Publications
Monographs

O. Marquardt, V.M. Kaganer, P. Corfdir, Chapter 12: Nanowires, in: Vol. 1 of Handbook of Optoelectronic Device Modeling and Simulations: Fundamentals, Materials, Nanostructures, LEDs, and Amplifiers, J. Piprek, ed., Series in Optics and Optoelectronics, CRC Press, Taylor & Francis Group, Boca Raton, 2017, pp. 395415, (Chapter Published).

S. Jachalski, D. Peschka, S. Bommer, R. Seemann, B. Wagner, Chapter 18: Structure Formation in Thin LiquidLiquid Films, in: Transport Processes at Fluidic Interfaces, D. Bothe, A. Reusken, eds., Advances in Mathematical Fluid Mechanics, Birkhäuser, Springer International Publishing AG, Cham, 2017, pp. 531574, (Chapter Published), DOI 10.1007/9783319566023 .
Abstract
We revisit the problem of a liquid polymer that dewets from another liquid polymer substrate with the focus on the direct comparison of results from mathematical modeling, rigorous analysis, numerical simulation and experimental investigations of rupture, dewetting dynamics and equilibrium patterns of a thin liquidliquid system. The experimental system uses as a model system a thin polystyrene (PS) / polymethylmethacrylate (PMMA) bilayer of a few hundred nm. The polymer systems allow for in situ observation of the dewetting process by atomic force microscopy (AFM) and for a precise ex situ imaging of the liquidliquid interface. In the present study, the molecular chain length of the used polymers is chosen such that the polymers can be considered as Newtonian liquids. However, by increasing the chain length, the rheological properties of the polymers can be also tuned to a viscoelastic flow behavior. The experimental results are compared with the predictions based on the thin film models. The system parameters like contact angle and surface tensions are determined from the experiments and used for a quantitative comparison. We obtain excellent agreement for transient drop shapes on their way towards equilibrium, as well as dewetting rim profiles and dewetting dynamics. 
P. Farrell, N. Rotundo, D.H. Doan, M. Kantner, J. Fuhrmann, Th. Koprucki, Chapter 50: DriftDiffusion Models, in: Vol. 2 of Handbook of Optoelectronic Device Modeling and Simulation: Lasers, Modulators, Photodetectors, Solar Cells, and Numerical Methods, J. Piprek, ed., Series in Optics and Optoelectronics, CRC Press, Taylor & Francis Group, Boca Raton, 2017, pp. 733771, (Chapter Published).

H.Chr. Kaiser, D. Knees, A. Mielke, J. Rehberg, E. Rocca, M. Thomas, E. Valdinoci, eds., PDE 2015: Theory and Applications of Partial Differential Equations, 10 of Discrete and Continuous Dynamical Systems  Series S, American Institute of Mathematical Science, Springfield, 2017, iv+933 pages, (Collection Published).
Abstract
HAGs von Christoph bestätigen lassen 
P. Colli, A. Favini, E. Rocca, G. Schimperna, J. Sprekels, eds., Solvability, Regularity, and Optimal Control of Boundary Value Problems for PDEs: In Honour of Prof. Gianni Gilardi, 22 of Springer INdAM Series, Springer International Publishing AG, Cham, 2017, xii+571 pages, (Collection Published).
Abstract
This volume gathers contributions in the field of partial differential equations, with a focus on mathematical models in phase transitions, complex fluids and thermomechanics. These contributions are dedicated to Professor Gianni Gilardi on the occasion of his 70th birthday. It particularly develops the following thematic areas: nonlinear dynamic and stationary equations; wellposedness of initial and boundary value problems for systems of PDEs; regularity properties for the solutions; optimal control problems and optimality conditions; feedback stabilization and stability results. Most of the articles are presented in a selfcontained manner, and describe new achievements and/or the state of the art in their line of research, providing interested readers with an overview of recent advances and future research directions in PDEs.
Articles in Refereed Journals

D. Peschka, N. Rotundo, M. Thomas, Doping optimization for optoelectronic devices, Optical and Quantum Electronics, (2018), 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. 
P. Colli, G. Gilardi, J. Sprekels, Optimal boundary control of a nonstandard viscous CahnHilliard system with dynamic boundary condition, Nonlinear Analysis. Theory, Methods & Applications. An International Multidisciplinary Journal. Series A: Theory and Methods, 170 (2018), pp. 171196, DOI 10.1016/j.na.2018.01.003 .
Abstract
In this paper, we study an optimal boundary control problem for a model for phase separation taking place in a spatial domain that was introduced by PodioGuidugli in Ric. Mat. 55 (2006), pp. 105118. The model consists of a strongly coupled system of nonlinear parabolic differential equations, in which products between the unknown functions and their time derivatives occur that are difficult to handle analytically. In contrast to the existing control literature about this PDE system, we consider here a dynamic boundary condition involving the LaplaceBeltrami operator for the order parameter of the system, which models an additional nonconserving phase transition occurring on the surface of the domain. We show the Fr&aecute;chenett differentiability of the associated controltostate operator in appropriate Banach spaces and derive results on the existence of optimal controls and on firstorder necessary optimality conditions in terms of a variational inequality and the adjoint state system. 
D. Horstmann, J. Rehberg, H. Meinlschmidt, The full KellerSegel model is wellposed on fairly general domains, Nonlinearity, 31 (2018), pp. 15601592, DOI 10.1088/13616544/aaa2e1 .
Abstract
In this paper we prove the wellposedness of the full KellerSegel system, a quasilinear strongly coupled reactioncrossdiffusion system, in the spirit that it always admits a unique localintime solution in an adequate function space, provided that the initial values are suitably regular. Apparently, there exists no comparable existence result for the full KellerSegel system up to now. The proof is carried out for general source terms and is based on recent nontrivial elliptic and parabolic regularity results which hold true even on fairly general spatial domains, combined with an abstract solution theorem for nonlocal quasilinear equations by Amann. 
P. Corfdir, H. Li, O. Marquardt, G. Gao, M.R. Molas, J.K. Zettler, D. VAN Treeck, T. Flissikowski, M. Potemski, C. Draxl, A. Trampert, S. FernándezGarrido, H.T. Grahn, O. Brandt, Crystalphase quantum wires: Onedimensional heterostructures with atomically flat interfaces, Nano Letters, 18 (2018), pp. 247254, DOI 10.1021/acs.nanolett.7b03997 .

B. Drees, A. Kraft, Th. Koprucki, Reproducible research through persistently linked and visualized data, Optical and Quantum Electronics, 50 (2018), pp. 59/159/10, DOI 10.1007/s1108201813271 .
Abstract
The demand of reproducible results in the numerical simulation of optoelectronic devices or more general in mathematical modeling and simulation requires the (longterm) accessibility of data and software that were used to generate those results. Moreover, to present those results in a comprehensible manner data visualizations such as videos are useful. Persistent identifier can be used to ensure the permanent connection of these different digital objects thereby preserving all information in the right context. Here we give an overview over the stateofthe art of data preservation, data and software citation and illustrate the benefits and opportunities of enhancing publications with visual simulation data by showing a use case from optoelectronics. 
TH. Koprucki, M. Kohlhase, K. Tabelow, D. Müller, F. Rabe, Model pathway diagrams for the representation of mathematical models, Optical and Quantum Electronics, (2018), published online on 23.01.2018, DOI 10.1007/s1108201813217 .
Abstract
Mathematical models are the foundation of numerical simulation of optoelectronic devices. We present a concept for a machineactionable as well as humanunderstandable representation of the mathematical knowledge they contain and the domainspecific knowledge they are based on. We propose to use theory graphs to formalize mathematical models and model pathway diagrams to visualize them. We illustrate our approach by application to the van Roosbroeck system describing the carrier transport in semiconductors by drift and diffusion. We introduce an approach for the blockbased composition of models from simpler components. 
K. Disser, A.F.M. TER Elst, J. Rehberg, On maximal parabolic regularity for nonautonomous parabolic operators, Journal of Differential Equations, 262 (2017), pp. 20392072.
Abstract
We consider linear inhomogeneous nonautonomous parabolic problems associated to sesquilinear forms, with discontinuous dependence of time. We show that for these problems, the property of maximal parabolic regularity can be extrapolated to time integrability exponents r ≠ 2. This allows us to prove maximal parabolic L^{r}regularity for discontinuous nonautonomous secondorder divergence form operators in very general geometric settings and to prove existence results for related quasilinear equations. 
K. Disser, J. Rehberg, A.F.M. TER Elst, Hölder estimates for parabolic operators on domains with rough boundary, Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie V, XVII (2017), pp. 6579.
Abstract
In this paper we investigate linear parabolic, secondorder boundary value problems with mixed boundary conditions on rough domains. Assuming only boundedness/ellipticity on the coefficient function and very mild conditions on the geometry of the domain  including a very weak compatibility condition between the Dirichlet boundary part and its complement  we prove Hölder continuity of the solution in space and time. 
S. Reichelt, Corrector estimates for a class of imperfect transmission problems, Asymptotic Analysis, 105 (2017), pp. 326, DOI 10.3233/ASY171432 .
Abstract
Based on previous homogenization results for imperfect transmission problems in twocomponent domains with periodic microstructure, we derive quantitative estimates for the difference between the microscopic and macroscopic solution. This difference is of order ερ, where ε > 0 describes the periodicity of the microstructure and ρ ∈ (0 , ½] depends on the transmission condition at the interface between the two components. The corrector estimates are proved without assuming additional regularity for the local correctors using the periodic unfolding method. 
M. Heida, A. Mielke, Averaging of timeperiodic dissipation potentials in rateindependent processes, Discrete and Continuous Dynamical Systems  Series S, 10 (2017), pp. 13031327.
Abstract
We study the existence and wellposedness of rateindependent systems (or hysteresis operators) with a dissipation potential that oscillates in time with period ε. In particular, for the case of quadratic energies in a Hilbert space, we study the averaging limit ε→0 and show that the effctive dissipation potential is given by the minimum of all friction thresholds in one period, more precisely as the intersection of all the characteristic domains. We show that the rates of the process do not converge weakly, hence our analysis uses the notion of energetic solutions and relies on a detailed estimates to obtain a suitable equicontinuity of the solutions in the limit ε→0. 
M. Heida, Stochastic homogenization of rateindependent systems, Continuum Mechanics and Thermodynamics, 29 (2017), pp. 853894, DOI 10.1007/s001610170564z .
Abstract
We study the stochastic and periodic homogenization 1homogeneous convex functionals. We proof some convergence results with respect to stochastic twoscale convergence, which are related to classical Gammaconvergence results. The main result is a general liminfestimate for a sequence of 1homogeneous functionals and a twoscale stability result for sequences of convex sets. We apply our results to the homogenization of rateindependent systems with 1homogeneous dissipation potentials and quadratic energies. In these applications, both the energy and the dissipation potential have an underlying stochastic microscopic structure. We study the particular homogenization problems of PrandltReuss plasticity, Coulomb friction on a macroscopic surface and Coulomb friction on microscopic fissure. 
M. Kantner, M. Mittnenzweig, Th. Koprucki, Hybrid quantumclassical modeling of quantum dot devices, Phys. Rev. B., 96 (2017), pp. 205301/1205301/17, DOI 10.1103/PhysRevB.96.205301 .
Abstract
The design of electrically driven quantum dot devices for quantum optical applications asks for modeling approaches combining classical device physics with quantum mechanics. We connect the wellestablished fields of semiclassical semiconductor transport theory and the theory of open quantum systems to meet this requirement. By coupling the van Roosbroeck system with a quantum master equation in Lindblad form, we obtain a new hybrid quantumclassical modeling approach, which enables a comprehensive description of quantum dot devices on multiple scales: It allows the calculation of quantum optical figures of merit and the spatially resolved simulation of the current flow in realistic semiconductor device geometries in a unified way. We construct the interface between both theories in such a way, that the resulting hybrid system obeys the fundamental axioms of (non)equilibrium thermodynamics. We show that our approach guarantees the conservation of charge, consistency with the thermodynamic equilibrium and the second law of thermodynamics. The feasibility of the approach is demonstrated by numerical simulations of an electrically driven singlephoton source based on a single quantum dot in the stationary and transient operation regime. 
M. Liero, A. Mielke, M.A. Peletier, D.R.M. Renger, On microscopic origins of generalized gradient structures, Discrete and Continuous Dynamical Systems  Series S, 10 (2017), pp. 135, DOI 10.3934/dcdss.2017001 .
Abstract
Classical gradient systems have a linear relation between rates and driving forces. In generalized gradient systems we allow for arbitrary relations derived from general nonquadratic dissipation potentials. This paper describes two natural origins for these structures. A first microscopic origin of generalized gradient structures is given by the theory of largedeviation principles. While Markovian diffusion processes lead to classical gradient structures, Poissonian jump processes give rise to coshtype dissipation potentials. A second origin arises via a new form of convergence, that we call EDPconvergence. Even when starting with classical gradient systems, where the dissipation potential is a quadratic functional of the rate, we may obtain a generalized gradient system in the evolutionary Gammalimit. As examples we treat (i) the limit of a diffusion equation having a thin layer of low diffusivity, which leads to a membrane model, and (ii) the limit of diffusion over a high barrier, which gives a reactiondiffusion system. 
M. Liero, A. Mielke, G. Savaré, Optimal entropytransport problems and a new HellingerKantorovich distance between positive measures, Inventiones mathematicae, (2017), 149, DOI 10.1007/s0022201707598 .
Abstract
We develop a full theory for the new class of Optimal EntropyTransport problems between nonnegative and finite Radon measures in general topological spaces. They arise quite naturally by relaxing the marginal constraints typical of Optimal Transport problems: given a couple of finite measures (with possibly different total mass), one looks for minimizers of the sum of a linear transport functional and two convex entropy functionals, that quantify in some way the deviation of the marginals of the transport plan from the assigned measures. As a powerful application of this theory, we study the particular case of Logarithmic EntropyTransport problems and introduce the new HellingerKantorovich distance between measures in metric spaces. The striking connection between these two seemingly far topics allows for a deep analysis of the geometric properties of the new geodesic distance, which lies somehow between the wellknown HellingerKakutani and KantorovichWasserstein distances. 
O. Marquardt, Th. Krause, V. Kaganer, J. MartinSánchez, M. Hanke, O. Brandt, Influence of strain relaxation in axial $In_xGa_1xN/GaN$ nanowire heterostructures on their electronic properties, Nanotechnology, 28 (2017), pp. 215204/1215204/6, DOI 10.1088/13616528/aa6b73 .
Abstract
We present a systematic theoretical study of the influence of elastic strain relaxation on the builtin electrostatic potentials and the electronic properties of axial In_{x}Ga_{1x}N/GaN nanowire (NW) heterostructures. Our simulations reveal that for a sufficiently large ratio between the thickness of the In_{x}Ga_{1x}N disk and the diameter of the NW, the elastic relaxation leads to a significant reduction of the builtin electrostatic potential in comparison to a planar system of similar layer thickness and In content. In this case, the ground state transition energies approach constant values with increasing thickness of the disk and only depend on the In content, a behavior usually associated to that of a quantum well free of builtin electrostatic potentials. We show that the structures under consideration are by no means fieldfree, and the builtin potentials continue to play an important role even for ultrathin NWs. In particular, strain and the resulting polarization potentials induce complex confinement features of electrons and holes, which depend on the In content, shape, and dimensions of the heterostructure. 
O. Marquardt, M. Ramsteiner, P. Corfdir, L. Geelhaar, O. Brandt, Modeling the electronic properties of GaAs polytype nanostructures: Impact of strain on the conduction band character, Phys. Rev. B., 95 (2017), pp. 245309/1245309/8, DOI 10.1103/PhysRevB.95.245309 .
Abstract
We study the electronic properties of GaAs nanowires composed of both the zincblende and wurtzite modifications using a tenband kp model. In the wurtzite phase, two energetically close conduction bands are of importance for the confinement and the energy levels of the electron ground state. These bands form two intersecting potential landscapes for electrons in zincblende/wurtzite nanostructures. The energy difference between the two bands depends sensitively on strain, such that even small strains can reverse the energy ordering of the two bands. This reversal may already be induced by the nonnegligible lattice mismatch between the two crystal phases in polytype GaAs nanostructures, a fact that was ignored in previous studies of these structures. We present a systematic study of the influence of intrinsic and extrinsic strain on the electron ground state for both purely zincblende and wurtzite nanowires as well as for polytype superlattices. The coexistence of the two conduction bands and their opposite strain dependence results in complex electronic and optical properties of GaAs polytype nanostructures. In particular, both the energy and the polarization of the lowest intersubband transition depends on the relative fraction of the two crystal phases in the nanowire. 
M. Mittnenzweig, A. Mielke, An entropic gradient structure for Lindblad equations and couplings of quantum systems to macroscopic models, Journal of Statistical Physics, 167 (2017), pp. 205233, DOI 10.1007/s1095501717564 .
Abstract
We show that all Lindblad operators (i.e. generators of quantum semigroups) on a finitedimensional Hilbert space satisfying the detailed balance condition with respect to the thermal equilibrium state can be written as a gradient system with respect to the relative entropy. We discuss also thermodynamically consistent couplings to macroscopic systems, either as damped Hamiltonian systems with constant temperature or as GENERIC systems. 
H. Neidhardt, A. Stephan, V.A. Zagrebnov, On convergence rate estimates for approximations of solution operators of linear nonautonomous evolution equations, Nanosystems: Physics, Chemistry, Mathematics, 8 (2017), pp. 202215, DOI 10.17586/22208054201782202215 .
Abstract
We improve some recent estimates of the rate of convergence for product approximations of solution operators for linear nonautonomous Cauchy problem. The Trotter product formula approximation is proved to converge to the solution operator in the operatornorm. We estimate the rate of convergence of this approximation. The result is applied to diffusion equation perturbed by a timedependent potential. 
R. Rossi, M. Thomas, Coupling rateindependent and ratedependent processes: Existence results, SIAM Journal on Mathematical Analysis, 49 (2017), pp. 14191494.
Abstract
We address the analysis of an abstract system coupling a rateindependet process with a second order (in time) nonlinear evolution equation. We propose suitable weak solution concepts and obtain existence results by passing to the limit in carefully devised timediscretization schemes. Our arguments combine techniques from the theory of gradient systems with the toolbox for rateindependent evolution, thus reflecting the mixed character of the problem. Finally, we discuss applications to a class of rateindependent processes in viscoelastic solids with inertia, and to a recently proposed model for damage with plasticity. 
R. Rossi, M. Thomas, From adhesive to brittle delamination in viscoelastodynamics, Mathematical Models & Methods in Applied Sciences, 27 (2017), pp. 14891546, DOI 10.1142/S0218202517500257 .
Abstract
In this paper we analyze a system for brittle delamination between two viscoelastic bodies, also subject to inertia, which can be interpreted as a model for dynamic fracture. The rateindependent flow rule for the delamination parameter is coupled with the momentum balance for the displacement, including inertia. This model features a nonsmooth constraint ensuring the continuity of the displacements outside the crack set, which is marked by the support of the delamination parameter. A weak solvability concept, generalizing the notion of energetic solution for rateindependent systems to the present mixed ratedependent/rateindependent frame, is proposed. Via refined variational convergence techniques, existence of solutions is proved by passing to the limit in approximating systems which regularize the nonsmooth constraint by conditions for adhesive contact. The presence of the inertial term requires the design of suitable recovery spaces small enough to provide compactness but large enough to recover the information on the crack set in the limit. 
J. Behrndt, M.M. Malamud, H. Neidhardt, Scattering matrices and DirichlettoNeumann maps, Journal of Functional Analysis, 273 (2017), pp. 19702025, DOI 10.1016/j.jfa.2017.06.001 .
Abstract
A general representation formula for the scattering matrix of a scattering system consisting of two selfadjoint operators in terms of an abstract operator valued Titchmarsh?Weyl mfunction is proved. This result is applied to scattering problems for different selfadjoint realizations of Schrödinger operators on unbounded domains, Schrödinger operators with singular potentials supported on hypersurfaces, and orthogonal couplings of Schrödinger operators. In these applications the scattering matrix is expressed in an explicit form with the help of DirichlettoNeumann maps. 
P. Colli, G. Gilardi, E. Rocca, J. Sprekels, Optimal distributed control of a diffuse interface model of tumor growth, Nonlinearity, 30 (2017), pp. 25182546.
Abstract
In this paper, a distributed optimal control problem is studied for a diffuse interface model of tumor growth which was proposed by HawkinsDaruud et al. in citeHZO. The model consists of a CahnHilliard equation for the tumor cell fraction $vp$ coupled to a reactiondiffusion equation for a function $s$ representing the nutrientrich extracellular water volume fraction. The distributed control $u$ monitors as a righthand side the equation for $s$ and can be interpreted as a nutrient supply or a medication, while the cost function, which is of standard tracking type, is meant to keep the tumor cell fraction under control during the evolution. We show that the controltostate operator is Fréchet differentiable between appropriate Banach spaces and derive the firstorder necessary optimality conditions in terms of a variational inequality involving the adjoint state variables. 
P. Colli, G. Gilardi, E. Rocca, J. Sprekels, Asymptotic analyses and error estimates for a CahnHilliard type phase field system modelling tumor growth, Discrete and Continuous Dynamical Systems, 10 (2017), pp. 3754.
Abstract
This paper is concerned with a phase field system of CahnHilliard type that is related to a tumor growth model and consists of three equations in gianni terms of the variables order parameter, chemical potential and nutrient concentration. This system has been investigated in the recent papers citeCGH and citeCGRS gianni from the viewpoint of wellposedness, long time bhv and asymptotic convergence as two positive viscosity coefficients tend to zero at the same time. Here, we continue the analysis performed in citeCGRS by showing two independent sets of results as just one of the coefficents tends to zero, the other remaining fixed. We prove convergence results, uniqueness of solutions to the two resulting limit problems, and suitable error estimates 
P. Colli, G. Gilardi, J. Sprekels, Distributed optimal control of a nonstandard nonlocal phase field system with double obstacle potential, Evolution Equations and Control Theory, 6 (2017), pp. 3558.
Abstract
This paper is concerned with a distributed optimal control problem for a nonlocal phase field model of CahnHilliard type, which is a nonlocal version of a model for twospecies phase segregation on an atomic lattice under the presence of diffusion. The local model has been investigated in a series of papers by P. PodioGuidugli and the present authors the nonlocal model studied here consists of a highly nonlinear parabolic equation coupled to an ordinary differential inclusion of subdifferential type. The inclusion originates from a free energy containing the indicator function of the interval in which the order parameter of the phase segregation attains its values. It also contains a nonlocal term modeling longrange interactions. Due to the strong nonlinear couplings between the state variables (which even involve products with time derivatives), the analysis of the state system is difficult. In addition, the presence of the differential inclusion is the reason that standard arguments of optimal control theory cannot be applied to guarantee the existence of Lagrange multipliers. In this paper, we employ recent results proved for smooth logarithmic potentials and perform a socalled `deep quench' approximation to establish existence and firstorder necessary optimality conditions for the nonsmooth case of the double obstacle potential. 
P. Colli, G. Gilardi, J. Sprekels, Global existence for a nonstandard viscous CahnHilliard system with dynamic boundary condition, SIAM Journal on Mathematical Analysis, 49 (2017), pp. 17321760, DOI 10.1137/16M1087539 .
Abstract
In this paper, we study a model for phase segregation taking place in a spatial domain that was introduced by PodioGuidugli in Ric. Mat. 55 (2006), pp. 105118. The model consists of a strongly coupled system of nonlinear parabolic differential equations, in which products between the unknown functions and their time derivatives occur that are difficult to handle analytically. In contrast to the existing literature about this PDE system, we consider here a dynamic boundary condition involving the LaplaceBeltrami operator for the order parameter. This boundary condition models an additional nonconserving phase transition occurring on the surface of the domain. Different wellposedness results are shown, depending on the smoothness properties of the involved bulk and surface free energies. 
P. Colli, G. Gilardi, J. Sprekels, Recent results on the CahnHilliard equation with dynamic boundary condition, Bulletin of the South Ural State University, Series: Mathematical Modelling, Programming and Computer Software, 10 (2017), pp. 521.

P. Exner, A.S. Kostenko, M.M. Malamud, H. Neidhardt, Infinite quantum graphs, Rossiiskaya Akademiya Nauk. Doklady Akademii Nauk, 472 (2017), pp. 253258, DOI 10.1134/S1064562417010136 .
Abstract
Infinite quantum graphs with ?interactions at vertices are studied without any assumptions on the lengths of edges of the underlying metric graphs. A connection between spectral properties of a quantum graph and a certain discrete Laplacian given on a graph with infinitely many vertices and edges is established. In particular, it is shown that these operators are selfadjoint, lower semibounded, nonnegative, discrete, etc. only simultaneously. 
P. Krejčí, E. Rocca, J. Sprekels, Unsaturated deformable porous media flow with thermal phase transition, Mathematical Models & Methods in Applied Sciences, 27 (2017), pp. 26752710, DOI 10.1142/S0218202517500555 .
Abstract
In the present paper, a continuum model is introduced for fluid flow in a deformable porous medium, where the fluid may undergo phase transitions. Typically, such problems arise in modeling liquidsolid phase transformations in groundwater flows. The system of equations is derived here from the conservation principles for mass, momentum, and energy and from the ClausiusDuhem inequality for entropy. It couples the evolution of the displacement in the matrix material, of the capillary pressure, of the absolute temperature, and of the phase fraction. Mathematical results are proved under the additional hypothesis that inertia effects and shear stresses can be neglected. For the resulting highly nonlinear system of two PDEs, one ODE and one ordinary differential inclusion with natural initial and boundary conditions, existence of global in time solutions is proved by means of cutoff techniques and suitable Mosertype estimates. 
M.M. Malamud, H. Neidhardt, H. Peller, A trace formula for functions of contractions and analytic operator Lipschitz functions, Comptes Rendus Mathematique. Academie des Sciences. Paris, 355 (2017), pp. 806811, DOI 10.1016/j.crma.2017.06.003 .
Abstract
In this note, we study the problem of evaluating the trace of $f(T)  F(R)$, where $T$ and $R$ are contractions on a Hilbert space with trace class difference, i.e. $TR in mathbf S_1$, and $f$ is a function analytic in the unit disk $mathbb D$. It is well known that if $f$ is an operator Lipschitz function analytic in $mathbb D$, then $f(T)  f(R) in mathbf S_1$. The main result of the note says that there exists a function $xi$ (a spectral shift function) on the unit circle $mathbb T$ of class $L^1(mathbb T)$ such that the following trace formula holds: $tr(f(T)  f(R))= int_mathbbT f'(zeta)xi(zeta)dzeta$, whenever $T$ and $R$ are contractions with $TR in mathbf S_1$, and $f$ is an operator Lipschitz function analytic in $mathbb D$. 
J. Sprekels, E. Valdinoci, A new type of identification problems: Optimizing the fractional order in a nonlocal evolution equation, SIAM Journal on Control and Optimization, 55 (2017), pp. 7093.
Abstract
In this paper, we consider a rather general linear evolution equation of fractional type, namely a diffusion type problem in which the diffusion operator is the power of a positive definite operator having a positive and discrete spectrum. We prove existence, uniqueness and differentiability properties with respect to the fractional parameter. These results are then employed to derive existence as well as firstorder necessary and secondorder sufficient optimality conditions for a minimization problem, which is inspired by considerations in mathematical biology. In this problem, the fractional parameter $s$ serves as the “control parameter” that needs to be chosen in such a way as to minimize a given cost functional. This problem constitutes a new classof identification problems: while usually in identification problems the type of the differential operator is prescribed and one or several of its coefficient functions need to be identified, in the present case one has to determine the type of the differential operator itself. This problem exhibits the inherent analytical difficulty that with changing fractional parameter also the domain of definition, and thus the underlying function space, of the fractional operator changes. 
A. Glitzky, M. Liero, Analysis of p(x)Laplace thermistor models describing the electrothermal behavior of organic semiconductor devices, Nonlinear Analysis. Real World Applications. An International Multidisciplinary Journal, 34 (2017), pp. 536562.
Abstract
We study a stationary thermistor model describing the electrothermal behavior of organic semiconductor devices featuring nonOhmic currentvoltage laws and selfheating effects. The coupled system consists of the currentflow equation for the electrostatic potential and the heat equation with Joule heating term as source. The selfheating in the device is modeled by an Arrheniuslike temperature dependency of the electrical conductivity. Moreover, the nonOhmic electrical behavior is modeled by a power law such that the electrical conductivity depends nonlinearly on the electric field. Notably, we allow for functional substructures with different power laws, which gives rise to a $p(x)$Laplacetype problem with piecewise constant exponent. We prove the existence and boundedness of solutions in the twodimensional case. The crucial point is to establish the higher integrability of the gradient of the electrostatic potential to tackle the Joule heating term. The proof of the improved regularity is based on Caccioppolitype estimates, Poincaré inequalities, and a Gehringtype Lemma for the $p(x)$Laplacian. Finally, Schauder's fixedpoint theorem is used to show the existence of solutions. 
M. Thomas, Ch. Zanini, Cohesive zonetype delamination in viscoelasticity, Discrete and Continuous Dynamical Systems  Series S, 10 (2017), pp. 14871517, DOI 10.3934/dcdss.2017077 .
Abstract
We study a model for the rateindependent evolution of cohesive zone delamination in a viscoelastic solid, also exposed to dynamics effects. The main feature of this model, inspired by [Ortiz&Pandoli99Int.J.Numer.Meth.Eng.], is that the surface energy related to the crack opening depends on the history of the crack separation between the two sides of the crack path, and allows for different responses upon loading and unloading.
Due to the presence of multivalued and unbounded operators featuring nonpenetration and the `memory'constraint in the strong formulation of the problem, we prove existence of a weaker notion of solution, known as semistable energetic solution, pioneered in [Roubicek09M2AS] and refined in [Rossi&Thomas15WIASPreprint2113]. 
P. Farrell, Th. Koprucki, J. Fuhrmann, Computational and analytical comparison of flux discretizations for the semiconductor device equations beyond Boltzmann statistics, Journal of Computational Physics, 346 (2017), pp. 497513, DOI 10.1016/j.jcp.2017.06.023 .
Abstract
For a Voronoï finite volume discretization of the van Roosbroeck system with general charge carrier statistics we compare three thermodynamically consistent numerical fluxes known in the literature. We discuss an extension of the ScharfetterGummel scheme to nonBoltzmann (e.g. FermiDirac) statistics. It is based on the analytical solution of a twopoint boundary value problem obtained by projecting the continuous differential equation onto the interval between neighboring collocation points. Hence, it serves as a reference flux. The exact solution of the boundary value problem can be approximated by computationally cheaper fluxes which modify certain physical quantities. One alternative scheme averages the nonlinear diffusion (caused by the nonBoltzmann nature of the problem), another one modifies the effective density of states. To study the differences between these three schemes, we analyze the Taylor expansions, derive an error estimate, visualize the flux error and show how the schemes perform for a carefully designed pin benchmark simulation. We present strong evidence that the flux discretization based on averaging the nonlinear diffusion has an edge over the scheme based on modifying the effective density of states. 
M. Liero, J. Fuhrmann, A. Glitzky, Th. Koprucki, A. Fischer, S. Reineke, 3D electrothermal simulations of organic LEDs showing negative differential resistance, Optical and Quantum Electronics, 49 (2017), pp. 330/1330/8, DOI 10.1007/s1108201711674 .
Abstract
Organic semiconductor devices show a pronounced interplay between temperatureactivated conductivity and selfheating which in particular causes inhomogeneities in the brightness of largearea OLEDs at high power. We consider a 3D thermistor model based on partial differential equations for the electrothermal behavior of organic devices and introduce an extension to multiple layers with nonlinear conductivity laws, which also take the diodelike behavior in recombination zones into account. We present a numerical simulation study for a red OLED using a finitevolume approximation of this model. The appearance of Sshaped currentvoltage characteristics with regions of negative differential resistance in a measured device can be quantitatively reproduced. Furthermore, this simulation study reveals a propagation of spatial zones of negative differential resistance in the electron and hole transport layers toward the contact. 
A. Mielke, M. Mittnenzweig, Convergence to equilibrium in energyreactiondiffusion systems using vectorvalued functional inequalities, Journal of Nonlinear Science, (2017), published online on 11.11.2017, DOI 10.1007/s0033201794279 .
Abstract
We discuss how the recently developed energydissipation methods for reactiondi usion systems can be generalized to the nonisothermal case. For this we use concave entropies in terms of the densities of the species and the internal energy, where the importance is that the equilibrium densities may depend on the internal energy. Using the logSobolev estimate and variants for lowerorder entropies as well as estimates for the entropy production of the nonlinear reactions we give two methods to estimate the relative entropy by the total entropy production, namely a somewhat restrictive convexity method, which provides explicit decay rates, and a very general, but weaker compactness method. 
A. Mielke, R. Rossi, G. Savaré, Global existence results for viscoplasticity at finite strain, Archive for Rational Mechanics and Analysis, (2017), published online on 20.9.2017, DOI 10.1007/s0020501711646 .
Abstract
We study a model for ratedependent gradient plasticity at finite strain based on the multiplicative decomposition of the strain tensor, and investigate the existence of globalintime solutions to the related PDE system. We reveal its underlying structure as a generalized gradient system, where the driving energy functional is highly nonconvex and features the geometric nonlinearities related to finitestrain elasticity as well as the multiplicative decomposition of finitestrain plasticity. Moreover, the dissipation potential depends on the leftinvariant plastic rate and thus, depends on the plastic state variable.
The existence theory is developed for a class of abstract, nonsmooth, and nonconvex gradient systems, for which we introduce suitable notions of solutions, namely energydissipationbalance (EDB) and energydissipationinequality (EDI) solutions. Hence, we resort to the toolbox of the direct method of the calculus of variations to check that the specific energy and dissipation functionals for our viscoplastic models comply with the conditions of the general theory. 
A. Mielke, C. Patz, Uniform asymptotic expansions for the infinite harmonic chain, Zeitschrift fur Analysis und ihre Anwendungen. Journal for Analysis and its Applications, 36 (2017), pp. 437475, DOI 10.4171/ZAA/1596 .
Abstract
We study the dispersive behavior of waves in linear oscillator chains. We show that for general general dispersions it is possible to construct an expansion such that the remainder can be estimated by $1/t$ uniformly in space. In particalur we give precise asymptotics for the transition from the $1/t^1/2$ decay of nondegenerate wave numbers to the generate $1/t^1/3$ decay of generate wave numbers. This involves a careful description of the oscillatory integral involving the Airy function. 
A. Mielke, R.I.A. Patterson, M.A. Peletier, D.R.M. Renger, Nonequilibrium thermodynamical principles for chemical reactions with massaction kinetics, SIAM Journal on Applied Mathematics, 77 (2017), pp. 15621585, DOI 10.1137/16M1102240 .
Abstract
We study stochastic interacting particle systems that model chemical reaction networks on the micro scale, converging to the macroscopic Reaction Rate Equation. One abstraction level higher, we study the ensemble of such particle systems, converging to the corresponding Liouville transport equation. For both systems, we calculate the corresponding large deviations and show that under the condition of detailed balance, the large deviations induce a nonlinear relation between thermodynamic fluxes and free energy driving force. 
M. Radziunas, A. Zeghuzi, J. Fuhrmann, Th. Koprucki, H.J. Wünsche, H. Wenzel, U. Bandelow, Efficient coupling of inhomogeneous current spreading and dynamic electrooptical models for broadarea edgeemitting semiconductor devices, Optical and Quantum Electronics, 49 (2017), pp. 332/1332/8, DOI 10.1007/s1108201711683 .
Abstract
We extend a 2 (space) + 1 (time)dimensional traveling wave model for broadarea edgeemitting semiconductor lasers by a model for inhomogeneous current spreading from the contact to the active zone of the laser. To speedup the performance of the device simulations, we suggest and discuss several approximations of the inhomogeneous current density in the active zone.
Contributions to Collected Editions

M. Kantner, M. Mittnenzweig, Th. Koprucki, A hybrid quantumclassical modeling approach for electrically driven quantum dot devices, in: Proceedings of ``SPIE Photonics West 2018: Physics and Simulation of Optoelectronic Devices XXVI'', San Francisco, USA, 29.01.2018  01.02.2018, 10526, Society of PhotoOptical Instrumentation Engineers (SPIE), Bellingham, 2018, pp. 10526/110526/6, DOI 10.1117/12.2289185 .
Abstract
The design of electrically driven quantum light sources based on semiconductor quantum dots, such as singlephoton emitters and nanolasers, asks for modeling approaches combining classical device physics with cavity quantum electrodynamics. In particular, one has to connect the wellestablished fields of semiclassical semiconductor transport theory and the theory of open quantum systems. We present a first step in this direction by coupling the van Roosbroeck system with a Markovian quantum master equation in Lindblad form. The resulting hybrid quantumclassical system obeys the fundamental laws of nonequilibrium thermodynamics and provides a comprehensive description of quantum dot devices on multiple scales: It enables the calculation of quantum optical figures of merit (e.g. the second order intensity correlation function) together with the spatially resolved simulation of the current flow in realistic semiconductor device geometries in a unified way. 
M. Kantner, U. Bandelow, Th. Koprucki, H.J. Wünsche, Simulation of quantum dot devices by coupling of quantum master equations and semiclassical transport theory, in: Proceedings of ``the 17th International Conference on Numerical Simulation of Optoelectronic Devices'', J. Piprek, M. Willatzen, eds., IEEE Conference Publications Management Group, Piscataway, 2017, pp. 217218.

TH. Koprucki, M. Kohlhaase, D. Müller, K. Tabelow, Mathematical models as research data in numerical simulation of optoelectronic devices, in: Numerical Simulation of Optoelectronic Devices (NUSOD), 2017, pp. 225 226, DOI 10.1109/NUSOD.2017.8010073 .
Abstract
Mathematical models are the foundation of numerical simulation of optoelectronic devices. We present a concept for a machineactionable as well as humanunderstandable representation of the mathematical knowledge they contain and the domainspecific knowledge they are based on. We propose to use theory graphs to formalize mathematical models and model pathway diagrams to visualize them. We illustrate our approach by application to the stationary onedimensional driftdiffusion equations (van Roosbroeck system). 
M. Liero, J. Fuhrmann, A. Glitzky, Th. Koprucki, A. Fischer, S. Reineke, Modeling and simulation of electrothermal feedback in largearea organic LEDs, in: Proceedings of ``the 17th International Conference on Numerical Simulation of Optoelectronic Devices'', J. Piprek, M. Willatzen, eds., IEEE Conference Publications Management Group, Piscataway, 2017, pp. 105106, DOI 10.1109/NUSOD.2017.8010013 .

M. Bulíček, A. Glitzky, M. Liero, Thermistor systems of p(x)Laplacetype with discontinuous exponents via entropy solutions, in: PDE 2015: Theory and Applications of Partial Differential Equations (PDE 2015), H.Chr. Kaiser, D. Knees, A. Mielke, J. Rehberg, E. Rocca, M. Thomas, E. Valdinoci, eds., 10 of Discrete and Continuous Dynamical Systems, Series S, American Institute of Mathematical Sciences, Springfield, 2017, pp. 697713.
Abstract
We show the existence of solutions to a system of elliptic PDEs, that was recently introduced to describe the electrothermal behavior of organic semiconductor devices. Here, two difficulties appear: (i) the elliptic term in the currentflow equation is of p(x)Laplaciantype with discontinuous exponent p, which limits the use of standard methods, and (ii) in the heat equation, we have to deal with an a priori L^{1} term on the right hand side describing the Joule heating in the device. We prove the existence of a weak solution under very weak assumptions on the data. Our existence proof is based on Schauder's fixed point theorem and the concept of entropy solutions for the heat equation. Here, the crucial point is the continuous dependence of the entropy solutions on the data of the problem. 
P. Colli, J. Sprekels, Optimal boundary control of a nonstandard CahnHilliard system with dynamic boundary condition and double obstacle inclusions, in: Solvability, Regularity, and Optimal Control of Boundary Value Problems for PDEs: In Honour of Prof. Gianni Gilardi, P. Colli, A. Favini, E. Rocca, G. Schimperna, J. Sprekels, eds., 22 of Springer INdAM Series, Springer International Publishing, 2017, pp. 151182, DOI 10.1007/9783319644899 .
Abstract
In this paper, we study an optimal boundary control problem for a model for phase separation taking place in a spatial domain that was introduced by P.PodioGuidugli in Ric. Mat. 55 (2006), pp.105118. The model consists of a strongly coupled system of nonlinear parabolic differential inclusions, in which products between the unknown functions and their time derivatives occur that are difficult to handle analytically; the system is complemented by initial and boundary conditions. For the order parameter of the phase separation process, a dynamic boundary condition involving the LaplaceBeltrami operator is assumed, which models an additional nonconserving phase transition occurring on the surface of the domain. We complement in this paper results that were established in the recent contribution appeared in Evol. Equ. Control Theory 6 (2017), pp. 3558, by the two authors and Gianni Gilardi. In contrast to that paper, in which differentiable potentials of logarithmic type were considered, we investigate here the (more difficult) case of nondifferentiable potentials of double obstacle type. For such nonlinearities, the standard techniques of optimal control theory to establish the existence of Lagrange multipliers for the state constraints are known to fail. To overcome these difficulties, we employ the following line of approach: we use the results contained in the preprint arXiv:1609.07046 [math.AP] (2016), pp. 130, for the case of (differentiable) logarithmic potentials and perform a socalled "deep quench limit". Using compactness and monotonicity arguments, it is shown that this strategy leads to the desired firstorder necessary optimality conditions for the case of (nondifferentiable) double obstacle potentials. 
Y. Granovskyi, M.M. Malamud, H. Neidhardt, A. Posilicano, To the spectral theory of vectorvalued SturmLiouville operators with summable potentials and point interactions, in: Functional Analysis and Operator Theory for Quantum Physics, J. Dittrich, H. Kovarik, A. Laptev, eds., EMS Series of Congress Reports, EMS Publishing House, 2017, pp. 271313, DOI 10.4171/1751/15 .

M. Kohlhase, Th. Koprucki, D. Müller, K. Tabelow, Mathematical models as research data via flexiformal theory graphs, in: Intelligent Computer Mathematics: 10th International Conference, CICM 2017, Edinburgh, UK, July 1721, 2017, Proceedings, H. Geuvers, M. England, O. Hasan, F. Rabe , O. Teschke, eds., 10383 of Lecture Notes in Artificial Intelligence, Springer International Publishing, Cham, 2017, pp. 224238, DOI 10.1007/9783319620756_16 .
Abstract
Mathematical modeling and simulation (MMS) has now been established as an essential part of the scientific work in many disciplines. It is common to categorize the involved numerical data and to some extent the corresponding scientific software as research data. But both have their origin in mathematical models, therefore any holistic approach to research data in MMS should cover all three aspects: data, software, and models. While the problems of classifying, archiving and making accessible are largely solved for data and first frameworks and systems are emerging for software, the question of how to deal with mathematical models is completely open. In this paper we propose a solution  to cover all aspects of mathematical models: the underlying mathematical knowledge, the equations, boundary conditions, numeric approximations, and documents in a flexiformal framework, which has enough structure to support the various uses of models in scientific and technology workflows. Concretely we propose to use the OMDoc/MMT framework to formalize mathematical models and show the adequacy of this approach by modeling a simple, but nontrivial model: van Roosbroeck's driftdiffusion model for onedimensional devices. This formalization  and future extensions  allows us to support the modeler by e.g. flexibly composing models, visualizing Model Pathway Diagrams, and annotating model equations in documents as induced from the formalized documents by flattening. This directly solves some of the problems in treating MMS as "research data” and opens the way towards more MKM services for models. 
B. Drees, Th. Koprucki, Make the most of your visual simulation data: The TIB AVPortal enables citation of simulation results and increases their visibility, in: Proceedings of ``the 17th International Conference on Numerical Simulation of Optoelectronic Devices'', J. Piprek, M. Willatzen, eds., IEEE Conference Publications Management Group, Piscataway, 2017, pp. 227 228, DOI 10.1109/NUSOD.2017.8010074 .
Abstract
There still exists no common standard on how to publish and cite visualisations of simulation data. We introduce the TIB AVPortal as a sustainable infrastructure for audiovisual data using a combination of digital object identifiers (DOI) and media fragment identifiers (MFID) to cite these data in accordance with scientific standards. The benefits and opportunities of enhancing publications with visual data are illustrated by showing a use case from optoelectronics. 
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, Singapore, 2017, 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. 
P. Farrell, Th. Koprucki, J. Fuhrmann, Comparison of consistent flux discretizations for drift diffusion beyond boltzmann statistics, in: Proceedings of ``the 17th International Conference on Numerical Simulation of Optoelectronic Devices'', J. Piprek, M. Willatzen, eds., IEEE Conference Publications Management Group, Piscataway, 2017, pp. 219220, DOI 10.1109/NUSOD.2017.8010070 .

J. Fuhrmann, A. Glitzky, M. Liero, Hybrid finitevolume/finiteelement schemes for p(x)Laplace thermistor models, in: Finite Volumes for Complex Applications VIII  Hyperbolic, Elliptic and Parabolic Problems  FVCA 8, Lille, France, June 2017, C. Cancès, P. Omnes, eds., 200 of Springer Proceedings in Mathematics & Statistics, Springer International Publishing, Cham et al., 2017, pp. 397405, DOI 10.1007/9783319573946_42 .

M. Radziunas, A. Zeghuzi, J. Fuhrmann, Th. Koprucki, H.J. Wünsche, H. Wenzel, U. Bandelow, Efficient coupling of inhomogeneous current spreading and electrooptical models for simulation of dynamics in broadarea semiconductor lasers, in: Proceedings of ``the 17th International Conference on Numerical Simulation of Optoelectronic Devices'', J. Piprek, M. Willatzen, eds., IEEE Conference Publications Management Group, Piscataway, 2017, pp. 231232.
Preprints, Reports, Technical Reports

D.H. Doan, A. Glitzky, M. Liero, Driftdiffusion modeling, analysis and simulation of organic semiconductor devices, Preprint no. 2493, WIAS, Berlin, 2018, DOI 10.20347/WIAS.PREPRINT.2493 .
Abstract, PDF (563 kByte)
We discuss driftdiffusion models for chargecarrier transport in organic semiconductor devices. The crucial feature in organic materials is the energetic disorder due to random alignment of molecules and the hopping transport of carriers between adjacent energetic sites. The former leads to socalled GaussFermi statistics, which describe the occupation of energy levels by electrons and holes. The latter gives rise to complicated mobility models with a strongly nonlinear dependence on temperature, density of carriers, and electric field strength. We present the stateoftheart modeling of the transport processes and provide a first existence result for the stationary driftdiffusion model taking all of the peculiarities of organic materials into account. The existence proof is based on Schauder's fixedpoint theorem. Finally, we discuss the numerical discretization of the model using finitevolume methods and a generalized ScharfetterGummel scheme for the GaussFermi statistics. 
P. Farrell, D. Peschka, Challenges for driftdiffusion simulations of semiconductors: A comparative study of different discretization philosophies, Preprint no. 2486, WIAS, Berlin, 2018, DOI 10.20347/WIAS.PREPRINT.2486 .
Abstract, PDF (2457 kByte)
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, Variational approach to contact line dynamics for thin films, Preprint no. 2477, WIAS, Berlin, 2018, DOI 10.20347/WIAS.PREPRINT.2477 .
Abstract, PDF (713 kByte)
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. 
S. Frigeri, M. Grasselli, J. Sprekels, Optimal distributed control of twodimensional nonlocal CahnHilliardNavierStokes systems with degenerate mobility and singular potential, Preprint no. 2473, WIAS, Berlin, 2018, DOI 10.20347/WIAS.PREPRINT.2473 .
Abstract, PDF (370 kByte)
In this paper, we consider a twodimensional diffuse interface model for the phase separation of an incompressible and isothermal binary fluid mixture with matched densities. This model consists of the NavierStokes equations, nonlinearly coupled with a convective nonlocal CahnHilliard equation. The system rules the evolution of the volumeaveraged velocity of the mixture and the (relative) concentration difference of the two phases. The aim of this work is to study an optimal control problem for such a system, the control being a timedependent external force acting on the fluid. We first prove the existence of an optimal control for a given tracking type cost functional. Then we study the differentiability properties of the controltostate map, and we establish firstorder necessary optimality conditions. These results generalize the ones obtained by the first and the third authors jointly with E. Rocca in [19]. There the authors assumed a constant mobility and a regular potential with polynomially controlled growth. Here, we analyze the physically more relevant case of a degenerate mobility and a singular (e.g., logarithmic) potential. This is made possible by the existence of a unique strong solution which was recently proved by the authors and C. G. Gal in [14]. 
M. Heida, S. Neukamm, M. Varga, Stochastic unfolding and homogenization, Preprint no. 2460, WIAS, Berlin, 2017, DOI 10.20347/WIAS.PREPRINT.2460 .
Abstract, PDF (596 kByte)
The notion of periodic twoscale convergence and the method of periodic unfolding are prominent and useful tools in multiscale modeling and analysis of PDEs with rapidly oscillating periodic coefficients. In this paper we are interested in the theory of stochastic homogenization for continuum mechanical models in form of PDEs with random coefficients, describing random heterogeneous materials. The notion of periodic twoscale convergence has been extended in different ways to the stochastic case. In this work we introduce a stochastic unfolding method that features many similarities to periodic unfolding. In particular it allows to characterize the notion of stochastic twoscale convergence in the mean by mere convergence in an extended space. We illustrate the method on the (classical) example of stochastic homogenization of convex integral functionals, and prove a stochastic homogenization result for an nonconvex evolution equation of AllenCahn type. Moreover, we discuss the relation of stochastic unfolding to previously introduced notions of (quenched and mean) stochastic twoscale convergence. The method introduced in this paper extends discrete stochastic unfolding, as recently introduced by the second and third author in the context of discretetocontinuum transition. 
P. Dondl, Th. Frenzel, A. Mielke, A gradient system with a wiggly energy and relaxed EDPconvergence, Preprint no. 2459, WIAS, Berlin, 2017, DOI 10.20347/WIAS.PREPRINT.2459 .
Abstract, PDF (1732 kByte)
If gradient systems depend on a microstructure, we want to derive a macroscopic gradient structure describing the effective behavior of the microscopic system. We introduce a notion of evolutionary Gammaconvergence that relates the microscopic energy and the microscopic dissipation potential with their macroscopic limits via Gammaconvergence. We call this notion relaxed EDPconvergence since the special structure of the dissipation functional may not be preserved under Gammaconvergence. However, by investigating the kinetic relation we derive the macroscopic dissipation potential. 
V. Laschos, A. Mielke, Geometric properties of cones with applications on the HellingerKantorovich space, and a new distance on the space of probability measures, Preprint no. 2458, WIAS, Berlin, 2017, DOI 10.20347/WIAS.PREPRINT.2458 .
Abstract, PDF (446 kByte)
By studying general geometric properties of cone spaces, we prove the existence of a distance on the space of Probability measures that turns the HellingerKantorovich space into a cone space over the space of probabilities measures. Here we exploit a natural twoparameter scaling property of the HellingerKantorovich distance. For the new space, we obtain a full characterization of the geodesics. We also provide new geometric properties for the original space, including a twoparameter rescaling and reparametrization of the geodesics, localangle condition and some partial Ksemiconcavity of the squared distance, that it will be used in a future paper to prove existence of gradient flows. 
M. Becker, Th. Frenzel, Th. Niedermeyer, S. Reichelt, A. Mielke, M. Bär, Local control of globally competing patterns in coupled SwiftHohenberg equations, Preprint no. 2457, WIAS, Berlin, 2017, DOI 10.20347/WIAS.PREPRINT.2457 .
Abstract, PDF (627 kByte)
We present analytical and numerical investigations of two antisymmetrically coupled 1D SwiftHohenberg equations (SHEs) with cubic nonlinearities. The SHE provides a generic formulation for pattern formation at a characteristic length scale. A linear stability analysis of the homogeneous state reveals a wave instability in addition to the usual Turing instability of uncoupled SHEs. We performed weakly nonlinear analysis in the vicinity of the codimensiontwo point of the Turingwave instability, resulting in a set of coupled amplitude equations for the Turing pattern as well as left and right traveling waves. In particular, these complex GinzburgLandautype equations predict two major things: there exists a parameter regime where multiple different patterns are stable with respect to each other; and that the amplitudes of different patterns interact by local mutual suppression. In consequence, different patterns can coexist in distinct spatial regions, separated by localized interfaces. We identified specific mechanisms for controlling the position of these interfaces, which distinguish what kinds of patterns the interface connects and thus allow for global pattern selection. Extensive simulations of the original SHEs confirm our results. 
M. Thomas, C. Bilgen, K. Weinberg, Analysis and simulations for a phasefield fracture model at finite strains based on modified invariants, Preprint no. 2456, WIAS, Berlin, 2017, DOI 10.20347/WIAS.PREPRINT.2456 .
Abstract, PDF (1990 kByte)
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. 
M. Heida, R. Kornhuber, J. Podlesny, Fractal homogenization of a multiscale interface problem, Preprint no. 2453, WIAS, Berlin, 2017, DOI 10.20347/WIAS.PREPRINT.2453 .
Abstract, PDF (762 kByte)
Inspired from geological problems, we introduce a new geometrical setting for homogenization of a well known and well studied problem of an elliptic second order differential operator with jump condition on a multiscale network of interfaces. The geometrical setting is fractal and hence neither periodic nor stochastic methods can be applied to the study of such kind of multiscale interface problem. Instead, we use the fractal nature of the geometric structure to introduce smoothed problems and apply methods from a posteriori theory to derive an estimate for the order of convergence. Computational experiments utilizing an iterative homogenization approach illustrate that the theoretically derived order of convergence of the approximate problems is close to optimal. 
O. Burylko, A. Mielke, M. Wolfrum, S. Yanchuk, Coexistence of Hamiltonianlike and dissipative dynamics in chains of coupled phase oscillators with skewsymmetric coupling, Preprint no. 2447, WIAS, Berlin, 2017, DOI 10.20347/WIAS.PREPRINT.2447 .
Abstract, PDF (3022 kByte)
We consider rings of coupled phase oscillators with anisotropic coupling. When the coupling is skewsymmetric, i. e. when the anisotropy is balanced in a specific way, the system shows robustly a coexistence of Hamiltonianlike and dissipative regions in the phase space. We relate this phenomenon to the timereversibility property of the system. The geometry of lowdimensional systems up to five oscillators is described in detail. In particular, we show that the boundary between the dissipative and Hamiltonianlike regions consists of families of heteroclinic connections. For larger chains with skewsymmetric coupling, some sufficient conditions for the coexistence are provided, and in the limit of N → ∞ oscillators, we formally derive an amplitude equation for solutions in the neighborhood of the synchronous solution. It has the form of a nonlinear Schrödinger equation and describes the Hamiltonianlike region existing around the synchronous state similarly to the case of finite rings. 
P. Colli, G. Gilardi, J. Sprekels, Optimal velocity control of a convective CahnHilliard system with double obstacles and dynamic boundary conditions: A `deep quench' approach, Preprint no. 2428, WIAS, Berlin, 2017, DOI 10.20347/WIAS.PREPRINT.2428 .
Abstract, PDF (257 kByte)
In this paper, we investigate a distributed optimal control problem for a convective viscous CahnHilliard system with dynamic boundary conditions. Such systems govern phase separation processes between two phases taking place in an incompressible fluid in a container and, at the same time, on the container boundary. The cost functional is of standard tracking type, while the control is exerted by the velocity of the fluid in the bulk. In this way, the coupling between the state (given by the associated order parameter and chemical potential) and control variables in the governing system of nonlinear partial differential equations is bilinear, which presents a difficulty for the analysis. In contrast to the previous paper Optimal velocity control of a viscous CahnHilliard system with convection and dynamic boundary conditions by the same authors, the bulk and surface free energies are of double obstacle type, which renders the state constraint nondifferentiable. It is well known that for such cases standard constraint qualifications are not satisfied so that standard methods do not apply to yield the existence of Lagrange multipliers. In this paper, we overcome this difficulty by taking advantage of results established in the quoted paper for logarithmic nonlinearities, using a socalled `deep quench approximation'. We derive results concerning the existence of optimal controls and the firstorder necessary optimality conditions in terms of a variational inequality and the associated adjoint system. 
P. Colli, G. Gilardi, J. Sprekels, Optimal velocity control of a viscous CahnHilliard system with convection and dynamic boundary conditions, Preprint no. 2427, WIAS, Berlin, 2017, DOI 10.20347/WIAS.PREPRINT.2427 .
Abstract, PDF (306 kByte)
In this paper, we investigate a distributed optimal control problem for a convective viscous CahnHilliard system with dynamic boundary conditions. Such systems govern phase separation processes between two phases taking place in an incompressible fluid in a container and, at the same time, on the container boundary. The cost functional is of standard tracking type, while the control is exerted by the velocity of the fluid in the bulk. In this way, the coupling between the state (given by the associated order parameter and chemical potential) and control variables in the governing system of nonlinear partial differential equations is bilinear, which presents an additional difficulty for the analysis. The nonlinearities in the bulk and surface free energies are of logarithmic type, which entails that the thermodynamic forces driving the phase separation process may become singular. We show existence for the optimal control problem under investigation, prove the Fréchet differentiability of the associated controltostate mapping in suitable Banach spaces, and derive the firstorder necessary optimality conditions in terms of a variational inequality and the associated adjoint system. Due to the strong nonlinear couplings between state variables and control, the corresponding proofs require a considerable analytical effort. 
P. Farrell, M. Patriarca, J. Fuhrmann, Th. Koprucki, Comparison of thermodynamically consistent charge carrier flux discretizations for FermiDirac and GaussFermi statistics, Preprint no. 2424, WIAS, Berlin, 2017, DOI 10.20347/WIAS.PREPRINT.2424 .
Abstract, PDF (1572 kByte)
We compare three thermodynamically consistent ScharfetterGummel schemes for different distribution functions for the carrier densities, including the FermiDirac integral of order 1/2 and the GaussFermi integral. The most accurate (but unfortunately also most costly) generalized ScharfetterGummel scheme requires the solution of an integral equation. We propose a new method to solve this integral equation numerically based on Gauss quadrature and Newton's method. We discuss the quality of this approximation and plot the resulting currents for FermiDirac and GaussFermi statistics. Finally, by comparing two modified (diffusionenhanced and inverse activity based) ScharfetterGummel schemes with the more accurate generalized scheme, we show that the diffusionenhanced ansatz leads to considerably lower flux errors, confirming previous results (J. Comp. Phys. 346:497513, 2017). 
L. Donati, M. Heida, M. Weber, B. Keller, Estimation of the infinitesimal generator by squareroot approximation, Preprint no. 2416, WIAS, Berlin, 2017, DOI 10.20347/WIAS.PREPRINT.2416 .
Abstract, PDF (1739 kByte)
For the analysis of molecular processes, the estimation of timescales, i.e., transition rates, is very important. Estimating the transition rates between molecular conformations is  from a mathematical point of view  an invariant subspace projection problem. A certain infinitesimal generator acting on function space is projected to a lowdimensional rate matrix. This projection can be performed in two steps. First, the infinitesimal generator is discretized, then the invariant subspace is approximated and used for the subspace projection. In our approach, the discretization will be based on a Voronoi tessellation of the conformational space. We will show that the discretized infinitesimal generator can simply be approximated by the geometric average of the Boltzmann weights of the Voronoi cells. Thus, there is a direct correlation between the potential energy surface of molecular structures and the transition rates of conformational changes. We present results for a 2ddiffusion process and Alanine dipeptide. 
P. Gurevich, S. Reichelt, Pulses in FitzHughNagumo systems with rapidly oscillating coefficients, Preprint no. 2413, WIAS, Berlin, 2017, DOI 10.20347/WIAS.PREPRINT.2413 .
Abstract, PDF (1751 kByte)
This paper is devoted to pulse solutions in FitzHughNagumo systems that are coupled parabolic equations with rapidly periodically oscillating coefficients. In the limit of vanishing periods, there arises a twoscale FitzHughNagumo system, which qualitatively and quantitatively captures the dynamics of the original system. We prove existence and stability of pulses in the limit system and show their proximity on any finite time interval to pulselike solutions of the original system. 
M. Liero, S. Melchionna, The weighted energydissipation principle and evolutionary Gammaconvergence for doubly nonlinear problems, Preprint no. 2411, WIAS, Berlin, 2017, DOI 10.20347/WIAS.PREPRINT.2411 .
Abstract, PDF (392 kByte)
We consider a family of doubly nonlinear evolution equations that is given by families of convex dissipation potentials, nonconvex energy functionals, and external forces parametrized by a small parameter ε. For each of these problems, we introduce the socalled weighted energydissipation (WED) functional, whose minimizer correspond to solutions of an ellipticintime regularization of the target problems with regularization parameter δ. We investigate the relation between the Γconvergence of the WED functionals and evolutionary Γconvergence of the associated systems. More precisely, we deal with the limits δ→0, ε→0, as well as δ+ ε→0 either in the sense of Γconvergence of functionals or in the sense of evolutionary Γconvergence of functionaldriven evolution problems, or both. Additionally, we provide some quantitative estimates on the rate of convergence for the limit ε→0, in the case of quadratic dissipation potentials and uniformly λconvex energy functionals. Finally, we discuss a homogenization problem as an example of application. 
R. Rossi, M. Thomas, From nonlinear to linear elasticity in a coupled ratedependent/independent system for brittle delamination, Preprint no. 2409, WIAS, Berlin, 2017, DOI 10.20347/WIAS.PREPRINT.2409 .
Abstract, PDF (291 kByte)
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. 
P. Dupuis, V. Laschos, K. Ramanan, Exit time risksensitive stochastic control problems related to systems of cooperative agents, Preprint no. 2407, WIAS, Berlin, 2017, DOI 10.20347/WIAS.PREPRINT.2407 .
Abstract, PDF (447 kByte)
We study sequences, parametrized by the number of agents, of exit time stochastic control problems with risksensitive costs structures generate by unbounded costs. We identify a fully characterizing assumption, under which, each of them corresponds to a riskneutral stochastic control problem with additive cost, and also to a riskneutral stochastic control problem on the simplex, where the specific information about the state of each agent can be discarded. We finally prove that, under some additional assumptions, the sequence of value functions converges to the value function of a deterministic control problem. 
A. Mielke, Three examples concerning the interaction of dry friction and oscillations, Preprint no. 2405, WIAS, Berlin, 2017, DOI 10.20347/WIAS.PREPRINT.2405 .
Abstract, PDF (3492 kByte)
We discuss recent work concerning the interaction of dry friction, which is a rate independent effect, and temporal oscillations. First, we consider the temporal averaging of highly oscillatory friction coefficients. Here the effective dry friction is obtained as an infimal convolution. Second, we show that simple models with statedependent friction may induce a Hopf bifurcation, where constant shear rates give rise to periodic behavior where sticking phases alternate with sliding motion. The essential feature here is the dependence of the friction coefficient on the internal state, which has an internal relaxation time. Finally, we present a simple model for rocking toy animal where walking is made possible by a periodic motion of the body that unloads the legs to be moved. 
M. Heida, On convergences of the squareroot approximation scheme to the FokkerPlanck operator, Preprint no. 2399, WIAS, Berlin, 2017, DOI 10.20347/WIAS.PREPRINT.2399 .
Abstract, PDF (506 kByte)
We study the qualitative convergence properties of a finite volume scheme that recently was proposed by Lie, Fackeldey and Weber [SIAM Journal on Matrix Analysis and Applications 2013 (34/2)] in the context of conformation dynamics. The scheme was derived from physical principles and is called the squareroot approximation (SQRA) scheme. We show that solutions to the SQRA equation converge to solutions of the FokkerPlanck equation using a discrete notion of Gconvergence. Hence the squareroot approximation turns out to be a usefull approximation scheme to the FokkerPlanck equation in high dimensional spaces. As an example, in the special case of stationary Voronoi tessellations we use stochastic twoscale convergence to prove that this setting satisfies the Gconvergence property. In particular, the class of tessellations for which the Gconvergence result holds is not trivial. 
P. Colli, G. Gilardi, J. Sprekels, On a CahnHilliard system with convection and dynamic boundary conditions, Preprint no. 2391, WIAS, Berlin, 2017, DOI 10.20347/WIAS.PREPRINT.2391 .
Abstract, PDF (291 kByte)
This paper deals with an initial and boundary value problem for a system coupling equation and boundary condition both of CahnHilliard type; an additional convective term with a forced velocity field, which could act as a control on the system, is also present in the equation. Either regular or singular potentials are admitted in the bulk and on the boundary. Both the viscous and pure CahnHilliard cases are investigated, and a number of results is proven about existence of solutions, uniqueness, regularity, continuous dependence, uniform boundedness of solutions, strict separation property. A complete approximation of the problem, based on the regularization of maximal monotone graphs and the use of a FaedoGalerkin scheme, is introduced and rigorously discussed. 
S. Bartels, M. Milicevic, M. Thomas, Numerical approach to a model for quasistatic damage with spatial $BV$regularization, Preprint no. 2388, WIAS, Berlin, 2017, DOI 10.20347/WIAS.PREPRINT.2388 .
Abstract, PDF (566 kByte)
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. 
A.F.M. TER Elst, J. Rehberg, Consistent operator semigroups and their interpolation, Preprint no. 2382, WIAS, Berlin, 2017, DOI 10.20347/WIAS.PREPRINT.2382 .
Abstract, PDF (231 kByte)
Under a mild regularity condition we prove that the generator of the interpolation of two C0semigroups is the interpolation of the two generators. 
F. Flegel, M. Heida, M. Slowik, Homogenization theory for the random conductance model with degenerate ergodic weights and unboundedrange jumps, Preprint no. 2371, WIAS, Berlin, 2017, DOI 10.20347/WIAS.PREPRINT.2371 .
Abstract, PDF (598 kByte)
We study homogenization properties of the discrete Laplace operator with random conductances on a large domain in Zd. More precisely, we prove almostsure homogenization of the discrete Poisson equation and of the top of the Dirichlet spectrum. We assume that the conductances are stationary, ergodic and nearestneighbor conductances are positive. In contrast to earlier results, we do not require uniform ellipticity but certain integrability conditions on the lower and upper tails of the conductances. We further allow jumps of arbitrary length. Without the longrange connections, the integrability condition on the lower tail is optimal for spectral homogenization. It coincides with a necessary condition for the validity of a local central limit theorem for the random walk among random conductances. As an application of spectral homogenization, we prove a quenched large deviation principle for thenormalized and rescaled local times of the random walk in a growing box. Our proofs are based on a compactness result for the Laplacian's Dirichlet energy, Poincaré inequalities, Moser iteration and twoscale convergence 
P. Colli, G. Gilardi, J. Sprekels, Limiting problems for a nonstandard viscous CahnHilliard system with dynamic boundary conditions, Preprint no. 2369, WIAS, Berlin, 2017, DOI 10.20347/WIAS.PREPRINT.2369 .
Abstract, PDF (353 kByte)
This note is concerned with a nonlinear diffusion problem of phasefield type, consisting of a parabolic system of two partial differential equations, complemented by boundary and initial conditions. The system arises from a model of twospecies phase segregation on an atomic lattice and was introduced by PodioGuidugli in Ric. Mat. 55 (2006), pp.105118. The two unknowns are the phase parameter and the chemical potential. In contrast to previous investigations about this PDE system, we consider here a dynamic boundary condition for the phase variable that involves the LaplaceBeltrami operator and models an additional nonconserving phase transition occurring on the surface of the domain. We are interested to some asymptotic analysis and first discuss the asymptotic limit of the system as the viscosity coefficient of the order parameter equation tends to 0: the convergence of solutions to the corresponding solutions for the limit problem is proven. Then, we study the longtime behavior of the system for both problems, with positive or zero viscosity coefficient, and characterize the omegalimit set in both cases. 
M. Heida, S. Nesenenko, Stochastic homogenization of ratedependent models of monotone type in plasticity, Preprint no. 2366, WIAS, Berlin, 2017, DOI 10.20347/WIAS.PREPRINT.2366 .
Abstract, PDF (548 kByte)
In this work we deal with the stochastic homogenization of the initial boundary value problems of monotone type. The models of monotone type under consideration describe the deformation behaviour of inelastic materials with a microstructure which can be characterised by random measures. Based on the Fitzpatrick function concept we reduce the study of the asymptotic behaviour of monotone operators associated with our models to the problem of the stochastic homogenization of convex functionals within an ergodic and stationary setting. The concept of Fitzpatrick's function helps us to introduce and show the existence of the weak solutions for ratedependent systems. The derivations of the homogenization results presented in this work are based on the stochastic twoscale convergence in Sobolev spaces. For completeness, we also present some twoscale homogenization results for convex functionals, which are related to the classical Gammaconvergence theory.
Talks, Poster

M. Heida, On convergences of the squareroot approximation scheme to the FokkerPlanck operator, Workshop ``Interplay of Analysis and Probability in Applied Mathematics'', February 11  17, 2018, Mathematisches Forschungsinstitut Oberwolfach, February 13, 2018.

M. Kantner, M. Mittnenzweig, Th. Koprucki, A hybrid quantumclassical modeling approach for electrically driven quantum dot devices, SPIE Photonics West 2018: Physics and Simulation of Optoelectronic Devices XXVI, January 29  February 1, 2018, The Moscone Center, San Francisco, USA, January 29, 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.

TH. Koprucki, Model pathway diagrams for the representation of mathematical models, 3rd Leibniz MMS Days 2018, February 28  March 2, 2018, Leibniz Institute for Surface Engineering (IOM) & LeibnizInstitut für Troposphärenforschung (TROPOS), Leipzig, February 28, 2018, DOI https://doi.org/10.5446/35360 .

TH. Koprucki, Numerical methods for driftdiffusion equations, sc Matheon Workshop ``11th Annual Meeting Photonic Devices'', February 8  9, 2018, KonradZuseZentrum für Informationstechnik Berlin, February 8, 2018.

A. Mielke, Construction of effective gradient systems via EDP convergence, Workshop on Mathematical Aspects of NonEquilibrium Thermodynamics, March 5  7, 2018, RheinischWestfälische Technische Hochschule, Aachen, March 6, 2018.

A. Mielke, Global existence for finitestrain viscoplasticity, Variational Methods for the Modelling of Inelastic Solids, February 5  9, 2018, Mathematisches Forschungsinstitut Oberwolfach, February 6, 2018.

S. Reichelt, Corrector estimates for elliptic and parabolic equations with periodic coefficients, Analysis Seminar, FriedrichAlexanderUniversität ErlangenNürnberg, Institut für Angewandte Mathematik, Erlangen, May 18, 2017.

S. Reichelt, Corrector estimates for elliptic and parabolic equations with periodic coefficients, Analysis Seminar, Universität Augsburg, Institut für Mathematik, May 23, 2017.

S. Reichelt, Corrector estimates for imperfect transmission problems, 88th Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM 2017), Section S14 ``Applied Analysis'', March 6  10, 2017, Bauhaus Universität Weimar/Technische Universität Ilmenau, Weimar, March 7, 2017.

S. Reichelt, Pulses in FitzHughNagumo systems with periodic coefficients, Seminar ``Dynamical Systems and Applications'', Technische Universität Berlin, Institut für Mathematik, May 3, 2017.

S. Reichelt, Traveling waves in FitzHughNagumo systems with rapidly oscillating coefficients, Workshop ``Control of Selforganizing Nonlinear Systems'', August 29  31, 2017, Collaborative Research Center 910: Control of selforganizing nonlinear systems: Theoretical methods and concepts of application, Lutherstadt Wittenberg, August 30, 2017.

M. Heida, A. Mielke, Effective models for interfaces with many scales, CRC 1114 Conference ''Scaling Cascades in Complex Systems 2017'', Berlin, March 27  29, 2017.

M. Heida, Averaging of timeperiodic dissipation potentials in rateindependent processes, 88th Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM 2017), Section S14 ``Applied Analysis'', March 6  10, 2017, Bauhaus Universität Weimar/Technische Universität Ilmenau, Weimar, March 9, 2017.

M. Heida, On Gconvergence and stochastic twoscale convergences of the squareroot approximation scheme to the FokkerPlanck operator, GAMMWorkshop on Analysis of Partial Differential Equations, September 27  29, 2017, Eindhoven University of Technology, Mathematics and Computer Science Department, Netherlands, September 28, 2017.

M. Heida, What is ... GENERIC?, CRC1114 Colloquium, Freie Universität Berlin, SFB 1114, June 29, 2017.

M. Liero, Modeling and simulation of electrothermal feedback in largearea organic LEDs, Numerical Simulation of Optoelectronic Devices (NUSOD 2017), session ``LightEmitting Diodes'', July 24  28, 2017, Technical University of Denmark, Lyngby Campus, Kopenhagen, Denmark, July 25, 2017.

M. Liero, On entropytransport problems and the HellingerKantorovich distance, Seminar of Team EDPAIRSEACVGI, Université Grenoble Alpes, Laboratoire Jean Kuntzmann, Grenoble, France, January 26, 2017.

M. Mittnenzweig, An entropic gradient structure Lindblad equations, 88th Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM 2017), Section S14 ``Applied Analysis'', March 6  10, 2017, Bauhaus Universität Weimar/Technische Universität Ilmenau, Weimar, March 9, 2017.

M. Mittnenzweig, An entropic gradient structure for quantum Markov semigroups, Workshop ``Applications of Optimal Transportation in the Natural Sciences'', January 30  February 3, 2017, Mathematisches Forschungszentrum Oberwolfach, January 31, 2017.

CH. Mukherjee, Asymptotic behavior of the meanfield polaron, Probability and Mathematical Physics Seminar, Courant Institute of Mathematical Sciences, Department of Mathematics, New York, USA, March 20, 2017.

D. Peschka, Doping optimization for optoelectronic devices, Numerical Simulation of Optoelectronic Devices (NUSOD 2017), PostDeadline session, July 27  28, 2017, Technical University, Lyngby Campus, Kopenhagen, Denmark, July 28, 2017.

D. Peschka, Mathematical and numerical approaches to moving contact lines, Scuola Internazionale Superiore di Studi Avanzati (SISSA), Trieste, Italy, December 6, 2017.

D. Peschka, Modelling and simulation of suspension flow, Graduate Seminar PDE in the Sciences, Universität Bonn, Institut für Angewandte Mathematik, January 20, 2017.

D. Peschka, Motion of thin droplets over surfaces, Making a Splash  Driplets, Jets and Other Singularities, March 20  24, 2017, Brown University, Institute for Computational and Experimental Research in Mathematics (ICERM), Providence, USA, March 22, 2017.

D. Peschka, Variational structure of fluid motion with contact lines in thinfilm models, Kolloquium Angewandte Mathematik, Universität der Bundeswehr, München, May 31, 2017.

D. Peschka, Variational structure of viscous flows with contact line motion, Seminar Numerical Mathematics, WIAS RG 3, July 18, 2017.

A. Fischer, M. Liero, A. Glitzky, Th. Koprucki, K. Vandewal, S. Lenk, S. Reinicke, Predicting electrothermal behavior from labsize OLEDs to large area lighting panels, MRS Spring Meeting, Phoenix, Arizona, USA, April 17  21, 2017.

J. Sprekels, A nonstandard viscous CahnHilliard system with dynamic boundary condition and the DCH, Analysis of Boundary Value Problems for PDEs, Italy, February 20, 2017.

J. Sprekels, Optimal control of PDEs: From basic principles to hard applications, International School ``Frontiers in Partial Differential Equations and Solvers'', May 22  26, 2017, University of Pavia, Department of Mathematics, Italy.

J. Sprekels, Wellposedness and optimal control of a nonstandard CahnHilliard system with dynamic boundary condition, Fudan University, School of Mathematical Sciences, China, April 10, 2017.

A. Glitzky, Electrothermal description of organic semiconductor devices by $p(x)$Laplace thermistor models, 88th Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM 2017), Section S14 ``Applied Analysis'', March 6  10, 2017, Bauhaus Universität Weimar/Technische Universität Ilmenau, Weimar, March 9, 2017.

M. Thomas, Delamination processes in solids: GENERIC structure & analytical results, CIMWIAS Workshop ``Topics in Applied Analysis and Optimisation'', December 6  8, 2017, Centro de Matemática, Lisboa, Portugal, December 8, 2017.

M. Thomas, Dynamics of rock dehydration on multiple scales, SCCS Days, November 8  10, 2017, SFB 1114 ``Scaling Cascades in Complex Systems'', Schmöckwitz, November 9, 2017.

M. Thomas, Mathematical modeling and analysis of evolution processes in solids and the influence of bulkinterfaceinteraction, HumboldtUniversität zu Berlin, Institut für Mathematik, October 20, 2017.

M. Thomas, Rateindependent delamination processes in viscoelasticity, Miniworkshop on Dislocations, Plasticity, and Fracture, February 13  16, 2017, Scuola Internazionale Superiore di Studi Avanzati (SISSA), Trieste, Italy, February 15, 2017.

M. Thomas, Why scientist in Academia?, I, SCIENTIST: The Conference on Gender, Career Paths and Networking, May 12  14, 2017, Freie Universität, Berlin, May 14, 2017.

D.H. Doan, A unified Scharfetter Gummel scheme, Halbleiterseminar, WIAS, March 2, 2017.

P.É. Druet, Analysis of recent NernstPlanckPoissonNavierStokes systems of electrolytes, 88th Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM 2017), Section S14 ``Applied Analysis'', March 6  10, 2017, Bauhaus Universität Weimar/Technische Universität Ilmenau, Weimar, March 7, 2017.

P.É. Druet, Existence of weak solutions for improved NernstPlanckPoisson models of compressible electrolytes, Seminar EDE, Institute of Mathematics, Department of Evolution Differential Equations (EDE), Prague, Czech Republic, January 10, 2017.

J. Fuhrmann, A. Glitzky, M. Liero, Hybrid finitevolume/finiteelement schemes for p(x)laplace thermistor models, 8th International Symposium on Finite Volumes for Complex Applications (FVCA 8), Villeneuve d'Ascq, France, June 15, 2017.

TH. Koprucki, Comparison of consistent flux discretizations for drift diffusion beyond Boltzmann statistics, Numerical Simulation of Optoelectronic Devices (NUSOD 2017), session ``Numerical Methods'', July 24  28, 2017, Technical University of Denmark, Lyngby Campus, Kopenhagen, Denmark, July 27, 2017.

TH. Koprucki, HalbleiterBauteilsimulation: Modelle und numerische Verfahren, BlockSeminar des SFB 787 ``Nanophotonik'', June 7  9, 2017, Technische Universität Berlin, GraalMüritz, June 8, 2017.

TH. Koprucki, How to tidy up the jungle of mathematical models? A prerequisite for sustainable research software, 2nd Conference 2017 on NonTextual Information ``Software and Services for Science (S3)'', May 10  11, 2017, Technische Informationsbibliothek, Hannover, May 11, 2017, DOI 10.5446/31023 .

TH. Koprucki, Mathematical knowledge management as a route to sustainability in mathematical modeling and simulation, 2nd Leibniz MMS Days 2017, February 22  24, 2017, Technische Informationsbibliothek (TIB), Hannover, February 22, 2017, DOI 10.5446/21908 .

TH. Koprucki, Mathematical models as research data in numerical simulation of optoelectronic devices, Numerical Simulation of Optoelectronic Devices (NUSOD 2017), session ``Model Representation'', July 24  28, 2017, Technical University of Denmark, Lyngby Campus, Kopenhagen, Denmark, July 27, 2017.

TH. Koprucki, Mathematical models as research data via flexiformal theory graphs, 10th Conference on Intelligent Computer Mathematics (CICM 2017), track ``Mathematical Knowledge Management'', July 16  21, 2017, University of Edinburgh, UK, July 20, 2017.

TH. Koprucki, Model Pathway Diagrams for knowledge representation in mathematical modeling and simulation, 19th ÖMG Congress and Annual DMV Meeting, minisymposium M3 ``From Information to Knowledge Management'', September 11  15, 2017, ParisLodron University of Salzburg, Austria, September 12, 2017.

TH. Koprucki, On current injection into single quantum dots through oxideconfined pndiodes, 10th Annual Meeting ``Photonic Devices'', February 9  10, 2017, Zuse Institute Berlin (ZIB), Berlin, February 9, 2017.

TH. Koprucki, On the ScharfetterGummel scheme for the discretization of driftdiffusion equations and its generalization beyond Boltzmann, Kolloquium Modellierung, Numerik, Differentialgleichungen, Technische Universität Berlin, Insittut für Mathematik, May 30, 2017.

TH. Koprucki, Über das LKonzept einer physikalischen Theorie, Seminar Wissensrepräsentation und verarbeitung, FriedrichAlexanderUniversität ErlangenNürnberg, Lehrstuhl für Informatik, Erlangen, May 17, 2017.

M. Liero, A. Glitzky, Th. Koprucki, J. Fuhrmann, 3D electrothermal simulations of organic LEDs showing negative differential resistance, Multiscale Modelling of Organic Semiconductors: From Elementary Processes to Devices, Grenoble, France, September 12  15, 2017.

M. Liero, The HellingerKantorovich distance as natural generalization of optimal transport distance to (scalar) reactiondiffusion equations, Variational Methods for Evolution, November 12  17, 2017, Mathematisches Forschungszentrum Oberwolfach, November 14, 2017.

M. Liero, The HellingerKantorovich distance as natural generalization of optimal transport distance to (scalar) reactiondiffusion equations, Oberseminar ``Angewandte Analysis'', Universität Dortmund, Institut für Mathematik, November 29, 2017.

A. Mielke, A geometric approach to reactiondiffusion equations, Institutskolloquium, Universität Potsdam, Institut für Mathematik, January 25, 2017.

A. Mielke, Entropyinduced geometry for classical and quantum Markov semigroups, SMS Colloquium, University College Cork, School of Mathematical Science, Ireland, September 11, 2017.

A. Mielke, Global existence results for viscoplasticity, 88th Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM 2017), Section S14 ``Applied Analysis'', March 6  10, 2017, Bauhaus Universität Weimar/Technische Universität Ilmenau, Weimar, March 10, 2017.

A. Mielke, Interfaces with many scales, Second CRC 1114 Days ''Scaling Cascades in Complex Systems'', November 8  10, 2017, Freie Universität Berlin, Schmöckwitz, November 10, 2017.

A. Mielke, Mathematical modeling of semiconductors: From quantum mechanics to devices, CIMWIAS Workshop ``Topics in Applied Analysis and Optimisation'', December 6  8, 2017, Centro de Matemática, Lisboa, Portugal, December 8, 2017.

A. Mielke, On selfinduced oscillations for friction reduction with applications to walking, Conference ``Dynamical Systems and Geometric Mechanics'', June 12  14, 2017, Technische Universität München, Zentrum für Mathematik, June 13, 2017.

A. Mielke, Optimal transport versus growth and decay, International Conference ``Calculus of Variations and Optimal Transportation'' in the Honor of Yann Brenier for his 60th Birthday, January 9  11, 2017, Institut Henri Poincaré, Paris, France, January 11, 2017.

A. Mielke, Oscillations in systems with hysteresis, SFB 910 Symposium ``Stability Versus Oscillations in Complex Systems'', Technische Universität Berlin, Institut für Theoretische Physik, February 10, 2017.

A. Mielke, Perspectives for gradient flows, GAMMWorkshop on Analysis of Partial Differential Equations, September 27  29, 2017, Eindhoven University of Technology, Mathematics and Computer Science Department, Netherlands, September 28, 2017.

A. Mielke, Uniform exponential decay for energyreactiondiffusion systems, Analysis Seminar, University of Pavia, Department of Mathematics, Italy, March 21, 2017.

M. Mittnenzweig, A variational approach to quantum master equations coupled to a semiconductor PDE, Variational Methods for Evolution, November 12  17, 2017, Mathematisches Forschungszentrum Oberwolfach, November 14, 2017.

M. Mittnenzweig, A variational approach to the Lindblad equations, Scientific computing seminar, Université École des Ponts, CERMICS, Paris, France, April 24, 2017.

M. Mittnenzweig, Gradient flow structures for quantum master equations, AnalysisSeminar AugsburgMünchen, Universität Augsburg, Institut für Mathematik, June 8, 2017.

M. Mittnenzweig, Variational methods for quantum master equations, Barcelona Graduate School of Mathematics Junior Meeting, October 9  10, 2017, Berlin Mathematical School, Spain, October 10, 2017.

J. Rehberg, Explicit and uniform resolvent estimates for second order divergence operators on $L^p$ spaces, Oberseminar Analysis, Technische Universität Darmstadt, Fachbereich Mathematik, Darmstadt, November 9, 2017.

J. Rehberg, On optimal elliptic Sobolev regularity, Oberseminar Prof. Ira Neitzel, Rheinische FriedrichWilhelmsUniversität Bonn, Institut für Numerische Simulation, February 2, 2017.
Research Groups
 Partial Differential Equations
 Laser Dynamics
 Numerical Mathematics and Scientific Computing
 Nonlinear Optimization and Inverse Problems
 Interacting Random Systems
 Stochastic Algorithms and Nonparametric Statistics
 Thermodynamic Modeling and Analysis of Phase Transitions
 Nonsmooth Variational Problems and Operator Equations