Publikationen

Artikel in Referierten Journalen

  • M. Heida, S. Nesenenko, Stochastic homogenization of rate-dependent models of monotone type in plasticity, Asymptotic Analysis, 112 (2019), pp. 185--212, DOI 10.3233/ASY-181502 .
    Abstract
    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.

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

  • A. Stephan, H. Stephan, Memory equations as reduced Markov processes, Discrete and Continuous Dynamical Systems, 39 (2019), pp. 2133--2155, DOI 10.3934/dcds.2019089 .
    Abstract
    A large class of linear memory differential equations in one dimension, where the evolution depends on the whole history, can be equivalently described as a projection of a Markov process living in a higher dimensional space. Starting with such a memory equation, we give an explicit construction of the corresponding Markov process. From a physical point of view the Markov process can be understood as the change of the type of some quasiparticles along one-way loops. Typically, the arising Markov process does not have the detailed balance property. The method leads to a more realisitc modeling of memory equations. Moreover, it carries over the large number of investigation tools for Markov processes to memory equations, like the calculation of the equilibrium state, the asymptotic behavior and so on. The method can be used for an approximative solution of some degenerate memory equations like delay differential equations.

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

  • A. Bacho, E. Emmrich, A. Mielke, An existence result and evolutionary Gamma-convergence for perturbed gradient systems, Journal of Evolution Equations, (2019), published online on 28.01.2019, DOI 10.1007/s00028-019-00484-x .
    Abstract
    We consider the initial-value problem for the perturbed gradient flows, where a differential inclusion is formulated in terms of a subdifferential of an energy functional, a subdifferential of a dissipation potential and a more general perturbation, which is assumed to be continuous and to satisfy a suitable growth condition. Under additional assumptions on the dissipation potential and the energy functional, existence of strong solutions is shown by proving convergence of a semi-implicit discretization scheme with a variational approximation technique.

  • 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, Journal of Convex Analysis, 26 (2019), pp. 485--514.
    Abstract
    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.

  • G. Gilardi, J. Sprekels, Asymptotic limits and optimal control for the Cahn--Hilliard system with convection and dynamic boundary conditions, Nonlinear Analysis. An International Mathematical Journal, 178 (2019), pp. 1--21.
    Abstract
    In this paper, we study initial-boundary value problems for the Cahn--Hilliard system with convection and nonconvex potential, where dynamic boundary conditions are assumed for both the associated order parameter and the corresponding chemical potential. While recent works addressed the case of viscous Cahn--Hilliard systems, the `pure' nonviscous case is investigated here. In its first part, the paper deals with the asymptotic behavior of the solutions as time approaches infinity. It is shown that the $omega$-limit of any trajectory can be characterized in terms of stationary solutions, provided the initial data are sufficiently smooth. The second part of the paper deals with the optimal control of the system by the fluid velocity. Results concerning existence and first-order necessary optimality conditions are proved. Here, we have to restrict ourselves to the case of everywhere defined smooth potentials. In both parts of the paper, we start from corresponding known results for the viscous case, derive sufficiently strong estimates that are uniform with respect to the (positive) viscosity parameter, and then let the viscosity tend to zero to establish the sought results for the nonviscous case.

  • J. Sprekels, H. Wu, Optimal distributed control of a Cahn--Hilliard--Darcy system with mass sources, Applied Mathematics and Optimization. An International Journal with Applications to Stochastics, published online on 24.01.2019, DOI 10.1007/s00245-019-09555-4 .
    Abstract
    In this paper, we study an optimal control problem for a two-dimensional Cahn--Hilliard--Darcy system with mass sources that arises in the modeling of tumor growth. The aim is to monitor the tumor fraction in a finite time interval in such a way that both the tumor fraction, measured in terms of a tracking type cost functional, is kept under control and minimal harm is inflicted to the patient by administering the control, which could either be a drug or nutrition. We first prove that the optimal control problem admits a solution. Then we show that the control-to-state operator is Fréchet differentiable between suitable Banach spaces and derive the first-order necessary optimality conditions in terms of the adjoint variables and the usual variational inequality.

  • A. Glitzky, M. Liero, Instationary drift-diffusion problems with Gauss--Fermi statistics and field-dependent mobility for organic semiconductor devices, Communications in Mathematical Sciences, 17 (2019), pp. 33--59, DOI 10.4310/cms.2019.v17.n1.a2 .
    Abstract
    This paper deals with the analysis of an instationary drift-diffusion model for organic semiconductor devices including Gauss--Fermi statistics and application-specific mobility functions. The charge transport in organic materials is realized by hopping of carriers between adjacent energetic sites and is described by complicated mobility laws with a strong nonlinear dependence on temperature, carrier densities and the electric field strength. To prove the existence of global weak solutions, we consider a problem with (for small densities) regularized state equations on any arbitrarily chosen finite time interval. We ensure its solvability by time discretization and passage to the time-continuous limit. Positive lower a priori estimates for the densities of its solutions that are independent of the regularization level ensure the existence of solutions to the original problem. Furthermore, we derive for these solutions global positive lower and upper bounds strictly below the density of transport states for the densities. The estimates rely on Moser iteration techniques.

  • S.P. Frigeri, C.G. Gal, M. Grasselli, J. Sprekels, Strong solutions to nonlocal 2D Cahn--Hilliard--Navier--Stokes systems with nonconstant viscosity, degenerate mobility and singular potential, Nonlinearity, 32 (2019), pp. 678--727, DOI 10.1088/1361-6544/aaedd0 .
    Abstract
    We consider a nonlinear system which consists of the incompressible Navier-Stokes equations coupled with a convective nonlocal Cahn-Hilliard equation. This is a diffuse interface model which describes the motion of an incompressible isothermal mixture of two (partially) immiscible fluids having the same density. We suppose that the viscosity depends smoothly on the order parameter as well as the mobility. Moreover, we assume that the mobility is degenerate at the pure phases and that the potential is singular (e.g. of logarithmic type). This system is endowed with no-slip boundary condition for the (average) velocity and homogeneous Neumann boundary condition for the chemical potential. Thus the total mass is conserved. In the two-dimensional case, this problem was already analyzed in some joint papers of the first three authors. However, in the present general case, only the existence of a global weak solution, the (conditional) weak-strong uniqueness and the existence of the global attractor were proven. Here we are able to establish the existence of a (unique) strong solution through an approximation procedure based on time discretization. As a consequence, we can prove suitable uniform estimates which allow us to show some smoothness of the global attractor. Finally, we discuss the existence of strong solutions for the convective nonlocal Cahn-Hilliard equation, with a given velocity field, in the three dimensional case as well.

  • M. Radziunas, J. Fuhrmann, A. Zeghuzi, H.-J. Wünsche, Th. Koprucki, C. Brée, H. Wenzel, U. Bandelow, Efficient coupling of electro-optical and heat-transport models for high-power broad-area semiconductor lasers, Optical and Quantum Electronics, 51 (2019), published online on 22.02.2019, DOI 10.1007/s11082-019-1792-1 .
    Abstract
    In this work, we discuss the modeling of edge-emitting high-power broad-area semiconductor lasers. We demonstrate an efficient iterative coupling of a slow heat transport (HT) model defined on multiple vertical-lateral laser cross-sections with a fast dynamic electro-optical (EO) model determined on the longitudinal-lateral domain that is a projection of the device to the active region of the laser. Whereas the HT-solver calculates temperature and thermally-induced refractive index changes, the EO-solver exploits these distributions and provides time-averaged field intensities, quasi-Fermi potentials, and carrier densities. All these time-averaged distributions are used repetitively by the HT-solver for the generation of the heat sources entering the HT problem solved in the next iteration step.

  • M. Heida, M. Röger, Large deviation principle for a stochastic Allen--Cahn equation, Journal of Theoretical Probability, 31 (2018), pp. 364--401, DOI 10.1007/s10959-016-0711-7 .
    Abstract
    The Allen-Cahn equation is a prototype model for phase separation processes, a fundamental example of a nonlinear spatial dynamic and an important approximation of a geometric evolution equation by a reaction-diffusion equation. Stochastic perturbations, especially in the case of additive noise, to the Allen-Cahn equation have attracted considerable attention. We consider here an alternative random perturbation determined by a Brownian flow of spatial diffeomorphism that was introduced by Röger and Weber [Stoch. Partial Differ. Equ. Anal. Comput. 1 (2013)]. We first provide a large deviation principle for stochastic flows in spaces of functions that are Hölder-continuous in time, which extends results by Budhiraja, Dupuis and Maroulas [Ann. Probab. 36 (2008)]. From this result and a continuity argument we deduce a large deviation principle for the Allen-Cahn equation perturbed by a Brownian flow in the limit of small noise. Finally, we present two asymptotic reductions of the large deviation functional.

  • M. Heida, B. Schweizer, Stochastic homogenization of plasticity equations, ESAIM. Control, Optimisation and Calculus of Variations, 24 (2018), pp. 153--176.
    Abstract
    In the context of infinitesimal strain plasticity with hardening, we derive a stochastic homogenization result. We assume that the coefficients of the equation are random functions: elasticity tensor, hardening parameter and flow-rule function are given through a dynamical system on a probability space. A parameter ε > 0 denotes the typical length scale of oscillations. We derive effective equations that describe the behavior of solutions in the limit ε → 0. The homogenization procedure is based on the fact that stochastic coefficients “allow averaging”: For one representative volume element, a strain evolution [0,T]∋ t ↦ξ(t) ∈ ℝsdxd induces a stress evolution [0,T]∋ t ↦Σ (ξ) (t)∈ℝsdxd. Once the hysteretic evolution law Σ is justified for averages, we obtain that the macroscopic limit equation is given by -∇ ⋅ Σ(∇su)=f.

  • M. Heida, R.I.A. Patterson, D.R.M. Renger, Topologies and measures on the space of functions of bounded variation taking values in a Banach or metric space, Journal of Evolution Equations, 19 (2018), pp. 111--152, DOI 10.1007/s00028-018-0471-1 .
    Abstract
    We study functions of bounded variation with values in a Banach or in a metric space. We provide several equivalent notions of variations and provide the notion of a time derivative in this abstract setting. We study four distinct topologies on the space of bounded variations and provide some insight into the structure of these topologies. In particular, we study the meaning of convergence, duality and regularity for these topologies and provide some useful compactness criteria, also related to the classical Aubin-Lions theorem. We finally provide some useful applications to stochastic processes.

  • M. Heida, On convergences of the squareroot approximation scheme to the Fokker--Planck operator, Mathematical Models & Methods in Applied Sciences, 28 (2018), pp. 2599--2635, DOI 10.1142/S0218202518500562 .
    Abstract
    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.

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

  • A.W. Achtstein, O. Marquardt, R. Scott, M. Ibrahim, Th. Riedl, A.V. Prudnikau, A. Antanovich, N. Owchimikow, J.K.N. Lindner, M. Artemyev, U. Woggon, Impact of shell growth on recombination dynamics and exciton-phonon interaction in CdSe-CdS core-shell nanoplatelets, ACS Nano, 12 (2018), pp. 9476--9483, DOI 10.1021/acsnano.8b04803 .

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

  • M. Becker, Th. Frenzel, Th. Niedermeyer, S. Reichelt, A. Mielke, M. Bär, Local control of globally competing patterns in coupled Swift--Hohenberg equations, Chaos. An Interdisciplinary Journal of Nonlinear Science, 28 (2018), pp. 043121/1--043121/11, DOI 10.1063/1.5018139 .
    Abstract
    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.

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

  • 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, SIAM Journal on Applied Dynamical Systems, 17 (2018), pp. 2076--2105, DOI 10.1137/17M1155685 .
    Abstract
    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.

  • P. Colli, G. Gilardi, J. Sprekels, On a Cahn--Hilliard system with convection and dynamic boundary conditions, Annali di Matematica Pura ed Applicata. Serie Quarta. Fondazione Annali di Matematica Pura ed Applicata, c/o Dipartimento di Matematica ``U. Dini'', Firenze; Springer-Verlag, Heidelberg. English, French, German, Italian, English abstracts., 197 (2018), pp. 1445--1475, DOI 10.1007/s10231-018-0732-1 .
    Abstract
    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.

  • P. Colli, G. Gilardi, J. Sprekels, On the longtime behavior of a viscous Cahn--Hilliard system with convection and dynamic boundary conditions, Journal of Elliptic and Parabolic Equations, 4 (2018), pp. 327--347, DOI 10.1007/s41808-018-0021-6 .
    Abstract
    In this paper, we study the longtime asymptotic behavior of a phase separation process occurring in a three-dimensional domain containing a fluid flow of given velocity. This process is modeled by a viscous convective Cahn--Hilliard system, which consists of two nonlinearly coupled second-order partial differential equations for the unknown quantities, the chemical potential and an order parameter representing the scaled density of one of the phases. In contrast to other contributions, in which zero Neumann boundary conditions were are assumed for both the chemical potential and the order parameter, we consider the case of dynamic boundary conditions, which model the situation when another phase transition takes place on the boundary. The phase transition processes in the bulk and on the boundary are driven by free energies functionals that may be nondifferentiable and have derivatives only in the sense of (possibly set-valued) subdifferentials. For the resulting initial-boundary value system of Cahn--Hilliard type, general well-posedness results have been established in piera recent contribution by the same authors. In the present paper, we investigate the asymptotic behavior of the solutions as times approaches infinity. More precisely, we study the ω-limit (in a suitable topology) of every solution trajectory. Under the assumptions that the viscosity coefficients are strictly positive and that at least one of the underlying free energies is differentiable, we prove that the omegalimit is meaningful and that all of its elements are solutions to the corresponding stationary system, where the component representing the chemical potential is a constant.

  • P. Colli, G. Gilardi, J. Sprekels, Optimal boundary control of a nonstandard viscous Cahn--Hilliard system with dynamic boundary condition, Nonlinear Analysis. An International Mathematical Journal, 170 (2018), pp. 171--196, DOI 10.1016/j.na.2018.01.003 .
    Abstract
    In this paper, we study an optimal boundary control problem for a model for phase separation taking place in a spatial domain that was introduced by 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 control literature about this PDE system, we consider here a dynamic boundary condition involving the Laplace-Beltrami operator for the order parameter of the system, which models an additional nonconserving phase transition occurring on the surface of the domain. We show the Fr&aecute;chenett differentiability of the associated control-to-state operator in appropriate Banach spaces and derive results on the existence of optimal controls and on first-order necessary optimality conditions in terms of a variational inequality and the adjoint state system.

  • P. Colli, G. Gilardi, J. Sprekels, Optimal distributed control of a generalized fractional Cahn--Hilliard system, Applied Mathematics and Optimization. An International Journal with Applications to Stochastics, pp. published online on 15.11.2018, urlhttps://doi.org/10.1007/s00245-018-9540-7, DOI 10.1007/s00245-018-9540-7 .
    Abstract
    In the recent paper “Well-posedness and regularity for a generalized fractional Cahn--Hilliard system” by the same authors, general well-posedness results have been established for a class of evolutionary systems of two equations having the structure of a viscous Cahn--Hilliard system, in which nonlinearities of double-well type occur. The operators appearing in the system equations are fractional versions in the spectral sense of general linear operators A,B, having compact resolvents, which are densely defined, unbounded, selfadjoint, and monotone in a Hilbert space of functions defined in a smooth domain. In this work we complement the results given in quoted paper by studying a distributed control problem for this evolutionary system. The main difficulty in the analysis is to establish a rigorous Fréchet differentiability result for the associated control-to-state mapping. This seems only to be possible if the state stays bounded, which, in turn, makes it necessary to postulate an additional global boundedness assumption. One typical situation, in which this assumption is satisfied, arises when B is the negative Laplacian with zero Dirichlet boundary conditions and the nonlinearity is smooth with polynomial growth of at most order four. Also a case with logarithmic nonlinearity can be handled. Under the global boundedness assumption, we establish existence and first-order necessary optimality conditions for the optimal control problem in terms of a variational inequality and the associated adjoint state system.

  • P. Colli, G. Gilardi, J. Sprekels, Optimal velocity control of a viscous Cahn--Hilliard system with convection and dynamic boundary conditions, SIAM Journal on Control and Optimization, 56 (2018), pp. 1665--1691, DOI 10.1137/17M1146786 .
    Abstract
    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.

  • A. Fischer, M. Pfalz, K. Vandewal, M. Liero, A. Glitzky, S. Lenk, S. Reineke, Full electrothermal OLED model including nonlinear self-heating effects, Physical Review Applied, 10 (2018), pp. 014023/1--014023/12, DOI 10.1103/PhysRevApplied.10.014023 .
    Abstract
    Organic light-emitting diodes (OLEDs) are widely studied semiconductor devices for which a simple description by a diode equation typically fails. In particular, a full description of the current-voltage relation, including temperature effects, has to take the low electrical conductivity of organic semiconductors into account. Here, we present a temperature-dependent resistive network, incorporating recombination as well as electron and hole conduction to describe the current-voltage characteristics of an OLED over the entire operation range. The approach also reproduces the measured nonlinear electrothermal feedback upon Joule self-heating in a self-consistent way. Our model further enables us to learn more about internal voltage losses caused by the charge transport from the contacts to the emission layer which is characterized by a strong temperature-activated electrical conductivity, finally determining the strength of the electrothermal feedback. In general, our results provide a comprehensive picture to understand the electrothermal operation of an OLED which will be essential to ensure and predict especially long-term stability and reliability in superbright OLED applications.

  • S. Frigeri, M. Grasselli, J. Sprekels, Optimal distributed control of two-dimensional nonlocal Cahn--Hilliard--Navier--Stokes systems with degenerate mobility and singular potential, Applied Mathematics and Optimization. An International Journal with Applications to Stochastics, pp. published online on 24.09.2018, urlhttps://doi.org/10.1007/s00245-018-9524-7, DOI 10.1007/s00245-018-9524-7 .
    Abstract
    In this paper, we consider a two-dimensional diffuse interface model for the phase separation of an incompressible and isothermal binary fluid mixture with matched densities. This model consists of the Navier-Stokes equations, nonlinearly coupled with a convective nonlocal Cahn-Hilliard equation. The system rules the evolution of the volume-averaged velocity of the mixture and the (relative) concentration difference of the two phases. The aim of this work is to study an optimal control problem for such a system, the control being a time-dependent external force acting on the fluid. We first prove the existence of an optimal control for a given tracking type cost functional. Then we study the differentiability properties of the control-to-state map, and we establish first-order necessary optimality conditions. These results generalize the ones obtained by the first and the third authors jointly with E. Rocca in [19]. There the authors assumed a constant mobility and a regular potential with polynomially controlled growth. Here, we analyze the physically more relevant case of a degenerate mobility and a singular (e.g., logarithmic) potential. This is made possible by the existence of a unique strong solution which was recently proved by the authors and C. G. Gal in [14].

  • P. Gurevich, S. Reichelt, Pulses in FitzHugh--Nagumo systems with rapidly oscillating coefficients, Multiscale Modeling & Simulation. A SIAM Interdisciplinary Journal, 16 (2018), pp. 833--856.
    Abstract
    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.

  • J. Haskovec, S. Hittmeir, P. Markowich, A. Mielke, Decay to equilibrium for energy-reaction-diffusion systems, SIAM Journal on Mathematical Analysis, 50 (2018), pp. 1037--1075, DOI 10.1137/16M1062065 .
    Abstract
    We derive thermodynamically consistent models of reaction-diffusion equations coupled to a heat equation. While the total energy is conserved, the total entropy serves as a driving functional such that the full coupled system is a gradient flow. The novelty of the approach is the Onsager structure, which is the dual form of a gradient system, and the formulation in terms of the densities and the internal energy. In these variables it is possible to assume that the entropy density is strictly concave such that there is a unique maximizer (thermodynamical equilibrium) given linear constraints on the total energy and suitable density constraints. We consider two particular systems of this type, namely, a diffusion-reaction bipolar energy transport system, and a drift-diffusion-reaction energy transport system with confining potential. We prove corresponding entropy-entropy production inequalities with explicitely calculable constants and establish the convergence to thermodynamical equilibrium, at first in entropy and further in L1 using Cziszar-Kullback-Pinsker type inequalities.

  • D. Horstmann, J. Rehberg, H. Meinlschmidt, The full Keller--Segel model is well-posed on fairly general domains, Nonlinearity, 31 (2018), pp. 1560--1592, DOI 10.1088/1361-6544/aaa2e1 .
    Abstract
    In this paper we prove the well-posedness of the full Keller-Segel system, a quasilinear strongly coupled reaction-crossdiffusion system, in the spirit that it always admits a unique local-in-time solution in an adequate function space, provided that the initial values are suitably regular. Apparently, there exists no comparable existence result for the full Keller-Segel system up to now. The proof is carried out for general source terms and is based on recent nontrivial elliptic and parabolic regularity results which hold true even on fairly general spatial domains, combined with an abstract solution theorem for nonlocal quasilinear equations by Amann.

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

  • A. Muntean, S. Reichelt, Corrector estimates for a thermo-diffusion model with weak thermal coupling, Multiscale Modeling & Simulation. A SIAM Interdisciplinary Journal, 16 (2018), pp. 807--832, DOI 10.1137/16M109538X .
    Abstract
    The present work deals with the derivation of corrector estimates for the two-scale homogenization of a thermo-diffusion model with weak thermal coupling posed in a heterogeneous medium endowed with periodically arranged high-contrast microstructures. The terminology “weak thermal coupling” refers here to the variable scaling in terms of the small homogenization parameter ε of the heat conduction-diffusion interaction terms, while the “high-contrast” is thought particularly in terms of the heat conduction properties of the composite material. As main target, we justify the first-order terms of the multiscale asymptotic expansions in the presence of coupled fluxes, induced by the joint contribution of Sorret and Dufour-like effects. The contrasting heat conduction combined with cross coupling lead to the main mathematical difficulty in the system. Our approach relies on the method of periodic unfolding combined with ε-independent estimates for the thermal and concentration fields and for their coupled fluxes

  • M. Patriarca, P. Farrell, J. Fuhrmann, Th. Koprucki, Highly accurate quadrature-based Scharfetter--Gummel schemes for charge transport in degenerate semiconductors, Computer Physics Communications. An International Journal and Program Library for Computational Physics and Physical Chemistry, 235 (2019), pp. 40--49 (published online on 16.10.2018), DOI 10.1016/j.cpc.2018.10.004 .
    Abstract
    We introduce a family of two point flux expressions for charge carrier transport described by drift-diffusion problems in degenerate semiconductors with non-Boltzmann statistics which can be used in Voronoï finite volume discretizations. In the case of Boltzmann statistics, Scharfetter and Gummel derived such fluxes by solving a linear two point boundary value problem yielding a closed form expression for the flux. Instead, a generalization of this approach to the nonlinear case yields a flux value given implicitly as the solution of a nonlinear integral equation. We examine the solution of this integral equation numerically via quadrature rules to approximate the integral as well as Newton's method to solve the resulting approximate integral equation. This approach results into a family of quadrature-based Scharfetter-Gummel flux approximations. We focus on four quadrature rules and compare the resulting schemes with respect to execution time and accuracy. A convergence study reveals that the solution of the approximate integral equation converges exponentially in terms of the number of quadrature points. With very few integration nodes they are already more accurate than a state-of-the-art reference flux, especially in the challenging physical scenario of high nonlinear diffusion. Finally, we show that thermodynamic consistency is practically guaranteed.

  • F.M. Sawatzki, D.H. Doan, H. Kleemann, M. Liero, A. Glitzky, Th. Koprucki, K. Leo, Balance of horizontal and vertical charge transport in organic field-effect transistors, Physical Review Applied, 10 (2018), pp. 034069/1--034069/10, DOI 10.1103/PhysRevApplied.10.034069 .
    Abstract
    High-performance organic field-effect transistors (OFETs) are an essential building block for future flexible electronics. Although there has been steady progress in the development of high-mobility organic semiconductors, the performance of lateral state-of-the-art OFETs still falls short, especially with regard to the transition frequency. One candidate to overcome the shortcomings of the lateral OFET is its vertical embodiment, the vertical organic field-effect transistor (VOFET). However, the detailed mechanism of VOFET operation is poorly understood and a matter of discussion. Proposed descriptions of the formation and geometry of the vertical channel vary significantly. In particular, values for lateral depth of the vertical channel reported so far show a large variation. This is an important question for the transistor integration, though, since a channel depth in the micrometer range would severely limit the possible integration density. Here, we investigate charge transport in such VOFETs via drift-diffusion simulations and experimental measurements. We use a (vertical) organic light-emitting transistor ((V)OLET) as a means to map the spatial distribution of charge transport within the vertical channel. Comparing simulation and experiment, we can conclusively describe the operation mechanism which is mainly governed by an accumulation of charges at the dielectric interface and the channel formation directly at the edge of the source electrode. In particular, we quantitatively describe how the channel depth depends on parameters such as gate-source voltage, drain-source voltage, and lateral and vertical mobility. Based on the proposed operation mechanism, we derive an analytical estimation for the lateral dimensions of the channel, helping to predict an upper limit for the integration density of VOFETs.

  • 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, Crystal-phase quantum wires: One-dimensional heterostructures with atomically flat interfaces, Nano Letters, 18 (2018), pp. 247--254, DOI 10.1021/acs.nanolett.7b03997 .

  • P. Corfdir, O. Marquardt, R.B. Lewis , Ch. Sinito, M. Ramsteiner, A. Trampert, U. Jahn, L. Geelhaar, O. Brandt, W.M. Fomin, Excitonic Aharonov--Bohm oscillations in core-shell nanowires, Advanced Materials, 31 (2019), pp. 1805645/1--1805645/6 (published online on 20.11.2018), DOI 10.1002/adma.201805645 .

  • B. Drees, A. Kraft, Th. Koprucki, Reproducible research through persistently linked and visualized data, Optical and Quantum Electronics, 50 (2018), pp. 59/1--59/10, DOI 10.1007/s11082-018-1327-1 .
    Abstract
    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.

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

  • P. Farrell, M. Patriarca, J. Fuhrmann, Th. Koprucki, Comparison of thermodynamically consistent charge carrier flux discretizations for Fermi--Dirac and Gauss--Fermi statistics, Optical and Quantum Electronics, 50 (2018), pp. 101/1--101/10, DOI 10.1007/s11082-018-1349-8 .
    Abstract
    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).

  • TH. Koprucki, M. Kohlhase, K. Tabelow, D. Müller, F. Rabe, Model pathway diagrams for the representation of mathematical models, Optical and Quantum Electronics, 50 (2018), pp. 70/1--70/9, DOI 10.1007/s11082-018-1321-7 .
    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 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.

  • M. Liero, S. Reichelt, Homogenization of Cahn--Hilliard-type equations via evolutionary Gamma-convergence, NoDEA. Nonlinear Differential Equations and Applications, 25 (2018), pp. 6/1--6/31, DOI 10.1007/s00030-018-0495-9 .
    Abstract
    In this paper we discuss two approaches to evolutionary Γ-convergence of gradient systems in Hilbert spaces. The formulation of the gradient system is based on two functionals, namely the energy functional and the dissipation potential, which allows us to employ Γ-convergence methods. In the first approach we consider families of uniformly convex energy functionals such that the limit passage of the time-dependent problems can be based on the theory of evolutionary variational inequalities as developed by Daneri and Savaré 2010. The second approach uses the equivalent formulation of the gradient system via the energy-dissipation principle and follows the ideas of Sandier and Serfaty 2004. We apply both approaches to rigorously derive homogenization limits for Cahn-Hilliard-type equations. Using the method of weak and strong two-scale convergence via periodic unfolding, we show that the energy and dissipation functionals Γ-converge. In conclusion, we will give specific examples for the applicability of each of the two approaches.

Beiträge zu Sammelwerken

  • A. Maltsi, Th. Koprucki, T. Niermann, T. Streckenbach, K. Tabelow, Model-based geometry reconstruction of quantum dots from TEM, in: 89th Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM), 18 of Proceedings in Applied Mathematics and Mechanics (PAMM), Wiley-VCH, Weinheim, 2018, pp. e201800398/1--e201800398/2, DOI 10.1002/pamm.201800398 .

  • M. Kantner, M. Mittnenzweig, Th. Koprucki, A hybrid quantum-classical modeling approach for electrically driven quantum dot devices, in: Proceedings of ``SPIE Photonics West 2018: Physics and Simulation of Optoelectronic Devices XXVI'', San Francisco, USA, 29.01.2018 - 01.02.2018, 10526, Society of Photo-Optical Instrumentation Engineers (SPIE), Bellingham, 2018, pp. 10526/1--10526/6, DOI 10.1117/12.2289185 .
    Abstract
    The design of electrically driven quantum light sources based on semiconductor quantum dots, such as singlephoton emitters and nanolasers, asks for modeling approaches combining classical device physics with cavity quantum electrodynamics. In particular, one has to connect the well-established fields of semi-classical semiconductor transport theory and the theory of open quantum systems. We present a first step in this direction by coupling the van Roosbroeck system with a Markovian quantum master equation in Lindblad form. The resulting hybrid quantum-classical system obeys the fundamental laws of non-equilibrium thermodynamics and provides a comprehensive description of quantum dot devices on multiple scales: It enables the calculation of quantum optical figures of merit (e.g. the second order intensity correlation function) together with the spatially resolved simulation of the current flow in realistic semiconductor device geometries in a unified way.

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

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

  • P. Colli, G. Gilardi, J. Sprekels, Limiting problems for a nonstandard viscous Cahn--Hilliard system with dynamic boundary conditions, in: Proceedings of the INdAM-ISIMM Workshop on Trends on Applications of Mathematics to Mechanics, Rome, Italy, September 2016, E. Rocca, U. Stefanelli, L. Truskinovsky, A. Visintin, eds., 27 of Springer INdAM Series, Springer International Publishing, Cham, 2018, pp. 217--242, DOI 10.1007/978-3-319-75940-1_11 .
    Abstract
    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. Patriarca, P. Farrell, J. Fuhrmann, Th. Koprucki, M. Auf DER Maur, Highly accurate discretizations for non-Boltzmann charge transport in semiconductors, in: Proceedings of the 18th International Conference on Numerical Simulation of Optoelectronic Devices (NUSOD 2018), A. Djurišić, J. Piprek, eds., IEEE Conference Publications Management Group, Piscataway, 2018, pp. 53--54.

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

  • TH. Koprucki, A. Maltsi, T. Niermann, T. Streckenbach, K. Tabelow, J. Polzehl, Towards model-based geometry reconstruction of quantum dots from TEM, in: Proceedings of the 18th International Conference on Numerical Simulation of Optoelectronic Devices (NUSOD 2018), A. Djurišić, J. Piprek, eds., IEEE Conference Publications Management Group, Piscataway, 2018, pp. 115--116.

  • O. Marquardt, P. Mathé, Th. Koprucki, M. Caro, M. Willatzen, Data-driven electronic structure calculations in semiconductor nanostructures -- beyond the eight-band k.p formalism, in: Proceedings of the 18th International Conference on Numerical Simulation of Optoelectronic Devices (NUSOD 2018), A. Djurišić, J. Piprek, eds., IEEE Conference Publications Management Group, 2018, pp. 55--56.

  • A. Mielke, Three examples concerning the interaction of dry friction and oscillations, in: Proceedings of the INdAM-ISIMM Workshop on Trends on Applications of Mathematics to Mechanics, Rome, Italy, September 2016, E. Rocca, U. Stefanelli, L. Truskinovsky, A. Visintin, eds., 27 of Springer INdAM Series, Springer International Publishing, Cham, 2018, pp. 159--177, DOI 10.1007/978-3-319-75940-1_8 .
    Abstract
    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.

  • A. Mielke, Uniform exponential decay for reaction-diffusion systems with complex-balanced mass-action kinetics, in: Patterns of Dynamics, P. Gurevich, J. Hell, B. Sandstede, A. Scheel, eds., Proceedings in Mathematics & Statistics, Springer, 2017, pp. 149--171, DOI 10.1007/978-3-319-64173-7_10 .
    Abstract
    We consider reaction-diffusion systems on a bounded domain with no-flux boundary conditions. All reactions are given by the mass-action law and are assumed to satisfy the complex-balance condition. In the case of a diagonal diffusion matrix, the relative entropy is a Liapunov functional. We give an elementary proof for the Liapunov property as well a few explicit examples for the condition of complex or detailed balancing.
     
    We discuss three methods to obtain energy-dissipation estimates, which guarantee exponential decay of the relative entropy, all of which rely on the log-Sobolev estimate and suitable handling of the reaction terms as well as the mass-conservation relations. The three methods are (i) a convexification argument based on the author's joint work with Haskovec and Markowich, (ii) a series of analytical estimates derived by Desvillettes, Fellner, and Tang, and (iii) a compactness argument of developed by Glitzky and Hünlich.

  • M. Radziunas, J. Fuhrmann, A. Zeghuzi, H.-J. Wünsche, Th. Koprucki, H. Wenzel, U. Bandelow, Efficient coupling of heat flow and electro-optical models for simulation of dynamics in high-power broad-area semiconductor devices, 18th International Conference on Numerical Simulation of Optoelectronic Devices, Hong Kong, China, November 5 - 9, 2018, J. Piprek, A.B. Djurisic, eds., IEEE, 2018, pp. 91--92.

Preprints, Reports, Technical Reports

  • O. Souček, M. Heida, J. Málek, On a thermodynamic framework for developing boundary conditions for Korteweg fluids, Preprint no. 2599, WIAS, Berlin, 2019, DOI 10.20347/WIAS.PREPRINT.2599 .
    Abstract, PDF (2111 kByte)
    We provide a derivation of several classes of boundary conditions for fluids of Korteweg-type using a simple and transparent thermodynamic approach that automatically guarentees that the derived boundary conditions are compatible with the second law of thermodynamics. The starting assumption of our approach is to describe the boundary of the domain as the membrane separating two different continua, one inside the domain, and the other outside the domain. With this viewpoint one may employ the framework of continuum thermodynamics involving singular surfaces. This approach allows us to identify, for various classes of surface Helmholtz free energies, the corresponding surface entropy production mechanisms. By establishing the constitutive relations that guarantee that the surface entropy production is non-negative, we identify a new class of boundary conditions, which on one hand generalizes in a nontrivial manner the Navier's slip boundary conditions, and on the other hand describes dynamic and static contact angle conditions. We explore the general model in detail for a particular case of Korteweg fluid where the Helmholtz free energy in the bulk is that of a van der Waals fluid. We perform a series of numerical experiments to document the basic qualitative features of the novel boundary conditions and their practical applicability to model phenomena such as the contact angle hysteresis.

  • G. Nika, B. Vernescu, Multiscale modeling of magnetorheological suspensions, Preprint no. 2598, WIAS, Berlin, 2019, DOI 10.20347/WIAS.PREPRINT.2598 .
    Abstract, PDF (3159 kByte)
    We develop a multiscale approach to describe the behavior of a suspension of solid magnetizable particles in a viscous non-conducting fluid in the presence of an externally applied magnetic field. By upscaling the quasi-static Maxwell equations coupled with the Stokes' equations we are able to capture the magnetorheological effect. The model we obtain generalizes the one introduced by Neuringer & Rosensweig for quasistatic phenomena. We derive the macroscopic constitutive properties explicitly in terms of the solutions of local problems. The effective coefficients have a nonlinear dependence on the volume fraction when chain structures are present. The velocity profiles computed for some simple flows, exhibit an apparent yield stress and the flowprofile resembles a Bingham fluid flow.

  • B. Franchi, M. Heida, S. Lorenzani, A mathematical model for Alzheimer's disease: An approach via stochastic homogenization of the Smoluchowski equation, Preprint no. 2595, WIAS, Berlin, 2019, DOI 10.20347/WIAS.PREPRINT.2595 .
    Abstract, PDF (452 kByte)
    In this note, we apply the theory of stochastic homogenization to find the asymptotic behavior of the solution of a set of Smoluchowski's coagulation-diffusion equations with non-homogeneous Neumann boundary conditions. This system is meant to model the aggregation and diffusion of β-amyloid peptide (Aβ) in the cerebral tissue, a process associated with the development of Alzheimer's disease. In contrast to the approach used in our previous works, in the present paper we account for the non-periodicity of the cellular structure of the brain by assuming a stochastic model for the spatial distribution of neurons. Further, we consider non-periodic random diffusion coefficients for the amyloid aggregates and a random production of Aβ in the monomeric form at the level of neuronal membranes.

  • M. Heida, S. Neukamm, M. Varga, Stochastic homogenization of Λ-convex gradient flows, Preprint no. 2594, WIAS, Berlin, 2019, DOI 10.20347/WIAS.PREPRINT.2594 .
    Abstract, PDF (429 kByte)
    In this paper we present a stochastic homogenization result for a class of Hilbert space evolutionary gradient systems driven by a quadratic dissipation potential and a Λ-convex energy functional featuring random and rapidly oscillating coefficients. Specific examples included in the result are Allen--Cahn type equations and evolutionary equations driven by the p-Laplace operator with p ∈ in (1, ∞). The homogenization procedure we apply is based on a stochastic two-scale convergence approach. In particular, we define a stochastic unfolding operator which can be considered as a random counterpart of the well-established notion of periodic unfolding. The stochastic unfolding procedure grants a very convenient method for homogenization problems defined in terms of (Λ-)convex functionals.

  • A. Glitzky, M. Liero, G. Nika, An existence result for a class of electrothermal drift-diffusion models with Gauss--Fermi statistics for organic semiconductors, Preprint no. 2593, WIAS, Berlin, 2019, DOI 10.20347/WIAS.PREPRINT.2593 .
    Abstract, PDF (387 kByte)
    This work is concerned with the analysis of a drift-diffusion model for the electrothermal behavior of organic semiconductor devices. A "generalized Van Roosbroeck” system coupled to the heat equation is employed, where the former consists of continuity equations for electrons and holes and a Poisson equation for the electrostatic potential, and the latter features source terms containing Joule heat contributions and recombination heat. Special features of organic semiconductors like Gauss--Fermi statistics and mobilities functions depending on the electric field strength are taken into account. We prove the existence of solutions for the stationary problem by an iteration scheme and Schauder's fixed point theorem. The underlying solution concept is related to weak solutions of the Van Roosbroeck system and entropy solutions of the heat equation. Additionally, for data compatible with thermodynamic equilibrium, the uniqueness of the solution is verified. It was recently shown that self-heating significantly influences the electronic properties of organic semiconductor devices. Therefore, modeling the coupled electric and thermal responses of organic semiconductors is essential for predicting the effects of temperature on the overall behavior of the device. This work puts the electrothermal drift-diffusion model for organic semiconductors on a sound analytical basis.

  • A.F.M. TER Elst, R. Haller-Dintelmann, J. Rehberg, P. Tolksdorf, On the Lp-theory for second-order elliptic operators in divergence form with complex coefficients, Preprint no. 2590, WIAS, Berlin, 2019, DOI 10.20347/WIAS.PREPRINT.2590 .
    Abstract, PDF (383 kByte)
    Given a complex, elliptic coefficient function we investigate for which values of p the corresponding second-order divergence form operator, complemented with Dirichlet, Neumann or mixed boundary conditions, generates a strongly continuous semigroup on Lp(Ω). Additional properties like analyticity of the semigroup, H-calculus and maximal regularity arealso discussed. Finally we prove a perturbation result for real coefficients that gives the whole range of p's for small imaginary parts of the coefficients. Our results are based on the recent notion of p-ellipticity, reverse Hölder inequalities and Gaussian estimates for the real coefficients.

  • P. Colli, G. Gilardi, J. Sprekels, Longtime behavior for a generalized Cahn--Hilliard system with fractional operators, Preprint no. 2588, WIAS, Berlin, 2019, DOI 10.20347/WIAS.PREPRINT.2588 .
    Abstract, PDF (248 kByte)
    In this contribution, we deal with the longtime behavior of the solutions to the fractional variant of the Cahn--Hilliard system, with possibly singular potentials, which we recently investigated in the paper "Well-posedness and regularity for a generalized fractional CahnHilliard system". More precisely, we give a complete characterization of the Omega-limit of the phase parameter. The characterization depends on the first eigenvalue of one of the involved operators: if this eigenvalue is positive, then the chemical potential vanishes at infinity, and every element of the Omega-limit is a stationary solution to the phase equation; if it is zero instead, then every element of the Omega-limit solves a problem containing a real function which is related to the chemical potential. Such a function is nonunique and time dependent, in general, as we show by means of an example; however, we give sufficient conditions for it to be uniquely determined and constant.

  • A. Mielke, T. Roubíček, Thermoviscoelasticity in Kelvin--Voigt rheology at large strains, Preprint no. 2584, WIAS, Berlin, 2019, DOI 10.20347/WIAS.PREPRINT.2584 .
    Abstract, PDF (472 kByte)
    The frame-indifferent thermodynamically-consistent model of thermoviscoelasticity at large strain is formulated in the reference configuration with using the concept of the second-grade nonsimple materials. We focus on physically correct viscous stresses that are frame indifferent under time-dependent rotations. Also elastic stresses are frame indifferent under rotations and respect positivity of the determinant of the deformation gradient. The heat transfer is governed by the Fourier law in the actual deformed configuration, which leads to a nontrivial description when pulled back into the reference configuration. Existence of weak solutions in the quasistatic setting, i.e. inertial forces are ignored, is shown by time discretization.

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

  • H. Meinlschmidt, Ch. Meyer, J. Rehberg, Regularization for optimal control problems associated to nonlinear evolution equations, Preprint no. 2576, WIAS, Berlin, 2019, DOI 10.20347/WIAS.PREPRINT.2576 .
    Abstract, PDF (419 kByte)
    It is well-known that in the case of a sufficiently nonlinear general optimal control problem there is very frequently the necessity for a compactness argument in order to pass to the limit in the state equation in the standard “calculus of variations” proof for the existence of optimal controls. For time-dependent state equations, i.e., evolution equations, this is in particular unfortunate due to the difficult structure of compact sets in Bochner-type spaces. In this paper, we propose an abstract function space and a suitable regularization- or Tychonov term for the objective functional which allows for the usual standard reasoning in the proof of existence of optimal controls and which admits a reasonably favorable structure in the characterization of optimal solutions via first order necessary conditions in, generally, the form of a variational inequality of obstacle-type in time. We establish the necessary properties of the function space and the Tychonov term and derive the aforementioned variational inequality. The variational inequality can then be reformulated as a projection identity for the optimal control under additional assumptions. We give sufficient conditions on when these are satisfied. The considerations are complemented with a series of practical examples of possible constellations and choices in dependence on the varying control spaces required for the evolution equations at hand.

  • M. Kantner, A. Mielke, M. Mittnenzweig, N. Rotundo, Mathematical modeling of semiconductors: From quantum mechanics to devices, Preprint no. 2575, WIAS, Berlin, 2019, DOI 10.20347/WIAS.PREPRINT.2575 .
    Abstract, PDF (3500 kByte)
    We discuss recent progress in the mathematical modeling of semiconductor devices. The central result of this paper is a combined quantum-classical model that self-consistently couples van Roosbroeck's drift-diffusion system for classical charge transport with a Lindblad-type quantum master equation. The coupling is shown to obey fundamental principles of non-equilibrium thermodynamics. The appealing thermodynamic properties are shown to arise from the underlying mathematical structure of a damped Hamitlonian system, which is an isothermal version of so-called GENERIC systems. The evolution is governed by a Hamiltonian part and a gradient part involving a Poisson operator and an Onsager operator as geoemtric structures, respectively. Both parts are driven by the conjugate forces given in terms of the derivatives of a suitable free energy.

  • A.F.M. TER Elst, H. Meinlschmidt, J. Rehberg, Essential boundedness for solutions of the Neumann problem on general domains, Preprint no. 2574, WIAS, Berlin, 2019, DOI 10.20347/WIAS.PREPRINT.2574 .
    Abstract, PDF (220 kByte)
    Let the domain under consideration be bounded. Under the suppositions of very weak Sobolev embeddings we prove that the solutions of the Neumann problem for an elliptic, second order divergence operator are essentially bounded, if the right hand sides are taken from the dual of a Sobolev space which is adapted to the above embedding.

  • P. Colli, G. Gilardi, J. Sprekels, Deep quench approximation and optimal control of general Cahn--Hilliard systems with fractional operators and double obstacle potentials, Preprint no. 2559, WIAS, Berlin, 2018, DOI 10.20347/WIAS.PREPRINT.2559 .
    Abstract, PDF (349 kByte)
    In the recent paper ”Well-posedness and regularity for a generalized fractional Cahn--Hilliard system”, the same authors derived general well-posedness and regularity results for a rather general system of evolutionary operator equations having the structure of a Cahn--Hilliard system. The operators appearing in the system equations were fractional versions in the spectral sense of general linear operators A and B having compact resolvents and are densely defined, unbounded, selfadjoint, and monotone in a Hilbert space of functions defined in a smooth domain. The associated double-well potentials driving the phase separation process modeled by the Cahn--Hilliard system could be of a very general type that includes standard physically meaningful cases such as polynomial, logarithmic, and double obstacle nonlinearities. In the subsequent paper ”Optimal distributed control of a generalized fractional Cahn--Hilliard system” (Appl. Math. Optim. (2018), https://doi.org/10.1007/s00245-018-9540-7) by the same authors, an analysis of distributed optimal control problems was performed for such evolutionary systems, where only the differentiable case of certain polynomial and logarithmic double-well potentials could be admitted. Results concerning existence of optimizers and first-order necessary optimality conditions were derived, where more restrictive conditions on the operators A and B had to be assumed in order to be able to show differentiability properties for the associated control-to-state operator. In the present paper, we complement these results by studying a distributed control problem for such evolutionary systems in the case of nondifferentiable nonlinearities of double obstacle type. For such nonlinearities, it is well known that the standard constraint qualifications cannot be applied to construct appropriate Lagrange multipliers. To overcome this difficulty, we follow here the so-called ”deep quench” method. This technique, in which the nondifferentiable double obstacle nonlinearity is approximated by differentiable logarithmic nonlinearities, was first developed by P. Colli, M.H. Farshbaf-Shaker and J. Sprekels in the paper ”A deep quench approach to the optimal control of an Allen--Cahn equation with dynamic boundary conditions and double obstacles” (Appl. Math. Optim. 71 (2015), pp. 1-24) and has proved to be a powerful tool in a number of optimal control problems with double obstacle potentials in the framework of systems of Cahn--Hilliard type. We first give a general convergence analysis of the deep quench approximation that includes an error estimate and then demonstrate that its use leads in the double obstacle case to appropriate first-order necessary optimality conditions in terms of a variational inequality and the associated adjoint state system.

  • P. Nestler, N. Schlömer, O. Klein, J. Sprekels, F. Tröltzsch, Optimal control of semiconductor melts by traveling magnetic fields, Preprint no. 2549, WIAS, Berlin, 2018, DOI 10.20347/WIAS.PREPRINT.2549 .
    Abstract, PDF (2938 kByte)
    In this paper, the optimal control of traveling magnetic fields in a process of crystal growth from the melt of semiconductor materials is considered. As controls, the phase shifts of the voltage in the coils of a heater-magnet module are employed to generate Lorentz forces for stirring the crystal melt in an optimal way. By the use of a new industrial heater-magnet module, the Lorentz forces have a stronger impact on the melt than in earlier technologies. It is known from experiments that during the growth process temperature oscillations with respect to time occur in the neighborhood of the solid-liquid interface. These oscillations may strongly influence the quality of the growing single crystal. As it seems to be impossible to suppress them completely, the main goal of optimization has to be less ambitious, namely, one tries to achieve oscillations that have a small amplitude and a frequency which is sufficiently high such that the solid-liquid interface does not have enough time to react to the oscillations. In our approach, we control the oscillations at a finite number of selected points in the neighborhood of the solidification front. The system dynamics is modeled by a coupled system of partial differential equations that account for instationary heat condution, turbulent melt flow, and magnetic field. We report on numerical methods for solving this system and for the optimization of the whole process. Different objective functionals are tested to reach the goal of optimization.

  • A. Mielke, J. Naumann, On the existence of global-in-time weak solutions and scaling laws for Kolmogorov's two-equation model of turbulence, Preprint no. 2545, WIAS, Berlin, 2018, DOI 10.20347/WIAS.PREPRINT.2545 .
    Abstract, PDF (467 kByte)
    This paper is concerned with Kolmogorov's two-equation model for free turbulence in space dimension 3, involving the mean velocity u, the pressure p, an average frequency omega, and a mean turbulent kinetic energy k. We first discuss scaling laws for a slightly more general two-equation models to highlight the special role of the model devised by Kolmogorov in 1942. The main part of the paper consists in proving the existence of weak solutions of Kolmogorov's two-equation model under space-periodic boundary conditions in cubes with positive side length l. To this end, we provide new a priori estimates and invoke existence result for pseudo-monotone operators.

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

  • F. Flegel, M. Heida, The fractional $p$-Laplacian emerging from homogenization of the random conductance model with degenerate ergodic weights and unbounded-range jumps, Preprint no. 2541, WIAS, Berlin, 2018, DOI 10.20347/WIAS.PREPRINT.2541 .
    Abstract, PDF (633 kByte)
    We study a general class of discrete p-Laplace operators in the random conductance model with long-range jumps and ergodic weights. Using a variational formulation of the problem, we show that under the assumption of bounded first moments and a suitable lower moment condition on the weights, the homogenized limit operator is a fractional p-Laplace operator. Under strengthened lower moment conditions, we can apply our insights also to the spectral homogenization of the discrete Lapalace operator to the continuous fractional Laplace operator.

  • M. Mittnenzweig, Hydrodynamic limit and large deviations of reaction-diffusion master equations, Preprint no. 2521, WIAS, Berlin, 2018, DOI 10.20347/WIAS.PREPRINT.2521 .
    Abstract, PDF (389 kByte)
    We derive the hydrodynamic limit of a reaction-diffusion master equation, that combines an exclusion process with a reversible chemical master equation expression for the reaction rates. The crucial assumption is that the associated macroscopic reaction network has a detailed balance equilibrium. The hydrodynamic limit is given by a system of reaction-diffusion equations with a modified mass action law for the reaction rates. We provide the upper bound for large deviations of the empirical measure from the hydrodynamic limit.

  • P. Colli, G. Gilardi, J. Sprekels, Well-posedness and regularity for a generalized fractional Cahn--Hilliard system, Preprint no. 2509, WIAS, Berlin, 2018, DOI 10.20347/WIAS.PREPRINT.2509 .
    Abstract, PDF (309 kByte)
    In this paper, we investigate a rather general system of two operator equations that has the structure of a viscous or nonviscous Cahn--Hilliard system in which nonlinearities of double-well type occur. Standard cases like regular or logarithmic potentials, as well as non-differentiable potentials involving indicator functions, are admitted. The operators appearing in the system equations are fractional versions of general linear operators A and B, where the latter are densely defined, unbounded, self-adjoint and monotone in a Hilbert space of functions defined in a smooth domain and have compact resolvents. In this connection, we remark the fact that our definition of the fractional power of operators uses the approach via spectral theory. Typical cases are given by standard second-order elliptic differential operators (e.g., the Laplacian) with zero Dirichlet or Neumann boundary conditions, but also other cases like fourth-order systems or systems involving the Stokes operator are covered by the theory. We derive in this paper general well-posedness and regularity results that extend corresponding results which are known for either the non-fractional Laplacian with zero Neumann boundary condition or the fractional Laplacian with zero Dirichlet condition. These results are entirely new if at least one of the operators A and B differs from the Laplacian. It turns out that the first eigenvalue λ1 of A plays an important und not entirely obvious role: if λ1 is positive, then the operators A and B may be completely unrelated; if, however, λ1 equals zero, then it must be simple and the corresponding one-dimensional eigenspace has to consist of the constant functions and to be a subset of the domain of definition of a certain fractional power of B. We are able to show general existence, uniqueness, and regularity results for both these cases, as well as for both the viscous and the nonviscous system.

  • K. Disser, J. Rehberg, The 3D transient semiconductor equations with gradient-dependent and interfacial recombination, Preprint no. 2507, WIAS, Berlin, 2018, DOI 10.20347/WIAS.PREPRINT.2507 .
    Abstract, PDF (325 kByte)
    We establish the well-posedness of the transient van Roosbroeck system in three space dimensions under realistic assumptions on the data: non-smooth domains, discontinuous coefficient functions and mixed boundary conditions. Moreover, within this analysis, recombination terms may be concentrated on surfaces and interfaces and may not only depend on charge-carrier densities, but also on the electric field and currents. In particular, this includes Avalanche recombination. The proofs are based on recent abstract results on maximal parabolic and optimal elliptic regularity of divergence-form operators.

  • A. Bacho, E. Emmrich, A. Mielke, An existence result and evolutionary Gamma-convergence for perturbed gradient systems, Preprint no. 2499, WIAS, Berlin, 2018, DOI 10.20347/WIAS.PREPRINT.2499 .
    Abstract, PDF (658 kByte)
    We consider the initial-value problem for the perturbed gradient flows, where a differential inclusion is formulated in terms of a subdifferential of an energy functional, a subdifferential of a dissipation potential and a more general perturbation, which is assumed to be continuous and to satisfy a suitable growth condition. Under additional assumptions on the dissipation potential and the energy functional, existence of strong solutions is shown by proving convergence of a semi-implicit discretization scheme with a variational approximation technique.

  • D.H. Doan, A. Glitzky, M. Liero, Drift-diffusion modeling, analysis and simulation of organic semiconductor devices, Preprint no. 2493, WIAS, Berlin, 2018, DOI 10.20347/WIAS.PREPRINT.2493 .
    Abstract, PDF (563 kByte)
    We discuss drift-diffusion models for charge-carrier transport in organic semiconductor devices. The crucial feature in organic materials is the energetic disorder due to random alignment of molecules and the hopping transport of carriers between adjacent energetic sites. The former leads to so-called Gauss-Fermi statistics, which describe the occupation of energy levels by electrons and holes. The latter gives rise to complicated mobility models with a strongly nonlinear dependence on temperature, density of carriers, and electric field strength. We present the state-of-the-art modeling of the transport processes and provide a first existence result for the stationary drift-diffusion model taking all of the peculiarities of organic materials into account. The existence proof is based on Schauder's fixed-point theorem. Finally, we discuss the numerical discretization of the model using finite-volume methods and a generalized Scharfetter-Gummel scheme for the Gauss-Fermi statistics.

  • P. Farrell, D. Peschka, Challenges for drift-diffusion simulations of semiconductors: A comparative study of different discretization philosophies, Preprint no. 2486, WIAS, Berlin, 2018, DOI 10.20347/WIAS.PREPRINT.2486 .
    Abstract, PDF (2457 kByte)
    We analyze and benchmark the error and the convergence order of finite difference, finite-element as well as Voronoi finite-volume discretization schemes for the drift-diffusion equations describing charge transport in bulk semiconductor devices. Three common challenges, that can corrupt the precision of numerical solutions, will be discussed: boundary layers at Ohmic contacts, discontinuties in the doping profile, and corner singularities in L-shaped domains. The influence on the order of convergence is assessed for each computational challenge and the different discretization schemes. Additionally, we provide an analysis of the inner boundary layer asymptotics near Ohmic contacts to support our observations.

  • D. Peschka, Variational approach to contact line dynamics for thin films, Preprint no. 2477, WIAS, Berlin, 2018, DOI 10.20347/WIAS.PREPRINT.2477 .
    Abstract, PDF (713 kByte)
    This paper investigates a variational approach to viscous flows with contact line dynamics based on energy-dissipation modeling. The corresponding model is reduced to a thin-film equation and its variational structure is also constructed and discussed. Feasibility of this modeling approach is shown by constructing a numerical scheme in 1D and by computing numerical solutions for the problem of gravity driven droplets. Some implications of the contact line model are highlighted in this setting.

Vorträge, Poster

  • M. Heida, Effective models for materials and interfaces with multiple scales, SCCS Days 2019 of the Collaborative Research Center - CRC 1114, Zeuthen, May 20 - 22, 2019.

  • M. Heida, The SQRA operator: convergence behaviour and applications, Universität Wien, Austria, March 19, 2019.

  • M. Heida, The fractional p-Laplacian emerging from discrete homogenization of the random conductance model with degenerate ergodic weights, 90th Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM 2019), Section S14 ``Applied Analysis'', February 18 - 22, 2019, Universität Wien, Technische Universität Wien, Austria, February 19, 2019.

  • M. Heida, What is... SQRA discretization of the Fokker--Planck equation?, CRC1114 Colloquium, Freie Universität Berlin, SFB 1114, April 25, 2019.

  • G. Nika, Optimal shape design and 3D printing, École Polytechnique, Laboratoire de Mécanique des Solides, Paris, France, March 20, 2019.

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

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

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

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

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

  • A. Stephan, Effective models for materials and interfaces with multiple scales, SCCS Days 2019 of the Collaborative Research Center - CRC 1114, Zeuthen, May 20 - 22, 2019.

  • A. Stephan, Evolutionary Gamma-convergence for a linear reaction-diffusion system with different time scales, COPDESC-Workshop ``Calculus of Variation and Nonlinear Partial Differential Equations", March 25 - 28, 2019, Universität Regensburg, March 26, 2019.

  • A. Stephan, Rigorous derivation of the effective equation of a linear reaction system with different time scales, 90th Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM 2019), Section S14 ``Applied Analysis'', February 18 - 22, 2019, Universität Wien, Technische Universität Wien, Austria, February 21, 2019.

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

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

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

  • A. Glitzky, Drift-diffusion problems with Gauss--Fermi statistics and field-dependent mobility for organic semiconductor devices, 90th Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM 2019), Section S14 ``Applied Analysis'', February 18 - 22, 2019, Universität Wien, Technische Universität Wien, Austria, February 22, 2019.

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

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

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

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

  • M. Heida, The SQRA operator: convergence behaviour and applications, Polytechnico Milano, Italy, March 13, 2019.

  • TH. Koprucki, Datenmanagement - Forschungsdaten in Modellierung und Simulation, Block-Seminar des SFB 787 ``Nanophotonik'', May 6 - 8, 2019, Technische Universität Berlin, Graal-Müritz, May 6, 2019.

  • M. Liero, Effective diffusion in thin structures via generalized gradient systems and EDP-convergence, 90th Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM 2019), Section S14 ``Applied Analysis'', February 18 - 22, 2019, Universität Wien, Technische Universität Wien, Austria, February 20, 2019.

  • A. Mielke, Effective kinetic relations and EDP convergence, COPDESC-Workshop ``Calculus of Variation and Nonlinear Partial Differential Equations", March 25 - 28, 2019, Universität Regensburg, March 28, 2019.

  • A. Mielke, Effective kinetic relations and EDP convergence for gradient systems, Necas Seminar on Continuum Mechanics, Charles University, Prague, Czech Republic, March 18, 2019.

  • A. Mielke, On Kolmogorov's two-equation model for turbulence, 90th Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM 2019), Section S14 ``Applied Analysis'', February 18 - 22, 2019, Universität Wien, Technische Universität Wien, Austria, February 21, 2019.

  • A. Mielke, Thermodynamical modeling via GENERIC: from quantum mechanics to semiconductor devices, Institute of Thermomechanics Seminar, Czech Academy of Sciences, Prague, Czech Republic, March 21, 2019.

  • A. Mielke, Effective models for materials and interfaces with multiple scales, SCCS Days 2019 of the Collaborative Research Center - CRC 1114, Zeuthen, May 20 - 22, 2019.

  • A. Mielke, Effective models for materials and interfaces with multiple scales, SCCS Days 2019 of the Collaborative Research Center - CRC 1114, May 20 - 22, 2019, SFB 1114, Freie Universität Berlin, Zeuthen, May 21, 2019.

  • A. Mielke, Transport versus growth and decay: The (spherical) Hellinger--Kantorovich distance between arbitrary measures, ``Optimal Transport: From Geometry to Numerics", May 13 - 17, 2019, Erwin Schrödinger International Institute for Mathematics and Physics, Universität Wien, Austria, May 17, 2019.

  • J. Rehberg, An extrapolation for the Lax-Milgram isomorphism for second order divergence operators, Oberseminar ``Angewandte Analysis", Technische Universität Darmstadt, February 7, 2019.

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

  • A. Maltsi, Th. Koprucki, T. Niermann, T. Streckenbach, K. Tabelow, J. Polzehl, Computing TEM images of semiconductor nanostructures, Applied Mathematics and Simulation for Semiconductors (AMaSiS 2018), WIAS Berlin, October 8 - 10, 2018.

  • A. Maltsi, Model-based geometry reconstruction of quantum dots from TEM, DPG-Frühjahrstagung der Sektion Kondensierte Materie (SKM), Fachverband Kristalline Festkörper und deren Mikrostruktur, March 12 - 16, 2018, Technische Universität Berlin, March 12, 2018.

  • A. Maltsi, Model-based geometry reconstruction of quantum dots from transmission electron microscopy (TEM), 89th Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM 2018), Section S21 ``Mathematical Signal and Image Processing'', March 19 - 23, 2018, Technische Universität München, March 22, 2018.

  • S. Reichelt, Pulses in FitzHugh--Nagumo systems with rapidly oscillating coefficients, 89th Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM 2018), Section S14 ``Applied Analysis'', March 19 - 23, 2018, Technische Universität München, March 23, 2018.

  • S. Reichelt, Pulses in FitzHugh-Nagumo systems with rapidly oscillating coefficients, SIAM Annual Meeting, Minisymposium 101 ``Multiscale Analysis and Simulation on Heterogeneous Media'', July 9 - 13, 2018, Society for Industrial and Applied Mathematics, Oregon Convention Center (OCC), Portland, USA, July 12, 2018.

  • N. Rotundo, Consistent modeling of optoelectronic semiconductors via gradient structures, Congress of the Italian Society of Applied and Industrial Mathematics (SIMAI), minisymposium MS-23 ``Mathematical Modeling of Charge Transport in Low Dimensional Structures (Part II)'', July 2 - 6, 2018, Sapienza Università di Roma, Faculty of Civil and Industrial Engineering, Cosenza, Italy, July 3, 2018.

  • N. Rotundo, On a thermodynamically consistent coupling of quantum system and device equations, The 20th European Conference on Mathematics for Industry, minisymposium ``Mathematical Modeling of Charge Transport in Graphene and Low Dimensional Structures'', August 18 - June 22, 2018, European Consortium for Mathematics in Industry, Budapest, Hungary, June 19, 2018.

  • D.H. Doan, J. Fuhrmann, A. Glitzky, Th. Koprucki, M. Liero, On van Roosbroeck systems with Gauss--Fermi statistics, Applied Mathematics and Simulation for Semiconductors (AMaSiS 2018), Berlin, October 8 - 10, 2018.

  • M. Heida, Mathematische Mehrskalenmethoden in Natur und Technik, Seminar ``Angewandte Analysis'', Universität Konstanz, Institut für Mathematik, October 31, 2018.

  • M. Heida, On G-convergence and stochastic two-scale convergences of the squareroot approximation scheme to the Fokker--Planck operator, 89th Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM 2018), Section S14 ``Applied Analysis'', March 19 - 23, 2018, Technische Universität München, March 21, 2018.

  • M. Heida, On convergence of the squareroot approximation scheme to the Fokker--Planck operator, Technische Universität Berlin, Institut für Mathematik, May 14, 2018.

  • M. Heida, On convergence of the squareroot approximation scheme to the Fokker--Planck operator, Oberseminar ``Optimierung'', Humboldt-Universität zu Berlin, Institut für Mathematik, May 29, 2018.

  • M. Heida, On convergences of the square root approximation scheme to the Fokker--Planck operator, Asymptotic Behavior of Systems of PDE Arising in Physics and Biology: Theoretical and Numerical Points of View (ABPDE III), August 28 - 31, 2018, University of Lille, LILLIAD Learning Center, France, August 30, 2018.

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

  • M. Heida, On convergences of the squareroot approximation scheme to the Fokker--Planck operator, Workshop ``Analysis of Evolutionary and Complex Systems'', September 24 - 28, 2018, WIAS Berlin, September 24, 2018.

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

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

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

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

  • A. Stephan, Rigorous derivation of the effective equation of a linear reaction system with different time scales, 3rd Berlin Dresden Prague Würzburg Workshop, ``Mathematics of Continuum Mechanics'', November 29 - 30, 2018.

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

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

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

  • K. Disser, Global existence and stability for dissipative processes coupled across volume and surface, Workshop ``Analysis of Evolutionary and Complex Systems'', September 25 - 28, 2018, WIAS Berlin, September 28, 2018.

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

  • J. Sprekels, Cahn--Hilliard systems with general fractional operators, Workshop ``Challenges in Optimal Control of Nonlinear PDE-Systems'', April 9 - 13, 2018, Mathematisches Forschungsinstitut Oberwolfach, April 9, 2018.

  • J. Sprekels, Cahn--Hilliard systems with general fractional-order operators, Workshop ``Special Materials and Complex Systems'' (SMACS 2018), June 18 - 22, 2018, University of Milan/University of Pavia, Gargnano, Italy, June 22, 2018.

  • J. Sprekels, Well-posedness, regularity, and optimal control of general Cahn--Hilliard systems with fractional operators, Workshop ``Analysis of Evolutionary and Complex Systems'', September 25 - 28, 2018, WIAS Berlin, September 24, 2018.

  • A. Glitzky, Electrothermal feedback in organic LEDs, Workshop ``Numerical Optimization of the PEM Fuel Cell Bipolar Plate'', March 20, 2018, Zentrum für Solarenergie- und Wasserstoff-Forschung (ZSW), Ulm, March 20, 2018.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

  • TH. Frenzel, Slip-stick motion via a wiggly energy model and relaxed EDP-convergence, Workshop ``Variational Methods for the Modelling of Inelastic Solids'', February 5 - 9, 2018, Mathematisches Forschungsinstitut Oberwolfach, February 8, 2018.

  • TH. Koprucki, A graph-based representation of mathematical modeling and models, 11th Conference on Intelligent Computer Mathematics (CICM 2018), Workshop on Mathematical Models and Mathematical Software as Research Data (M3SRD), August 13 - 17, 2018, Research Institute for Symbolic Computation, Hagenberg, Austria, August 13, 2018.

  • TH. Koprucki, A graph-based representation of mathematical modeling and models, 11th Conference on Intelligent Computer Mathematics (CICM 2018), Workshop on Mathematical Models and Mathematical Software as Research Data (M3SRD), August 13 - 17, 2018, Johannes Kepler Universität Linz, Research Institute for Symbolic Computation (RISC), Hagenberg, Austria, August 13, 2018.

  • TH. Koprucki, Highly accurate discretizations for non-Boltzmann charge transport in semiconductors, 18th International Conference on Numerical Simulation of Optoelectronic Devices (NUSOD 2018), Session ``Numerical Methods'', November 5 - 9, 2018, The University of Hong Kong, China, November 6, 2018.

  • TH. Koprucki, Model pathway diagrams for the representation of mathematical models, The Leibniz ``Mathematical Modeling and Simulation'' Days 2018, February 28 - March 2, 2018, Leibniz Institute for Surface Engineering (IOM) & Leibniz-Institut für Troposphärenforschung (TROPOS), Leipzig, February 28, 2018, DOI 10.5446/35360 .

  • TH. Koprucki, Multi-dimensional modeling und simulation of nanophotonic devices, Block-Seminar des SFB 787 ``Nanophotonik'', May 7 - 9, 2018, Technische Universität Berlin, Graal-Müritz, May 9, 2018.

  • TH. Koprucki, Numerical methods for drift-diffusion equations, sc Matheon 11th Annual Meeting ``Photonic Devices'', February 8 - 9, 2018, Konrad-Zuse-Zentrum für Informationstechnik Berlin, February 8, 2018.

  • TH. Koprucki, Towards model-based geometry reconstruction of quantum dots from TEM, 18th International Conference on Numerical Simulation of Optoelectronic Devices (NUSOD 2018), Session ``Nanostructures'', November 5 - 9, 2018, The University of Hong Kong, China, November 8, 2018.

  • M. Liero, Feel the heat---Modeling of electrothermal feedback in organic devices, A Joint meeting of the Society for Natural Philosophy and the International Society for the Interaction of Mathematics and Mechanics ``Mathematics & Mechanics: Natural Philosophy in the 21st Century'', June 24 - 27, 2018, University of Oxford, Mathematical Institute, UK, June 25, 2018.

  • M. Liero, On entropy-transport problems and the Hellinger--Kantorovich distance, IFIP TC 7 Conference on System Modelling and Optimization, Minisymposium ``Optimal Transport and Applications'', July 26 - 27, 2018, Universität Duisburg-Essen, Fakultät für Mathematik, Essen, July 27, 2018.

  • O. Marquardt, Computational design of core-shell nanowire crystal-phase quantum rings for the observation of Aharonov--Bohm oscillations, The Leibniz ``Mathematical Modeling and Simulation'' Days 2018, February 28 - March 2, 2018, Leibniz Institute for Surface Engineering (IOM) & Leibniz-Institut für Troposphärenforschung (TROPOS), Leipzig, March 1, 2018.

  • O. Marquardt, Computational design of core-shell nanowire crystal-phase quantum rings for the observation of Aharonov--Bohm oscillations, 18th International Conference on Numerical Simulation of Optoelectronic Devices (NUSOD 2018) , Session " Nanostructures", November 5 - 9, 2018, The University of Hong Kong, China, November 6, 2018.

  • O. Marquardt, Data-driven electronic structure calculations for nanostructures, Applied Mathematics and Simulation for Semiconductors (AMaSiS 2018), October 8 - 10, 2018, WIAS, October 10, 2018.

  • O. Marquardt, Data-driven electronic structure calculations in semiconductor nanostructures --- Beyond the eight-band k&cdot&p formalism, 18th International Conference on Numerical Simulation of Optoelectronic Devices (NUSOD 2018), Session ``Numerical Methods'', November 5 - 9, 2018, The University of Hong Kong, China, November 6, 2018.

  • O. Marquardt, Electronic properties of semiconductor nanostructures - eight band k.p and beyond, Nanostructures Seminar, Beijing Institute of Nanoenergy and Nanosystems (BINN), Chinese Academy of Science, China, April 12, 2018.

  • O. Marquardt, Modelling the electronic properties of polytype heterostructure, QuantumWise (Synopsis), Lyngby, Denmark, August 21, 2018.

  • O. Marquardt, Observation of Aharonov--Bohm oscillations in core-shell nanowire crystal-phase quantum rings, DPG-Frühjahrstagung der Sektion Kondensierte Materie (SKM), Fachverband Halbleiterphysik, March 12 - 16, 2018, Technische Universität Berlin, March 13, 2018.

  • A. Mielke, Coarse graining of energy and dissipation, Festkolloquium zu Ehren von Martin Brokate, November 8 - 10, 2018, Technische Universität München, Zentrum Mathematik, Garching, Germany, November 9, 2018.

  • A. Mielke, Construction of effective gradient systems via EDP convergence, Workshop on Mathematical Aspects of Non-Equilibrium Thermodynamics, March 5 - 7, 2018, Rheinisch-Westfälische Technische Hochschule, Aachen, March 6, 2018.

  • A. Mielke, EDP convergence and optimal transport, Workshop ``Optimal Transportation and Applications'', November 12 - 15, 2018, Scuola Normale Superiore, Universià di Pisa, Università di Pavia, Pisa, Italy, November 13, 2018.

  • A. Mielke, EDP-convergence: Gamma-convergence for gradient systems in the sense of the energy-dissipation principle, 89th Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM 2018), Section S14 ``Applied Analysis'', March 19 - 23, 2018, Technische Universität München, March 20, 2018.

  • A. Mielke, Energy, dissipation, and evolutionary Gamma convergence for gradient systems, Kolloquium ``Applied Analysis'', Universität Bremen, December 18, 2018.

  • A. Mielke, Entropy and gradient structures for quantum Markov semigroups and couplings to macroscopic thermodynamical systems, Nonlinear Mechanics Seminar, University of Bath, Mathematical Sciences, UK, May 22, 2018.

  • A. Mielke, Entropy-induced geometry for classical and quantum Markov semigroups, Mathematisches Kolloquium, Technische Universität Darmstadt, Fachbereich Mathematik, June 6, 2018.

  • A. Mielke, Finding limiting dissipative potentials via EDP convergence, Applied Mathematics Seminar, Università di Pavia, Dipartimento di Matematica, Italy, April 23, 2018.

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

  • A. Mielke, On notions of evolutionary Gamma convergence for gradient systems, Workshop ``Gradient Flows: Challenges and New Directions'', September 10 - 14, 2018, International Centre for Mathematical Sciences (ICMS), Edinburgh, UK, September 13, 2018.

  • M. Mittnenzweig, Hydrodynamic limit and large deviations of reaction-diffusion master equations, Workshop ``Analysis of Evolutionary and Complex Systems'', September 24 - 28, 2018, WIAS Berlin, September 27, 2018.