Publications

Monographs

  • O. Marquardt, V.M. Kaganer, P. Corfdir, Chapter 12 ``Nanowires'' in Handbook of Optoelectronic Device Modeling and Simulations: Fundamentals, Materials, Nanostructures, LEDs, and Amplifiers, J. Piprek, ed., 1 of Series in Optics and Optoelectronics, CRC Press, 2017, pp. 395--415, (Chapter Published).

  • S. Jachalski, D. Peschka, S. Bommer, R. Seemann, B. Wagner, Chapter 18: Structure Formation in Thin Liquid--Liquid Films, in: Transport Processes at Fluidic Interfaces, D. Bothe, A. Reusken, eds., Advances in Mathematical Fluid Mechanics, Birkhäuser, Springer International Publishing AG, Cham, Switzerland, 2017, pp. 531--574, (Chapter Published), DOI 10.1007/978-3-319-56602-3 .
    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 liquid-liquid 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 liquid--liquid 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 ``Drift-Diffusion Models'' in Volume 2 of Handbook of Optoelectronic Device Modeling and Simulation: Fundamentals, Materials, Nanostructures, LEDs, and Amplifiers, J. Piprek, ed., Series in Optics and Optoelectronics, CRC Press Taylor & Francis Group, 2017, pp. 733--771, (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; well-posedness 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 self-contained 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

  • 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. Fernández-Garrido, H.T. Grahn, O. Brandt, Nano Letters, 18 (2018), pp. 247--254, DOI 10.1021/acs.nanolett.7b03997 .

  • K. Disser, A.F.M. TER Elst, J. Rehberg, On maximal parabolic regularity for non-autonomous parabolic operators, Journal of Differential Equations, 262 (2017), pp. 2039--2072.
    Abstract
    We consider linear inhomogeneous non-autonomous 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 Lr-regularity for discontinuous non-autonomous second-order 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. 65--79.
    Abstract
    In this paper we investigate linear parabolic, second-order 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. 3--26, DOI 10.3233/ASY-171432 .
    Abstract
    Based on previous homogenization results for imperfect transmission problems in two-component 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 time-periodic dissipation potentials in rate-independent processes, Discrete and Continuous Dynamical Systems -- Series S, 10 (2017), pp. 1303--1327.
    Abstract
    We study the existence and well-posedness of rate-independent 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 equi-continuity of the solutions in the limit ε→0.

  • M. Heida, Stochastic homogenization of rate-independent systems, Continuum Mechanics and Thermodynamics, 29 (2017), pp. 853--894, DOI 10.1007/s00161-017-0564-z .
    Abstract
    We study the stochastic and periodic homogenization 1-homogeneous convex functionals. We proof some convergence results with respect to stochastic two-scale convergence, which are related to classical Gamma-convergence results. The main result is a general liminf-estimate for a sequence of 1-homogeneous functionals and a two-scale stability result for sequences of convex sets. We apply our results to the homogenization of rateindependent systems with 1-homogeneous 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 Prandlt-Reuss plasticity, Coulomb friction on a macroscopic surface and Coulomb friction on microscopic fissure.

  • M. Kantner, M. Mittnenzweig, Th. Koprucki, Hybrid quantum-classical modeling of quantum dot devices, Phys. Rev. B., 96 (2017), pp. 205301/1--205301/17, 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 well-established fields of semi-classical 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 quantum-classical 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 single-photon 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. 1--35, 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 non-quadratic 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 large-deviation principles. While Markovian diffusion processes lead to classical gradient structures, Poissonian jump processes give rise to cosh-type dissipation potentials. A second origin arises via a new form of convergence, that we call EDP-convergence. 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 Gamma-limit. 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 reaction-diffusion system.

  • M. Liero, A. Mielke, G. Savaré, Optimal entropy-transport problems and a new Hellinger--Kantorovich distance between positive measures, Inventiones mathematicae, (2017), published online on 14.12.2017, DOI 10.1007/s00222-017-0759-8 .
    Abstract
    We develop a full theory for the new class of Optimal Entropy-Transport 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 Entropy-Transport problems and introduce the new Hellinger-Kantorovich 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 well-known Hellinger-Kakutani and Kantorovich-Wasserstein distances.

  • O. Marquardt, Th. Krause, V. Kaganer, J. Martin-Sánchez, M. Hanke, O. Brandt, Influence of strain relaxation in axial $In_xGa_1-xN/GaN$ nanowire heterostructures on their electronic properties, Nanotechnology, 28 (2017), pp. 215204/1--215204/6, DOI 10.1088/1361-6528/aa6b73 .
    Abstract
    We present a systematic theoretical study of the influence of elastic strain relaxation on the built-in electrostatic potentials and the electronic properties of axial InxGa1-xN/GaN nanowire (NW) heterostructures. Our simulations reveal that for a sufficiently large ratio between the thickness of the InxGa1-xN disk and the diameter of the NW, the elastic relaxation leads to a significant reduction of the built-in 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 built-in electrostatic potentials. We show that the structures under consideration are by no means field-free, and the built-in 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. 245309/1--245309/8, DOI 10.1103/PhysRevB.95.245309 .
    Abstract
    We study the electronic properties of GaAs nanowires composed of both the zinc-blende and wurtzite modifications using a ten-band k-p 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 zinc-blende/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 non-negligible 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 zinc-blende 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. 205--233, DOI 10.1007/s10955-017-1756-4 .
    Abstract
    We show that all Lindblad operators (i.e. generators of quantum semigroups) on a finite-dimensional 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 non-autonomous evolution equations, Nanosystems: Physics, Chemistry, Mathematics, 8 (2017), pp. 202--215, DOI 10.17586/2220-8054-2017-8-2-202-215 .
    Abstract
    We improve some recent estimates of the rate of convergence for product approximations of solution operators for linear non-autonomous Cauchy problem. The Trotter product formula approximation is proved to converge to the solution operator in the operator-norm. We estimate the rate of convergence of this approximation. The result is applied to diffusion equation perturbed by a time-dependent potential.

  • R. Rossi, M. Thomas, Coupling rate-independent and rate-dependent processes: Existence results, SIAM Journal on Mathematical Analysis, 49 (2017), pp. 1419--1494.
    Abstract
    We address the analysis of an abstract system coupling a rate-independet 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 time-discretization schemes. Our arguments combine techniques from the theory of gradient systems with the toolbox for rate-independent evolution, thus reflecting the mixed character of the problem. Finally, we discuss applications to a class of rate-independent processes in visco-elastic solids with inertia, and to a recently proposed model for damage with plasticity.

  • R. Rossi, M. Thomas, From adhesive to brittle delamination in visco-elastodynamics, Mathematical Models & Methods in Applied Sciences, 27 (2017), pp. 1489--1546, DOI 10.1142/S0218202517500257 .
    Abstract
    In this paper we analyze a system for brittle delamination between two visco-elastic bodies, also subject to inertia, which can be interpreted as a model for dynamic fracture. The rate-independent 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 rate-independent systems to the present mixed rate-dependent/rate-independent 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 Dirichlet-to-Neumann maps, Journal of Functional Analysis, 273 (2017), pp. 1970--2025, DOI 10.1016/j.jfa.2017.06.001 .
    Abstract
    A general representation formula for the scattering matrix of a scattering system consisting of two self-adjoint operators in terms of an abstract operator valued Titchmarsh?Weyl m-function is proved. This result is applied to scattering problems for different self-adjoint 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 Dirichlet-to-Neumann maps.

  • P. Colli, G. Gilardi, E. Rocca, J. Sprekels, Optimal distributed control of a diffuse interface model of tumor growth, Nonlinearity, 30 (2017), pp. 2518--2546.
    Abstract
    In this paper, a distributed optimal control problem is studied for a diffuse interface model of tumor growth which was proposed by Hawkins--Daruud et al. in citeHZO. The model consists of a Cahn-Hilliard equation for the tumor cell fraction $vp$ coupled to a reaction-diffusion equation for a function $s$ representing the nutrient-rich extracellular water volume fraction. The distributed control $u$ monitors as a right-hand 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 control-to-state operator is Fréchet differentiable between appropriate Banach spaces and derive the first-order 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 Cahn--Hilliard type phase field system modelling tumor growth, Discrete and Continuous Dynamical Systems, 10 (2017), pp. 37--54.
    Abstract
    This paper is concerned with a phase field system of Cahn--Hilliard 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 well-posedness, 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. 35--58.
    Abstract
    This paper is concerned with a distributed optimal control problem for a nonlocal phase field model of Cahn-Hilliard type, which is a nonlocal version of a model for two-species phase segregation on an atomic lattice under the presence of diffusion. The local model has been investigated in a series of papers by P. Podio-Guidugli 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 long-range 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 so-called `deep quench' approximation to establish existence and first-order necessary optimality conditions for the nonsmooth case of the double obstacle potential.

  • P. Colli, G. Gilardi, J. Sprekels, Global existence for a nonstandard viscous Cahn--Hilliard system with dynamic boundary condition, SIAM Journal on Mathematical Analysis, 49 (2017), pp. 1732--1760, 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 Podio-Guidugli in Ric. Mat. 55 (2006), pp. 105-118. 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 Laplace-Beltrami operator for the order parameter. This boundary condition models an additional nonconserving phase transition occurring on the surface of the domain. Different well-posedness 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 Cahn--Hilliard equation with dynamic boundary condition, Bulletin of the South Ural State University, Series: Mathematical Modelling, Programming and Computer Software, 10 (2017), pp. 5--21.

  • P. Exner, A.S. Kostenko, M.M. Malamud, H. Neidhardt, Infinite quantum graphs, Rossiiskaya Akademiya Nauk. Doklady Akademii Nauk, 472 (2017), pp. 253--258, 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 self-adjoint, 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. 2675--2710, DOI 10.20347/WIAS.PREPRINT.2384 .
    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 liquid-solid phase transformations in groundwater flows. The system of equations is derived here from the conservation principles for mass, momentum, and energy and from the Clausius-Duhem 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 cut-off techniques and suitable Moser-type 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. 806--811, 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. $T-R in mathbf S_1$, 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 $T-R in mathbf S_1$, 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. 70--93.
    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 first-order necessary and second-order 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. 536--562.
    Abstract
    We study a stationary thermistor model describing the electrothermal behavior of organic semiconductor devices featuring non-Ohmic current-voltage laws and self-heating effects. The coupled system consists of the current-flow equation for the electrostatic potential and the heat equation with Joule heating term as source. The self-heating in the device is modeled by an Arrhenius-like temperature dependency of the electrical conductivity. Moreover, the non-Ohmic 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 $p(x)$-Laplace-type problem with piecewise constant exponent. We prove the existence and boundedness of solutions in the two-dimensional 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 Caccioppoli-type estimates, Poincaré inequalities, and a Gehring-type Lemma for the $p(x)$-Laplacian. Finally, Schauder's fixed-point theorem is used to show the existence of solutions.

  • M. Thomas, Ch. Zanini, Cohesive zone-type delamination in visco-elasticity, Discrete and Continuous Dynamical Systems -- Series S, 10 (2017), pp. 1487--1517, DOI 10.20347/WIAS.PREPRINT.2350 .
    Abstract
    We study a model for the rate-independent evolution of cohesive zone delamination in a visco-elastic 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 non-penetration 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&Thomas15WIAS-Preprint2113].

  • 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. 497--513, 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 Scharfetter--Gummel scheme to non-Boltzmann (e.g. Fermi--Dirac) statistics. It is based on the analytical solution of a two-point 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 non-Boltzmann 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 p-i-n 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. 330/1--330/8, DOI 10.1007/s11082-017-1167-4 .
    Abstract
    Organic semiconductor devices show a pronounced interplay between temperature-activated conductivity and self-heating which in particular causes inhomogeneities in the brightness of large-area 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 diode-like behavior in recombination zones into account. We present a numerical simulation study for a red OLED using a finite-volume approximation of this model. The appearance of S-shaped current-voltage 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 energy-reaction-diffusion systems using vector-valued functional inequalities, Journal of Nonlinear Science, (2017), published online on 11.11.2017, DOI 10.1007/s00332-017-9427-9 .
    Abstract
    We discuss how the recently developed energy-dissipation methods for reactiondi usion systems can be generalized to the non-isothermal 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 log-Sobolev estimate and variants for lower-order 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/s00205-017-1164-6 .
    Abstract

    We study a model for rate-dependent gradient plasticity at finite strain based on the multiplicative decomposition of the strain tensor, and investigate the existence of global-in-time 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 finite-strain elasticity as well as the multiplicative decomposition of finite-strain plasticity. Moreover, the dissipation potential depends on the left-invariant 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 energy-dissipation-balance (EDB) and energy-dissipation-inequality (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. 437--475, 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, Non-equilibrium thermodynamical principles for chemical reactions with mass-action kinetics, SIAM Journal on Applied Mathematics, 77 (2017), pp. 1562--1585, DOI 10.20347/WIAS.PREPRINT.2165 .
    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 non-linear 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 electro-optical models for broad-area edge-emitting semiconductor devices, Optical and Quantum Electronics, 49 (2017), pp. 332/1--332/8, DOI 10.20347/WIAS.PREPRINT.2421 .
    Abstract
    We extend a 2 (space) + 1 (time)-dimensional traveling wave model for broad-area edge-emitting 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, U. Bandelow, Th. Koprucki, H.-J. Wünsche, Simulation of quantum dot devices by coupling of quantum master equations and semi-classical 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. 217--218.

  • TH. Koprucki, M. Kohlhaase, D. Müller, K. Tabelow, Mathematical models as research data in numerical simulation of opto-electronic 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 machine-actionable as well as human-understandable representation of the mathematical knowledge they contain and the domain-specific 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 one-dimensional drift-diffusion equations (van Roosbroeck system).

  • M. Liero, J. Fuhrmann, A. Glitzky, Th. Koprucki, A. Fischer, S. Reineke, Modeling and simulation of electrothermal feedback in large-area 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. 105--106, DOI 10.1109/NUSOD.2017.8010013 .

  • M. Bulíček, A. Glitzky, M. Liero, Thermistor systems of p(x)-Laplace-type 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. 697--713.
    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 current-flow equation is of p(x)-Laplacian-type 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 L1 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 Cahn--Hilliard 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. 151--182, DOI 10.20347/WIAS.PREPRINT.2370 .
    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.Podio-Guidugli in Ric. Mat. 55 (2006), pp.105-118. 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 Laplace-Beltrami 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. 35-58, 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. 1-30, for the case of (differentiable) logarithmic potentials and perform a so-called "deep quench limit". Using compactness and monotonicity arguments, it is shown that this strategy leads to the desired first-order 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 vector-valued Sturm--Liouville 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. 271--313, DOI 10.4171/175-1/15 .

  • 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 17-21, 2017, Proceedings, H. Geuvers, M. England, O. Hasan, F. Rabe , O. Teschke, eds., Springer International Publishing, Cham, 2017, pp. 224--238, DOI 10.1007/978-3-319-62075-6_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 non-trivial model: van Roosbroeck's drift-diffusion model for one-dimensional 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 AV-Portal 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 AV-Portal as a sustainable infrastructure for audio-visual 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 opto-electronics.

  • 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. 27--38, DOI 10.1007/978-981-10-6283-4_3 .
    Abstract
    This contribution presents recent results in the modeling and the analysis of delamination problems. It addresses adhesive contact, brittle, and cohesive zone models both in a quasistatic and a viscous, dynamic setting for the bulk part. Also different evolution laws for the delaminating surface are discussed.

  • 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. 219--220, DOI 10.1109/NUSOD.2017.8010070 .

  • J. Fuhrmann, A. Glitzky, M. Liero, Hybrid finite-volume/finite-element 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. 397--405, DOI 10.1007/978-3-319-57394-6_42 .

  • M. Radziunas, A. Zeghuzi, J. Fuhrmann, Th. Koprucki, H.-J. Wünsche, H. Wenzel, U. Bandelow, Efficient coupling of inhomogeneous current spreading and electro-optical models for simulation of dynamics in broad-area 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. 231--232.

Preprints, Reports, Technical Reports

  • 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 two-scale 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 two-scale 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 two-scale 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 non-convex evolution equation of Allen-Cahn type. Moreover, we discuss the relation of stochastic unfolding to previously introduced notions of (quenched and mean) stochastic two-scale convergence. The method introduced in this paper extends discrete stochastic unfolding, as recently introduced by the second and third author in the context of discrete-to-continuum transition.

  • P. Dondl, Th. Frenzel, A. Mielke, A gradient system with a wiggly energy and relaxed EDP-convergence, 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 Gamma-convergence that relates the microscopic energy and the microscopic dissipation potential with their macroscopic limits via Gamma-convergence. We call this notion relaxed EDP-convergence since the special structure of the dissipation functional may not be preserved under Gamma-convergence. However, by investigating the kinetic relation we derive the macroscopic dissipation potential.

  • V. Laschos, A. Mielke, Geometric properties of cones with applications on the Hellinger--Kantorovich 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 Hellinger--Kantorovich space into a cone space over the space of probabilities measures. Here we exploit a natural two-parameter scaling property of the Hellinger-Kantorovich 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 two-parameter rescaling and reparametrization of the geodesics, local-angle condition and some partial K-semiconcavity 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 Swift--Hohenberg equations, Preprint no. 2457, WIAS, Berlin, 2017, DOI 10.20347/WIAS.PREPRINT.2457 .
    Abstract, PDF (693 kByte)
    We present analytical and numerical investigations of two anti-symmetrically coupled 1D Swift--Hohenberg 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 codimension-two point of the Turing-wave 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 Ginzburg--Landau-type 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 phase-field 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)
    Phase-field models have already been proven to predict complex fracture patterns in two and three dimensions for brittle fracture at small strains. In this paper we discuss a model for phase-field fracture at finite deformations in more detail. Among the identification of crack location and projection of crack growth the numerical stability is one of the main challenges in solid mechanics. We here present a phase-field model at finite strains, which takes into account the anisotropy of damage by applying an anisotropic split and the modified invariants of the right Cauchy-Green strain tensor. We introduce a suitable weak notion of solution that also allows for a spatial and temporal discretization of the model. In this framework we study the existence of solutions %Second the mathematical background of the approach is examined and and we show that the time-discrete solutions converge in a weak sense to a solution of the time-continuous formulation of the model. Numerical examples in two and three space dimensions are carried out in the range of validity of the analytical results.

  • 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 Hamiltonian-like and dissipative dynamics in chains of coupled phase oscillators with skew-symmetric 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 skew-symmetric, i. e. when the anisotropy is balanced in a specific way, the system shows robustly a coexistence of Hamiltonian-like and dissipative regions in the phase space. We relate this phenomenon to the time-reversibility property of the system. The geometry of low-dimensional systems up to five oscillators is described in detail. In particular, we show that the boundary between the dissipative and Hamiltonian-like regions consists of families of heteroclinic connections. For larger chains with skew-symmetric 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 Hamiltonian-like region existing around the synchronous state similarly to the case of finite rings.

  • TH. Koprucki, M. Kohlhase, K. Tabelow, D. Müller, F. Rabe, Model pathway diagrams for the representation of mathematical models, Preprint no. 2431, WIAS, Berlin, 2017, DOI 10.20347/WIAS.PREPRINT.2431 .
    Abstract, PDF (421 kByte)
    Mathematical models are the foundation of numerical simulation of optoelectronic devices. We present a concept for a machine-actionable as well as human-understandable representation of the mathematical knowledge they contain and the domain-specific 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 block-based composition of models from simpler components.

  • B. Drees, A. Kraft, Th. Koprucki, Reproducible research through persistently linked and visualized data, Preprint no. 2430, WIAS, Berlin, 2017, DOI 10.20347/WIAS.PREPRINT.2430 .
    Abstract, PDF (1945 kByte)
    The demand of reproducible results in the numerical simulation of opto-electronic devices or more general in mathematical modeling and simulation requires the (long-term) 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 state-of-the 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 opto-electronics.

  • P. Colli, G. Gilardi, J. Sprekels, Optimal velocity control of a convective Cahn--Hilliard 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 Cahn-Hilliard 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 Cahn-Hilliard 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 so-called `deep quench approximation'. We derive results concerning the existence of optimal controls and the first-order 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 Cahn--Hilliard 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 Cahn--Hilliard 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 control-to-state mapping in suitable Banach spaces, and derive the first-order 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 Fermi--Dirac and Gauss--Fermi statistics, Preprint no. 2424, WIAS, Berlin, 2017, DOI 10.20347/WIAS.PREPRINT.2424 .
    Abstract, PDF (1572 kByte)
    We compare three thermodynamically consistent Scharfetter--Gummel schemes for different distribution functions for the carrier densities, including the Fermi--Dirac integral of order 1/2 and the Gauss--Fermi integral. The most accurate (but unfortunately also most costly) generalized Scharfetter--Gummel 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 Fermi--Dirac and Gauss--Fermi statistics. Finally, by comparing two modified (diffusion-enhanced and inverse activity based) Scharfetter--Gummel schemes with the more accurate generalized scheme, we show that the diffusion-enhanced ansatz leads to considerably lower flux errors, confirming previous results (J. Comp. Phys. 346:497-513, 2017).

  • L. Donati, M. Heida, M. Weber, B. Keller, Estimation of the infinitesimal generator by square-root 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 time-scales, 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 low-dimensional 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 2d-diffusion process and Alanine dipeptide.

  • P. Gurevich, S. Reichelt, Pulses in FitzHugh--Nagumo 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 FitzHugh-Nagumo systems that are coupled parabolic equations with rapidly periodically oscillating coefficients. In the limit of vanishing periods, there arises a two-scale FitzHugh-Nagumo 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 pulse-like solutions of the original system.

  • M. Liero, S. Melchionna, The weighted energy-dissipation principle and evolutionary Γ-convergence 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 so-called weighted energy-dissipation (WED) functional, whose minimizer correspond to solutions of an elliptic-in-time regularization of the target problems with regularization parameter δ. We investigate the relation between the Γ-convergence of the WED functionals and evolutionary Γ-convergence 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 Γ-convergence of functionals or in the sense of evolutionary Γ-convergence of functional-driven 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 λ-convex 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 rate-dependent/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, energetic-type existence results obtained in [Rossi/Thomas-ESAIM-COCV-21(1):1-59,2015] for a system for rate-independent, brittle delamination between two visco-elastic, physically nonlinear bulk materials and explain how to rigorously extend such results to the case of visco-elastic, linearly elastic bulk materials. Our approximation result is essentially based on deducing the Mosco-convergence of the functionals involved in the energetic formulation of the system. We apply this approximation result in two different situations: Firstly, to pass from a nonlinearly elastic to a linearly elastic, brittle model on the time-continuous level, and secondly, to pass from a time-discrete to a time-continuous model using an adhesive contact approximation of the brittle model, in combination with a vanishing, super-quadratic regularization of the bulk energy. The latter approach is beneficial if the model also accounts for the evolution of temperature.

  • P. Dupuis, V. Laschos, K. Ramanan, Exit time risk-sensitive stochastic control problems related to systems of cooperative agents, Preprint no. 2407, WIAS, Berlin, 2017, DOI 10.20347/WIAS.PREPRINT.2407 .
    Abstract, PDF (443 kByte)
    We study sequences, parametrized by the number of agents, of exit time stochastic control problems with risk-sensitive costs structures generate by unbounded costs. We identify a fully characterizing assumption, under which, each of them corresponds to a risk-neutral stochastic control problem with additive cost, and also to a risk-neutral 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 state-dependent 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 Fokker--Planck 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 Fokker-Planck equation using a discrete notion of G-convergence. Hence the squareroot approximation turns out to be a usefull approximation scheme to the Fokker-Planck equation in high dimensional spaces. As an example, in the special case of stationary Voronoi tessellations we use stochastic two-scale convergence to prove that this setting satisfies the G-convergence property. In particular, the class of tessellations for which the G-convergence result holds is not trivial.

  • P. Colli, G. Gilardi, J. Sprekels, On a Cahn--Hilliard 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 Cahn--Hilliard 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 Cahn--Hilliard 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 Faedo--Galerkin 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 rate-independent, partial, isotropic damage in quasistatic small strain linear elasticity, featuring a damage variable with spatial BV-regularization. Discrete solutions are obtained using an alternate time-discrete scheme and the Variable-ADMM algorithm to solve the constrained nonsmooth optimization problem that determines the damage variable at each time step. We prove convergence of the method and show that discrete solutions approximate a semistable energetic solution of the rate-independent system. Moreover, we present our numerical results for two benchmark problems.

  • 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 C0-semigroups 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 unbounded-range 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 almost-sure homogenization of the discrete Poisson equation and of the top of the Dirichlet spectrum. We assume that the conductances are stationary, ergodic and nearest-neighbor 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 long-range 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 two-scale convergence

  • P. Colli, G. Gilardi, J. Sprekels, Limiting problems for a nonstandard viscous Cahn--Hilliard 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 phase-field type, consisting of a parabolic system of two partial differential equations, complemented by boundary and initial conditions. The system arises from a model of two-species phase segregation on an atomic lattice and was introduced by Podio-Guidugli in Ric. Mat. 55 (2006), pp.105--118. 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 Laplace-Beltrami 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 long-time behavior of the system for both problems, with positive or zero viscosity coefficient, and characterize the omega-limit set in both cases.

  • M. Heida, S. Nesenenko, Stochastic homogenization of rate-dependent 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 rate-dependent systems. The derivations of the homogenization results presented in this work are based on the stochastic two-scale convergence in Sobolev spaces. For completeness, we also present some two-scale homogenization results for convex functionals, which are related to the classical Gamma-convergence theory.

Talks, Poster

  • S. Reichelt, Corrector estimates for elliptic and parabolic equations with periodic coefficients, Analysis Seminar, Friedrich-Alexander-Universität Erlangen-Nürnberg, 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 FitzHugh-Nagumo systems with periodic coefficients, Seminar ``Dynamical Systems and Applications'', Technische Universität Berlin, Institut für Mathematik, May 3, 2017.

  • S. Reichelt, Traveling waves in FitzHugh--Nagumo systems with rapidly oscillating coefficients, Workshop ``Control of Self-organizing Nonlinear Systems'', August 29 - 31, 2017, Collaborative Research Center 910: Control of self-organizing 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 time-periodic dissipation potentials in rate-independent 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 G-convergence and stochastic two-scale convergences of the squareroot approximation scheme to the Fokker--Planck operator, GAMM-Workshop 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 large-area organic LEDs, Numerical Simulation of Optoelectronic Devices (NUSOD 2017), session ``Light-Emitting Diodes'', July 24 - 28, 2017, Technical University of Denmark, Lyngby Campus, Kopenhagen, Denmark, July 25, 2017.

  • M. Liero, On entropy-transport problems and the Hellinger--Kantorovich distance, Seminar of Team EDP-AIRSEA-CVGI, 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 mean-field 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), Post-Deadline 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 thin-film 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 lab-size OLEDs to large area lighting panels, MRS Spring Meeting, Phoenix, Arizona, USA, April 17 - 21, 2017.

  • J. Sprekels, A nonstandard viscous Cahn--Hilliard 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, Well-posedness and optimal control of a nonstandard Cahn--Hilliard 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, CIM-WIAS 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 bulk-interface-interaction, Humboldt-Universität zu Berlin, Institut für Mathematik, October 20, 2017.

  • M. Thomas, Rate-independent delamination processes in visco-elasticity, 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 Nernst--Planck--Poisson--Navier--Stokes 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 Nernst--Planck--Poisson 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 finite-volume/finite-element 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, Halbleiter-Bauteilsimulation: Modelle und numerische Verfahren, Block-Seminar des SFB 787 ``Nanophotonik'', June 7 - 9, 2017, Technische Universität Berlin, Graal-Müritz, June 8, 2017.

  • TH. Koprucki, How to tidy up the jungle of mathematical models? A prerequisite for sustainable research software, 2nd Conference 2017 on Non-Textual 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 opto-electronic 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, Paris-Lodron University of Salzburg, Austria, September 12, 2017.

  • TH. Koprucki, On current injection into single quantum dots through oxide-confined pn-diodes, 10th Annual Meeting ``Photonic Devices'', February 9 - 10, 2017, Zuse Institute Berlin (ZIB), Berlin, February 9, 2017.

  • TH. Koprucki, On the Scharfetter-Gummel scheme for the discretization of drift-diffusion equations and its generalization beyond Boltzmann, Kolloquium Modellierung, Numerik, Differentialgleichungen, Technische Universität Berlin, Insittut für Mathematik, May 30, 2017.

  • TH. Koprucki, Über das L-Konzept einer physikalischen Theorie, Seminar Wissensrepräsentation und -verarbeitung, Friedrich-Alexander-Universität Erlangen-Nürnberg, 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 Hellinger--Kantorovich distance as natural generalization of optimal transport distance to (scalar) reaction-diffusion equations, Variational Methods for Evolution, November 12 - 17, 2017, Mathematisches Forschungszentrum Oberwolfach, November 14, 2017.

  • M. Liero, The Hellinger--Kantorovich distance as natural generalization of optimal transport distance to (scalar) reaction-diffusion equations, Oberseminar ``Angewandte Analysis'', Universität Dortmund, Institut für Mathematik, November 29, 2017.

  • A. Mielke, A geometric approach to reaction-diffusion equations, Institutskolloquium, Universität Potsdam, Institut für Mathematik, January 25, 2017.

  • A. Mielke, Entropy-induced 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, CIM-WIAS Workshop ``Topics in Applied Analysis and Optimisation'', December 6 - 8, 2017, Centro de Matemática, Lisboa, Portugal, December 8, 2017.

  • A. Mielke, On self-induced 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, GAMM-Workshop 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 energy-reaction-diffusion 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, Analysis-Seminar Augsburg-München, 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 Friedrich-Wilhelms-Universität Bonn, Institut für Numerische Simulation, February 2, 2017.