 257283, 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 GeonSi microbridge are given. The highly favorable electronic properties of this design are demonstrated by steadystate simulations of the corresponding van Roosbroeck (driftdiffusion) system. 
P. Farrell, D. Peschka, Challenges for driftdiffusion 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, finiteelement as well as Voronoi finitevolume discretization schemes for the driftdiffusion 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 Lshaped 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. 125/1125/9, DOI 10.1007/s1108201813934 .
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 edgeemitting laser, we consider a driftdiffusion 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. 082115/1082115/11, DOI 10.1063/1.5040985 .
Abstract
This paper investigates a variational approach to viscous flows with contact line dynamics based on energydissipation modeling. The corresponding model is reduced to a thinfilm 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. 
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. 257283, 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 GeonSi microbridge are given. The highly favorable electronic properties of this design are demonstrated by steadystate simulations of the corresponding van Roosbroeck (driftdiffusion) system. 
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. 13295/113295/11, DOI 10.1038/s41598018314181 .
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 twolayer liquid system. As a key result we show that the dewetting rates of such a liquid bilayer 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 PSPMMA interfaces using in situ atomic force microscopy (AFM), and they show excellent agreement. 
G. Lazzaroni, R. Rossi, M. Thomas, R. Toader, Rateindependent damage in thermoviscoelastic materials with inertia, Journal of Dynamics and Differential Equations, 30 (2018), pp. 13111364, DOI 10.1007/s108840189666y .
Abstract
We present a model for rateindependent, unidirectional, partial damage in viscoelastic materials with inertia and thermal effects. The damage process is modeled by means of an internal variable, governed by a rateindependent 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 AmbrosioTortorelli phasefield 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 timediscrete scheme and variational convergence methods. We also carry out the asymptotic analysis for vanishing viscosity and inertia and obtain a fully rateindependent limit model for displacements and damage, which is independent of temperature. 
M. Thomas, C. Bilgen, K. Weinberg, Phasefield fracture at finite strains based on modified invariants: A note on its analysis and simulations, GAMMMitteilungen, 40 (2018), pp. 207237, DOI 10.1002/gamm.201730004 .
Abstract
Phasefield 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 phasefield 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 phasefield model at finite strains, which takes into account the anisotropy of damage by applying an anisotropic split and the modified invariants of the right CauchyGreen 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 timediscrete solutions converge in a weak sense to a solution of the timecontinuous 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 ratedependent/independent system for brittle delamination, in: Proceedings of the INdAMISIMM 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. 127157, DOI 10.1007/9783319759401_7 .
Abstract
We revisit the weak, energetictype existence results obtained in [Rossi/ThomasESAIMCOCV21(1):159,2015] for a system for rateindependent, brittle delamination between two viscoelastic, physically nonlinear bulk materials and explain how to rigorously extend such results to the case of viscoelastic, linearly elastic bulk materials. Our approximation result is essentially based on deducing the Moscoconvergence 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 timecontinuous level, and secondly, to pass from a timediscrete to a timecontinuous model using an adhesive contact approximation of the brittle model, in combination with a vanishing, superquadratic 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 INdAMISIMM Workshop on Trends on Applications of Mathematics to Mechanics, Rome, Italy, September 2016, E. Rocca, U. Stefanelli, L. Truskinovsky, eds., 27 of Springer INdAM Series, Springer International Publishing, Cham, 2018, pp. 179203, DOI 10.1007/9783319759401_9 .
Abstract
We address a model for rateindependent, partial, isotropic damage in quasistatic small strain linear elasticity, featuring a damage variable with spatial BVregularization. Discrete solutions are obtained using an alternate timediscrete scheme and the VariableADMM 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 rateindependent 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. 2738, DOI 10.1007/9789811062834_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

R. Rossi, U. Stefanelli, M. Thomas, Rateindependent 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 rateindependent evolution of sets with finite perimeter. The evolution of the admissible sets is driven by that of a given timedependent 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 timeincremental minimization scheme. In the brittle case, this timediscretization procedure gives rise to evolving sets satisfying the stability condition, but it remains an open problem to additionally deduce energydissipation balance in the timecontinuous 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 twophase 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 nonsmooth twohomogeneous 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, Banff, Canada, April 30, 2019.

D. Peschka, Gradient formulations with flow maps  mathematical and numerical approaches to free boundary problems, Kolloquium des Graduiertenkollegs, May 24  June 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 substrateflow 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.

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, 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 nonisothermal CahnHilliard 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 gradientregularized 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 gradientregularized damage models, PDE Afternoon, Universität Wien, Austria, April 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, Rateindependent 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.

S. Tornquist, Towards the analysis of dynamic phasefield fracture, Spring School on Variational Analysis 2019, Paseky nad Jizerou, Czech Republic, May 19  25, 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 phasefield fracture, Berlin Dresden Prague Würzburg Workshop ``Mathematics of Continuum Mechanics'', November 29  30, 2018.

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

A. Zafferi, Regularity results for a thermodynamically consistent nonisothermal CahnHilliard 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 driftdiffusion simulations of semiconductors: A comparative study of different discretization philosophies, Applied Mathematics and Simulation for Semiconductors (AMaSiS 2018), 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, ZuseInstitut Berlin (ZIB), Berlin, October 31, 2018.

M. Thomas, Analysis and simulation for a phasefield 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 Nonstandard Discretization Methods, Mechanical and Mathematical Analysis'', March 19  23, 2018, Technische Universität München, March 20, 2018.

M. Thomas, Analysis and simulation for a phasefield 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 phasefield 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 Differntial Equations, Germany, June 29, 2018.

M. Thomas, Analysis for the discrete approximation of gradientregularized 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, Malta, May 24, 2018.

M. Thomas, Phasefield fracture at finite strains based on modified invariants, Special Materials and Complex Systems (SMACS 2018), June 17  22, 2018, University of Milan, Department of Mathematics, Gargnano, Italy, June 18, 2018.

M. Thomas, Rateindependent 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 phasefield models of brittle fracture, MATH+ Center Days 2018, October 31  November 2, 2018, ZuseInstitut Berlin (ZIB), Berlin, October 31, 2018.