Publications

Articles in Refereed Journals

  • P. Colli, G. Gilardi, A. Signori, J. Sprekels, Optimal control of a nonconserved phase field model of Caginalp type with thermal memory and double obstacle potential, Discrete and Continuous Dynamical Systems -- Series S, published online in January 2023, DOI 10.3934/dcdss.2022210 .
    Abstract
    In this paper, we investigate optimal control problems for a nonlinear state system which constitutes a version of the Caginalp phase field system modeling nonisothermal phase transitions with a nonconserved order parameter that takes thermal memory into account. The state system, which is a first-order approximation of a thermodynamically consistent system, is inspired by the theories developed by Green and Naghdi. It consists of two nonlinearly coupled partial differential equations that govern the phase dynamics and the universal balance law for internal energy, written in terms of the phase variable and the so-called thermal displacement, i.e., a primitive with respect to time of temperature. We extend recent results obtained for optimal control problems in which the free energy governing the phase transition was differentiable (i.e., of regular or logarithmic type) to the nonsmooth case of a double obstacle potential. As is well known, in this nondifferentiable case standard methods to establish the existence of appropriate Lagrange multipliers fail. This difficulty is overcome utilizing of the so-called deep quench approach. Namely, the double obstacle potential is approximated by a family of (differentiable) logarithmic ones for which the existence of optimal controls and first-order necessary conditions of optimality in terms of the adjoint state variables and a variational inequality are known. By proving appropriate bounds for the adjoint states of the approximating systems, we can pass to the limit in the corresponding first-order necessary conditions, thereby establishing meaningful first-order necessary optimality conditions also for the case of the double obstacle potential.

  • M. Heida, Stochastic homogenization on perforated domains II -- Application to nonlinear elasticity models, ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik, published online on 26.09.2022, DOI 10.1002/zamm.202100407 .
    Abstract
    Based on a recent work that exposed the lack of uniformly bounded W1,p → W1,p extension operators on randomly perforated domains, we study stochastic homogenization of nonlinear elasticity on such structures using instead the extension operators constructed in [11]. We thereby introduce two-scale convergence methods on such random domains under the intrinsic loss of regularity and prove some generally useful calculus theorems on the probability space Ω, e.g. abstract Gauss theorems.

  • P. Pelech, K. Tůma, M. Pavelka, M. Šípka, M. Sýkora, On compatibility of the natural configuration framework with general equation for non-equilibrium reversible-irreversible coupling (GENERIC): Derivation of anisotropic rate-type models, Journal of Non-Newtonian Fluid Mechanics, 305 (2022), pp. 104808/1--104808/19, DOI 10.1016/j.jnnfm.2022.104808 .
    Abstract
    Within the framework of natural configurations developed by Rajagopal and Srinivasa, evolution within continuum thermodynamics is formulated as evolution of a natural configuration linked with the current configuration. On the other hand, withing the General Equation for Non-Equilibrium Reversible-Irreversible Coupling (GENERIC) framework, the evolution is split into Hamiltonian mechanics and (generalized) gradient dynamics. These seemingly radically different approaches have actually a lot in common and we show their compatibility on a wide range of models. Both frameworks are illustrated on isotropic and anisotropic rate-type fluid models. We propose an interpretation of the natural configurations within GENERIC and vice versa (when possible).

  • P. Vágner, M. Pavelka, J. Fuhrmann, V. Klika, A multiscale thermodynamic generalization of Maxwell--Stefan diffusion equations and of the dusty gas model, International Journal of Heat and Mass Transfer, 199 (2022), pp. 123405/1--123405/14, DOI 10.1016/j.ijheatmasstransfer.2022.123405 .
    Abstract
    Despite the fact that the theory of mixtures has been part of non-equilibrium thermodynamics and engineering for a long time, it is far from complete. While it is well formulated and tested in the case of mechanical equilibrium (where only diffusion-like processes take place), the question how to properly describe homogeneous mixtures that flow with multiple independent velocities that still possess some inertia (before mechanical equilibrium is reached) is still open. Moreover, the mixtures can have several temperatures before they relax to a common value. In this paper, we derive a theory of mixtures from Hamiltonian mechanics in interaction with electromagnetic fields. The resulting evolution equations are then reduced to the case with only one momentum (classical irreversible thermodynamics), providing a generalization of the Maxwell-Stefan diffusion equations. In a next step, we reduce that description to the mechanical equilibrium (no momentum) and derive a non-isothermal variant of the dusty gas model. These reduced equations are solved numerically, and we illustrate the results on effciency analysis, showing where in a concentration cell effciency is lost. Finally, the theory of mixtures identifies the temperature difference between constituents as a possible new source of the Soret coeffcient. For the sake of clarity, we restrict the presentation to the case of binary mixtures; the generalization is straightforward.

  • P. Colli, G. Gilardi, E. Rocca, J. Sprekels, Well-posedness and optimal control for a Cahn--Hilliard--Oono system with control in the mass term, Discrete and Continuous Dynamical Systems -- Series S, 15 (2022), pp. 2135--2172, DOI 10.3934/dcdss.2022001 .
    Abstract
    The paper treats the problem of optimal distributed control of a Cahn--Hilliard--Oono system in Rd, 1 ≤ d ≤ 3 with the control located in the mass term and admitting general potentials that include both the case of a regular potential and the case of some singular potential. The first part of the paper is concerned with the dependence of the phase variable on the control variable. For this purpose, suitable regularity and continuous dependence results are shown. In particular, in the case of a logarithmic potential, we need to prove an ad hoc strict separation property, and for this reason we have to restrict ourselves to the case d = 2. In the rest of the work, we study the necessary first-order optimality conditions, which are proved under suitable compatibility conditions on the initial datum of the phase variable and the time derivative of the control, at least in case of potentials having unbounded domain

  • P. Colli, G. Gilardi, J. Sprekels, Optimal control of a phase field system of Caginalp type with fractional operators, Pure and Applied Functional Analysis, 7 (2022), pp. 1597--1635.
    Abstract
    In their recent work “Well-posedness, regularity and asymptotic analyses for a fractional phase field system” (Asymptot. Anal. 114 (2019), 93--128), two of the present authors have studied phase field systems of Caginalp type, which model nonconserved, nonisothermal phase transitions and in which the occurring diffusional operators are given by fractional versions in the spectral sense of unbounded, monotone, selfadjoint, linear operators having compact resolvents. In this paper, we complement this analysis by investigating distributed optimal control problems for such systems. It is shown that the associated control-to-state operator is Fréchet differentiable between suitable Banach spaces, and meaningful first-order necessary optimality conditions are derived in terms of a variational inequality and the associated adjoint state variables.

  • P. Colli, G. Gilardi, J. Sprekels, Well-posedness for a class of phase-field systems modeling prostate cancer growth with fractional operators and general nonlinearities, Atti della Accademia Nazionale dei Lincei. Rendiconti Lincei. Matematica e Applicazioni, 33 (2022), pp. 193--228, DOI 10.4171/rlm/969 .
    Abstract
    This paper deals with a general system of equations and conditions arising from a mathematical model of prostate cancer growth with chemotherapy and antiangiogenic therapy that has been recently introduced and analyzed (see [P. Colli et al., Mathematical analysis and simulation study of a phase-field model of prostate cancer growth with chemotherapy and antiangiogenic therapy effects, Math. Models Methods Appl. Sci. bf 30 (2020), 1253--1295]). The related system includes two evolutionary operator equations involving fractional powers of selfadjoint, nonnegative, unbounded linear operators having compact resolvents. Both equations contain nonlinearities and in particular the equation describing the dynamics of the tumor phase variable has the structure of a Allen--Cahn equation with double-well potential and additional nonlinearity depending also on the other variable, which represents the nutrient concentration. The equation for the nutrient concentration is nonlinear as well, with a term coupling both variables. For this system we design an existence, uniqueness and continuous dependence theory by setting up a careful analysis which allows the consideration of nonsmooth potentials and the treatment of continuous nonlinearities with general growth properties.

  • P. Colli, A. Signori, J. Sprekels, Analysis and optimal control theory for a phase field model of Caginalp type with thermal memory, Communications in Optimization Theory, 2022 (2022), pp. 4/1--4/31, DOI 10.23952/cot.2022.4 .
    Abstract
    A nonlinear extension of the Caginalp phase field system is considered that takes thermal memory into account. The resulting model, which is a first-order approximation of a thermodynamically consistent system, is inspired by the theories developed by Green and Naghdi. Two equations, resulting from phase dynamics and the universal balance law for internal energy, are written in terms of the phase variable (representing a non-conserved order parameter) and the so-called thermal displacement, i.e., a primitive with respect to time of temperature. Existence and continuous dependence results are shown for weak and strong solutions to the corresponding initial-boundary value problem. Then, an optimal control problem is investigated for a suitable cost functional, in which two data act as controls, namely, the distributed heat source and the initial temperature. Fréchet differentiability between suitable Banach spaces is shown for the control-to-state operator, and meaningful first-order necessary optimality conditions are derived in terms of variational inequalities involving the adjoint variables. Eventually, characterizations of the optimal controls are given.

  • P. Colli, A. Signori, J. Sprekels, Optimal control problems with sparsity for tumor growth models involving variational inequalities, Journal of Optimization Theory and Applications, 194 (2022), pp. 25--58 (published online on 28.02.2022), DOI 10.1007/s10957-022-02000-7 .
    Abstract
    This paper treats a distributed optimal control problem for a tumor growth model of Cahn--Hilliard type including chemotaxis. The evolution of the tumor fraction is governed by a variational inequality corresponding to a double obstacle nonlinearity occurring in the associated potential. In addition, the control and state variables are nonlinearly coupled and, furthermore, the cost functional contains a nondifferentiable term like the $L^1$--norm in order to include sparsity effects which is of utmost relevance, especially time sparsity, in the context of cancer therapies as applying a control to the system reflects in exposing the patient to an intensive medical treatment. To cope with the difficulties originating from the variational inequality in the state system, we employ the so-called “deep quench approximation” in which the convex part of the double obstacle potential is approximated by logarithmic functions. For such functions, first-order necessary conditions of optimality can be established by invoking recent results. We use these results to derive corresponding optimality conditions also for the double obstacle case, by deducing a variational inequality in terms of the associated adjoint state variables. The resulting variational inequality can be exploited to also obtain sparsity results for the optimal controls.

  • J. Fischer, K. Hopf, M. Kniely, A. Mielke, Global existence analysis of energy-reaction-diffusion systems, SIAM Journal on Mathematical Analysis, 54 (2022), pp. 220--267 (published online on 04.01.2022), DOI 10.1137/20M1387237 .
    Abstract
    We establish global-in-time existence results for thermodynamically consistent reaction-(cross-)diffusion systems coupled to an equation describing heat transfer. Our main interest is to model species-dependent diffusivities, while at the same time ensuring thermodynamic consistency. A key difficulty of the non-isothermal case lies in the intrinsic presence of cross-diffusion type phenomena like the Soret and the Dufour effect: due to the temperature/energy dependence of the thermodynamic equilibria, a nonvanishing temperature gradient may drive a concentration flux even in a situation with constant concentrations; likewise, a nonvanishing concentration gradient may drive a heat flux even in a case of spatially constant temperature. We use time discretisation and regularisation techniques and derive a priori estimates based on a suitable entropy and the associated entropy production. Renormalised solutions are used in cases where non-integrable diffusion fluxes or reaction terms appear.

  • P. Krejčí, E. Rocca, J. Sprekels, Analysis of a tumor model as a multicomponent deformable porous medium, Interfaces and Free Boundaries. Mathematical Modelling, Analysis and Computation, 24 (2022), pp. 235--262, DOI 10.4171/IFB/472 .
    Abstract
    We propose a diffuse interface model to describe tumor as a multicomponent deformable porous medium. We include mechanical effects in the model by coupling the mass balance equations for the tumor species and the nutrient dynamics to a mechanical equilibrium equation with phase-dependent elasticity coefficients. The resulting PDE system couples two Cahn--Hilliard type equations for the tumor phase and the healthy phase with a PDE linking the evolution of the interstitial fluid to the pressure of the system, a reaction-diffusion type equation for the nutrient proportion, and a quasistatic momentum balance. We prove here that the corresponding initial-boundary value problem has a solution in appropriate function spaces.

  • V. Miloš, P. Vágner, D. Budáč, M. Carda, M. Paidar, J. Fuhrmann, K. Bouzek, Generalized Poisson--Nernst--Planck-based physical model of the O$_2$ I LSM I YSZ electrode, Journal of The Electrochemical Society, 169 (2022), pp. 044505/1--044505/17, DOI 10.1149/1945-7111/ac4a51 .
    Abstract
    The paper presents a generalized Poisson--Nernst--Planck model of an yttria-stabilized zirconia electrolyte developed from first principles of nonequilibrium thermodynamics which allows for spatial resolution of the space charge layer. It takes into account limitations in oxide ion concentrations due to the limited availability of oxygen vacancies. The electrolyte model is coupled with a reaction kinetic model describing the triple phase boundary with electron conducting lanthanum strontium manganite and gaseous phase oxygen. By comparing the outcome of numerical simulations based on different formulations of the kinetic equations with results of EIS and CV measurements we attempt to discern the existence of separate surface lattice sites for oxygen adatoms and O2- from the assumption of shared ones. Furthermore, we discern mass-action kinetics models from exponential kinetics models.

  • M. O'Donovan, P. Farrell, T. Streckenbach, Th. Koprucki, S. Schulz, Multiscale simulations of uni-polar hole transport in (In,Ga)N quantum well systems, Optical and Quantum Electronics, 54 (2022), pp. 405/1--405/23, DOI 10.1007/s11082-022-03752-2 .
    Abstract
    Understanding the impact of the alloy micro-structure on carrier transport becomes important when designing III-nitride-based LED structures. In this work, we study the impact of alloy fluctuations on the hole carrier transport in (In,Ga)N single and multi-quantum well systems. To disentangle hole transport from electron transport and carrier recombination processes, we focus our attention on uni-polar (p-i-p) systems. The calculations employ our recently established multi-scale simulation framework that connects atomistic tight-binding theory with a macroscale drift-diffusion model. In addition to alloy fluctuations, we pay special attention to the impact of quantum corrections on hole transport. Our calculations indicate that results from a virtual crystal approximation present an upper limit for the hole transport in a p-i-p structure in terms of the current-voltage characteristics. Thus we find that alloy fluctuations can have a detrimental effect on hole transport in (In,Ga)N quantum well systems, in contrast to uni-polar electron transport. However, our studies also reveal that the magnitude by which the random alloy results deviate from virtual crystal approximation data depends on several factors, e.g. how quantum corrections are treated in the transport calculations.

  • D.R.M. Renger, S. Schindler, Gradient flows for bounded linear evolution equations, Zeitschrift fur Analysis und ihre Anwendungen. Journal for Analysis and its Applications, 41 (2022), pp. 229--238, DOI 10.4171/ZAA/1706 .
    Abstract
    We study linear evolution equations in separable Hilbert spaces defined by a bounded linear operator. We answer the question which of these equations can be written as a gradient flow, namely those for which the operator is real diagonalisable. The proof is constructive, from which we also derive geodesic lambda-convexity.

  • A.F.M. TER Elst, A. Linke, J. Rehberg, On the numerical range of sectorial forms, Pure and Applied Functional Analysis, 7 (2022), pp. 1931--1940.
    Abstract
    We provide a sharp and optimal generic bound for the angle of the sectorial form associated to a non-symmetric second-order elliptic differential operator with various boundary conditions. Consequently this gives an, in general, sharper H-angle for the H-calculus on Lp for all p ∈ (1, ∞) if the coefficients are real valued.

  • A. Glitzky, M. Liero, G. Nika, A coarse-grained electrothermal model for organic semiconductor devices, Mathematical Methods in the Applied Sciences, 45 (2022), pp. 4809--4833 (published on 26.01.2022), DOI 10.1002/mma.8072 .
    Abstract
    We derive a coarse-grained model for the electrothermal interaction of organic semiconductors. The model combines stationary drift-diffusion based electrothermal models with thermistor type models on subregions of the device and suitable transmission conditions. Moreover, we prove existence of a solution using a regularization argument and Schauder's fixed point theorem. In doing so, we extend recent work by taking into account the statistical relation given by the Gauss--Fermi integral and mobility functions depending on the temperature, charge-carrier density, and field strength, which is required for a proper description of organic devices.

  • K. Hopf, M. Burger, On multi-species diffusion with size exclusion, Nonlinear Analysis. Theory, Methods & Applications. An International Multidisciplinary Journal. Series A: Theory and Methods, 224 (2022), pp. 113092/1--113092/27, DOI 10.1016/j.na.2022.113092 .
    Abstract
    We revisit a classical continuum model for the diffusion of multiple species with size-exclusion constraint, which leads to a degenerate nonlinear cross-diffusion system. The purpose of this article is twofold: first, it aims at a systematic study of the question of existence of weak solutions and their long-time asymptotic behaviour. Second, it provides a weak-strong stability estimate for a wide range of coefficients, which had been missing so far. In order to achieve the results mentioned above, we exploit the formal gradient-flow structure of the model with respect to a logarithmic entropy, which leads to best estimates in the full-interaction case, where all cross-diffusion coefficients are non-zero. Those are crucial to obtain the minimal Sobolev regularity needed for a weak-strong stability result. For meaningful cases when some of the coefficients vanish, we provide a novel existence result based on approximation by the full-interaction case.

  • K. Hopf, Weak-strong uniqueness for energy-reaction-diffusion systems, Mathematical Models & Methods in Applied Sciences, 21 (2022), pp. 1015--1069, DOI 10.1142/S0218202522500233 .
    Abstract
    We establish weak-strong uniqueness and stability properties of renormalised solutions to a class of energy-reaction-diffusion systems, which genuinely feature cross-diffusion effects. The systems considered are motivated by thermodynamically consistent models, and their formal entropy structure allows us to use as a key tool a suitably adjusted relative entropy method. Weak-strong uniqueness is obtained for general entropy-dissipating reactions without growth restrictions, and certain models with a non-integrable diffusive flux. The results also apply to a class of (isoenergetic) reaction-cross-diffusion systems.

  • P.-É. Druet, Maximal mixed parabolic-hyperbolic regularity for the full equations of multicomponent fluid dynamics, Nonlinearity, 35 (2022), pp. 3812--3882, DOI 10.1088/1361-6544/ac5679 .
    Abstract
    We consider a Navier--Stokes--Fick--Onsager--Fourier system of PDEs describing mass, energy and momentum balance in a Newtonian fluid with composite molecular structure. For the resulting parabolic-hyperbolic system, we introduce the notion of optimal regularity of mixed type, and we prove the short-time existence of strong solutions for a typical initial boundary-value-problem. By means of a partial maximum principle, we moreover show that such a solution cannot degenerate in finite time due to blow-up or vanishing of the temperature or the partial mass densities. This second result is however only valid under certain growth conditions on the phenomenological coefficients. In order to obtain some illustration of the theory, we set up a special constitutive model for volume-additive mixtures.

  • TH. Eiter, K. Hopf, R. Lasarzik, Weak-strong uniqueness and energy-variational solutions for a class of viscoelastoplastic fluid models, Advances in Nonlinear Analysis, 12 (2023), pp. 20220274/1--20220274/31 (published online on 03.10.2022), DOI 10.1515_anona-2022-0274 .
    Abstract
    We study a model for a fluid showing viscoelastic and viscoplastic behavior, which describes the flow in terms of the fluid velocity and an internal stress. This stress tensor is transported via the Zaremba--Jaumann rate, and it is subject to two dissipation processes: one induced by a nonsmooth convex potential and one by stress diffusion. We show short-time existence of strong solutions as well as their uniqueness in a class of Leray--Hopf type weak solutions satisfying the tensorial component in the sense of an evolutionary variational inequality. The global-in-time existence of such generalized solutions has been established in a previous work. We further study the limit when stress diffusion vanishes. In this case, the above notion of generalized solutions is no longer suitable, and we introduce the concept of energy-variational solutions, which is based on an inequality for the relative energy. We derive general properties of energy-variational solutions and show their existence by passing to the non-diffusive limit in the relative energy inequality satisfied by generalized solutions for non-zero stress diffusion.

  • TH. Eiter, On the Oseen-type resolvent problem associated with time-periodic flow past a rotating body, SIAM Journal on Mathematical Analysis, 54 (2022), pp. 4987--5012, DOI 10.1137/21M1456728 .
    Abstract
    Consider the time-periodic flow of an incompressible viscous fluid past a body performing a rigid motion with non-zero translational and rotational velocity. We introduce a framework of homogeneous Sobolev spaces that renders the resolvent problem of the associated linear problem well posed on the whole imaginary axis. In contrast to the cases without translation or rotation, the resolvent estimates are merely uniform under additional restrictions, and the existence of time-periodic solutions depends on the ratio of the rotational velocity of the body motion to the angular velocity associated with the time period. Provided that this ratio is a rational number, time-periodic solutions to both the linear and, under suitable smallness conditions, the nonlinear problem can be established. If this ratio is irrational, a counterexample shows that in a special case there is no uniform resolvent estimate and solutions to the time-periodic linear problem do not exist.

  • TH. Eiter, On the Stokes-type resolvent problem associated with time-periodic flow around a rotating obstacle, Journal of Mathematical Fluid Mechanics, 24 (2022), pp. 52/1--17, DOI 10.1007/s00021-021-00654-3 .
    Abstract
    Consider the resolvent problem associated with the linearized viscous flow around a rotating body. Within a setting of classical Sobolev spaces, this problem is not well posed on the whole imaginary axis. Therefore, a framework of homogeneous Sobolev spaces is introduced where existence of a unique solution can be guaranteed for every purely imaginary resolvent parameter. For this purpose, the problem is reduced to an auxiliary problem, which is studied by means of Fourier analytic tools in a group setting. In the end, uniform resolvent estimates can be derived, which lead to the existence of solutions to the associated time-periodic linear problem.

  • TH. Eiter, On the regularity of weak solutions to time-periodic Navier--Stokes equations in exterior domains, Mathematics - Open Access Journal, 11 (2023), pp. 141/1--141/17 (published online on 27.12.2022), DOI 10.3390/math11010141 .
    Abstract
    Consider the time-periodic viscous incompressible fluid flow past a body with non-zero velocity at infinity. This article gives sufficient conditions such that weak solutions to this problem are smooth. Since time-periodic solutions do not have finite kinetic energy in general, the well-known regularity results for weak solutions to the corresponding initial-value problem cannot be transferred directly. The established regularity criterion demands a certain integrability of the purely periodic part of the velocity field or its gradient, but it does not concern the time mean of these quantities.

  • TH. Koprucki, A. Maltsi, A. Mielke, Symmetries in transmission electron microscopy imaging of crystals with strain, Proceedings of the Royal Society of Edinburgh. Section A. Mathematics, 478 (2022), pp. 20220317/1--20220317/23, DOI 10.1098/rspa.2022.0317 .
    Abstract
    TEM images of strained crystals often exhibit symmetries, the source of which is not always clear. To understand these symmetries we distinguish between symmetries that occur from the imaging process itself and symmetries of the inclusion that might affect the image. For the imaging process we prove mathematically that the intensities are invariant under specific transformations. A combination of these invariances with specific properties of the strain profile can then explain symmetries observed in TEM images. We demonstrate our approach to the study of symmetries in TEM images using selected examples in the field of semiconductor nanostructures such as quantum wells and quantum dots.

  • A. Mielke, S. Reichelt, Traveling fronts in a reaction-diffusion equation with a memory term, Journal of Dynamics and Differential Equations, (2022), published online on 23.02.2022, DOI 10.1007/s10884-022-10133-6 .
    Abstract
    Based on a recent work on traveling waves in spatially nonlocal reaction-diffusion equations, we investigate the existence of traveling fronts in reaction-diffusion equations with a memory term. We will explain how such memory terms can arise from reduction of reaction-diffusion systems if the diffusion constants of the other species can be neglected. In particular, we show that two-scale homogenization of spatially periodic systems can induce spatially homogeneous systems with temporal memory.

    The existence of fronts is proved using comparison principles as well as a reformulation trick involving an auxiliary speed that allows us to transform memory terms into spatially nonlocal terms. Deriving explicit bounds and monotonicity properties of the wave speed of the arising traveling front, we are able to establish the existence of true traveling fronts for the original problem with memory. Our results are supplemented by numerical simulations.

  • A. Mielke, J. Naumann, On the existence of global-in-time weak solutions and scaling laws for Kolmogorov's two-equation model of turbulence, ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik, 102 (2022), pp. 1--31 (published online on 01.07.2022), DOI 10.1002/zamm.202000019 .
    Abstract
    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.

Contributions to Collected Editions

  • M. Heida, M. Thomas, GENERIC for dissipative solids with bulk-interface interaction, in: Research in the Mathematics of Materials Science, A. Schlömerkemper, ed., 31 of Association for Women in Mathematics Series, Springer, Cham, 2022, pp. 333--364, DOI 10.1007/978-3-031-04496-0_15 .
    Abstract
    The modeling framework of GENERIC was originally introduced by Grmela and Öttinger for thermodynamically closed systems. It is phrased with the aid of the energy and entropy as driving functionals for reversible and dissipative processes and suitable geometric structures. Based on the definition functional derivatives we propose a GENERIC framework for systems with bulk-interface interaction and apply it to discuss the GENERIC structure of models for delamination processes.

  • O. Marquardt, M. O'Donovan, S. Schulz, O. Brandt, Th. Koprucki, Influence of random alloy fluctuations on the electronic properties of axial (In,Ga)N/GaN nanowire heterostructures, in: 2022 International Conference on Numerical Simulation of Optoelectronic Devices (NUSOD), IEEE Conference Publications Management Group, Piscataway, 2022, pp. 117--118, DOI 10.1109/NUSOD54938.2022.9894777 .
    Abstract
    Compound semiconductor heterostructures such as quantum dots, nanowires, or thin films, are commonly subject to randomly fluctuating alloy compositions if they contain ternary and quaternary alloys. These effects are obviously of an atomistic nature and thus rarely considered in heterostructure designs that require simulations on a continuum level for theory-guided design or interpretation of observations. In the following, we present a systematic approach to the treatment of alloy fluctuations in (In,Ga)N/GaN thin films and axial nanowire heterostructures. We demonstrate to what extent random alloy fluctuations can be treated in a continuum picture and discuss the impact of alloy fluctuations on the electronic properties of planar and nano wire-based (In,Ga)N/GaN heterostructures.

  • M. O'Donovan, P. Farrell, T. Streckenbach, Th. Koprucki, S. Schulz, Carrier transport in (In,Ga)N quantum well systems: Connecting atomistic tight-binding electronic structure theory to drift-diffusion simulations, in: 2022 International Conference on Numerical Simulation of Optoelectronic Devices (NUSOD), IEEE Conference Publications Management Group, Piscataway, 2022, pp. 97--98, DOI 10.1109/NUSOD54938.2022.9894745 .

Preprints, Reports, Technical Reports

  • A. Mielke, S. Schindler, Self-similar pattern in coupled parabolic systems as non-equilibrium steady states, Preprint no. 2992, WIAS, Berlin, 2023, DOI 10.20347/WIAS.PREPRINT.2992 .
    Abstract, PDF (370 kByte)
    We consider reaction-diffusion systems and other related dissipative systems on unbounded domains which would have a Liapunov function (and gradient structure) when posed on a finite domain. In this situation, the system may reach local equilibrium on a rather fast time scale but the infinite amount of mass or energy leads to persistent mass or energy flow for all times. In suitably rescaled variables the system converges to a steady state that corresponds to asymptotically self-similar behavior in the original system.

  • TH. Eiter, R. Lasarzik, Existence of energy-variational solutions to hyperbolic conservation laws, Preprint no. 2974, WIAS, Berlin, 2022, DOI 10.20347/WIAS.PREPRINT.2974 .
    Abstract, PDF (546 kByte)
    oduce the concept of energy-variational solutions for hyperbolic conservation laws. Intrinsically, these energy-variational solutions fulfill the weak-strong uniqueness principle and the semi-flow property, and the set of solutions is convex and weakly-star closed. The existence of energy-variational solutions is proven via a suitable time-discretization scheme under certain assumptions. This general result yields existence of energy-variational solutions to the magnetohydrodynamical equations for ideal incompressible fluids and to the Euler equations in both the incompressible and the compressible case. Moreover, we show that energy-variational solutions to the Euler equations coincide with dissipative weak solutions.

  • V. Laschos, A. Mielke, Evolutionary variational inequalities on the Hellinger--Kantorovich and spherical Hellinger--Kantorovich spaces, Preprint no. 2973, WIAS, Berlin, 2022, DOI 10.20347/WIAS.PREPRINT.2973 .
    Abstract, PDF (491 kByte)
    We study the minimizing movement scheme for families of geodesically semiconvex functionals defined on either the Hellinger--Kantorovich or the Spherical Hellinger--Kantorovich space. By exploiting some of the finer geometric properties of those spaces, we prove that the sequence of curves, which are produced by geodesically interpolating the points generated by the minimizing movement scheme, converges to curves that satisfy the Evolutionary Variational Inequality (EVI), when the time step goes to 0.

  • M. Mirahmadi, B. Friedrich, B. Schmidt, J. Pérez-Ríos, Mapping atomic trapping in an optical superlattice onto the libration of a planar rotor in electric fields, Preprint no. 2972, WIAS, Berlin, 2022, DOI 10.20347/WIAS.PREPRINT.2972 .
    Abstract, PDF (4889 kByte)
    We show that two seemingly unrelated problems -- the trapping of an atom in a one-dimensional optical superlattice (OSL) formed by the interference of optical lattices whose spatial periods differ by a factor of two, and the libration of a polar polarizable planar rotor (PR) in combined electric and optical fields -- have isomorphic Hamiltonians. Since the OSL gives rise to a periodic potential that acts on atomic translation via the AC Stark effect, it is possible to establish a map between the translations of atoms in this system and the rotations of the PR due to the coupling of the rotor's permanent and induced electric dipole moments with the external fields. The latter system belongs to the class of conditionally quasi-exactly solvable (C-QES) problems in quantum mechanics and shows intriguing spectral properties, such as avoided and genuine crossings, studied in details in our previous works [our works]. We make use of both the spectral characteristics and the quasi-exact solvability to treat ultracold atoms in an optical superlattice as a semifinite-gap system. The band structure of this system follows from the eigenenergies and their genuine and avoided crossings obtained as solutions of the Whittaker--Hill equation. Furthermore, the mapping makes it possible to establish correspondence between concepts developed for the two eigenproblems individually, such as localization on the one hand and orientation/alignment on the other. This correspondence may pave the way to unraveling the dynamics of the OSL system in analytic form.

  • P. Bella, M. Kniely, Regularity of random elliptic operators with degenerate coefficients and applications to stochastic homogenization, Preprint no. 2971, WIAS, Berlin, 2022, DOI 10.20347/WIAS.PREPRINT.2971 .
    Abstract, PDF (354 kByte)
    We consider degenerate elliptic equations of second order in divergence form with a symmetric random coefficient field a. Extending the work of the first author, Fehrman, and Otto [Ann. Appl. Probab. 28 (2018), no. 3, 1379-1422], who established the large-scale regularity of a-harmonic functions in a degenerate situation, we provide stretched exponential moments for the minimal radius describing the minimal scale for this regularity. As an application to stochastic homogenization, we partially generalize results by Gloria, Neukamm, and Otto [Anal. PDE 14 (2021), no. 8, 2497-2537] on the growth of the corrector, the decay of its gradient, and a quantitative two-scale expansion to the degenerate setting. On a technical level, we demand the ensemble of coefficient fields to be stationary and subject to a spectral gap inequality, and we impose moment bounds on the coefficient field and its inverse. We also introduce the ellipticity radius, which encodes the minimal scale where these moments are close to their positive expectation value.

  • P.-É. Druet, K. Hopf, A. Jüngel, Hyperbolic-parabolic normal form and local classical solutions for cross-diffusion systems with incomplete diffusion, Preprint no. 2967, WIAS, Berlin, 2022, DOI 10.20347/WIAS.PREPRINT.2967 .
    Abstract, PDF (380 kByte)
    We investigate degenerate cross-diffusion equations with a rank-deficient diffusion matrix that are considered to model populations which move as to avoid spatial crowding and have recently been found to arise in a mean-field limit of interacting stochastic particle systems. To date, their analysis in multiple space dimensions has been confined to the purely convective case with equal mobility coefficients. In this article, we introduce a normal form for an entropic class of such equations which reveals their structure of a symmetric hyperbolic-parabolic system. Due to the state-dependence of the range and kernel of the singular diffusive matrix, our way of rewriting the equations is different from that classically used for symmetric second-order systems with a nullspace invariance property. By means of this change of variables, we solve the Cauchy problem for short times and positive initial data in H^s(mathbbT^d) for s>d/2+1.

  • R. Haller, H. Meinlschmidt, J. Rehberg, Hölder regularity for domains of fractional powers of elliptic operators with mixed boundary conditions, Preprint no. 2959, WIAS, Berlin, 2022, DOI 10.20347/WIAS.PREPRINT.2959 .
    Abstract, PDF (330 kByte)
    This work is about global Hölder regularity for solutions to elliptic partial differential equations subject to mixed boundary conditions on irregular domains. There are two main results. In the first, we show that if the domain of the realization of an elliptic differential operator in a negative Sobolev space with integrability q > d embeds into a space of Hölder continuous functions, then so do the domains of suitable fractional powers of this operator. The second main result then establishes that the premise of the first is indeed satisfied. The proof goes along the classical techniques of localization, transformation and reflection which allows to fall back to the classical results of Ladyzhenskaya or Kinderlehrer. One of the main features of our approach is that we do not require Lipschitz charts for the Dirichlet boundary part, but only an intriguing metric/measure-theoretic condition on the interface of Dirichlet- and Neumann boundary parts. A similar condition was posed in a related work by ter Elst and Rehberg in 2015 [10], but the present proof is much simpler, if only restricted to space dimension up to 4.

  • M. Liero, A. Mielke, G. Savaré, Fine properties of geodesics and geodesic lambda-convexity for the Hellinger--Kantorovich distance, Preprint no. 2956, WIAS, Berlin, 2022, DOI 10.20347/WIAS.PREPRINT.2956 .
    Abstract, PDF (691 kByte)
    We study the fine regularity properties of optimal potentials for the dual formulation of the Hellinger--Kantorovich problem (HK), providing sufficient conditions for the solvability of the primal Monge formulation. We also establish new regularity properties for the solution of the Hamilton--Jacobi equation arising in the dual dynamic formulation of HK, which are sufficiently strong to construct a characteristic transport-dilation flow driving the geodesic interpolation between two arbitrary positive measures. These results are applied to study relevant geometric properties of HK geodesics and to derive the convex behaviour of their Lebesgue density along the transport flow. Finally, exact conditions for functionals defined on the space of measures are derived that guarantee the geodesic lambda-convexity with respect to the Hellinger--Kantorovich distance.

  • R. Bazaes, A. Mielke, Ch. Mukherjee, Stochastic homogenization of Hamilton--Jacobi--Bellman equations on continuum percolation clusters, Preprint no. 2955, WIAS, Berlin, 2022, DOI 10.20347/WIAS.PREPRINT.2955 .
    Abstract, PDF (598 kByte)
    We prove homogenization properties of random Hamilton--Jacobi--Bellman (HJB) equations on continuum percolation clusters, almost surely w.r.t. the law of the environment when the origin belongs to the unbounded component in the continuum. Here, the viscosity term carries a degenerate matrix, the Hamiltonian is convex and coercive w.r.t. the degenerate matrix and the underlying environment is non-elliptic and its law is non-stationary w.r.t. the translation group. We do not assume uniform ellipticity inside the percolation cluster, nor any finite-range dependence (i.i.d.) assumption on the percolation models and the effective Hamiltonian admits a variational formula which reflects some key properties of percolation. The proof is inspired by a method of Kosygina--Rezakhanlou--Varadhan developed for the case of HJB equations with constant viscosity and uniformly coercive Hamiltonian in a stationary, ergodic and elliptic random environment. In the non-stationary and non-elliptic set up, we leverage the coercivity property of the underlying Hamiltonian as well as a relative entropy structure (both being intrinsic properties of HJB, in any framework) and make use of the random geometry of continuum percolation.

  • A. Mielke, T. Roubíček, Qualitative study of a geodynamical rate-and-state model for elastoplastic shear flows in crustal faults, Preprint no. 2954, WIAS, Berlin, 2022, DOI 10.20347/WIAS.PREPRINT.2954 .
    Abstract, PDF (3349 kByte)
    The Dieterich--Ruina rate-and-state friction model is transferred to a bulk variant and the state variable (aging) influencing the dissipation mechanism is here combined also with a damage influencing standardly the elastic response. As the aging has a separate dynamics, the overall model does not have a standard variational structure. A one-dimensional model is investigated as far as the steady-state existence, localization of the cataclastic core, and its time response, too. Computational experiments with a damage-free variant show stick-slip behavior (i.e. seismic cycles of tectonic faults) as well as stable slip under very large velocities.

  • P. Colli, G. Gilardi, A. Signori, J. Sprekels, On a Cahn--Hilliard system with source term and thermal memory, Preprint no. 2950, WIAS, Berlin, 2022, DOI 10.20347/WIAS.PREPRINT.2950 .
    Abstract, PDF (322 kByte)
    A nonisothermal phase field system of Cahn--Hilliard type is introduced and analyzed mathematically. The system constitutes an extension of the classical Caginalp model for nonisothermal phase transitions with a conserved order parameter. It couples a Cahn--Hilliard type equation with source term for the order parameter with the universal balance law of internal energy. In place of the standard Fourier form, the constitutive law of the heat flux is assumed in the form given by the theory developed by Green and Naghdi, which accounts for a possible thermal memory of the evolution. This has the consequence that the balance law of internal energy becomes a second-order in time equation for the thermal displacement or freezing index, that is, a primitive with respect to time of the temperature. Another particular feature of our system is the presence of the source term in the equation for the order parameter, which entails additional mathematical difficulties because the mass conservation of the order parameter is lost. We provide several mathematical results under general assumptions on the source term and the double-well nonlinearity governing the evolution: existence and continuous dependence results are shown for weak and strong solutions to the corresponding initial-boundary value problem.

  • M. Heida, On quenched homogenization of long-range random conductance models on stationary ergodic point processes, Preprint no. 2942, WIAS, Berlin, 2022, DOI 10.20347/WIAS.PREPRINT.2942 .
    Abstract, PDF (359 kByte)
    We study the homogenization limit on bounded domains for the long-range random conductance model on stationary ergodic point processes on the integer grid. We assume that the conductance between neares neighbors in the point process are always positive and satisfy certain weight conditions. For our proof we use long-range two-scale convergence as well as methods from numerical analysis of finite volume methods.

  • P. Colli, G. Gilardi, A. Signori, J. Sprekels, Cahn--Hilliard--Brinkman model for tumor growth with possibly singular potentials, Preprint no. 2939, WIAS, Berlin, 2022, DOI 10.20347/WIAS.PREPRINT.2939 .
    Abstract, PDF (350 kByte)
    We analyze a phase field model for tumor growth consisting of a Cahn--Hilliard--Brinkman system, ruling the evolution of the tumor mass, coupled with an advection-reaction-diffusion equation for a chemical species acting as a nutrient. The main novelty of the paper concerns the discussion of the existence of weak solutions to the system covering all the meaningful cases for the nonlinear potentials; in particular, the typical choices given by the regular, the logarithmic, and the double obstacle potentials are admitted in our treatise. Compared to previous results related to similar models, we suggest, instead of the classical no-flux condition, a Dirichlet boundary condition for the chemical potential appearing in the Cahn--Hilliard-type equation. Besides, abstract growth conditions for the source terms that may depend on the solution variables are postulated.

  • A. Mielke, On two coupled degenerate parabolic equations motivated by thermodynamics, Preprint no. 2937, WIAS, Berlin, 2022, DOI 10.20347/WIAS.PREPRINT.2937 .
    Abstract, PDF (3772 kByte)
    We discuss a system of two coupled parabolic equations that have degenerate diffusion constants depending on the energy-like variable. The dissipation of the velocity-like variable is fed as a source term into the energy equation leading to conservation of the total energy. The motivation of studying this system comes from Prandtl's and Kolmogorov's one and two-equation models for turbulence, where the energy-like variable is the mean turbulent kinetic energy. Because of the degeneracies there are solutions with time-dependent support like in the porous medium equation, which is contained in our system as a special case. The motion of the free boundary may be driven by either self-diffusion of the energy-like variable or by dissipation of the velocity-like variable. The cross-over of these two phenomena is exemplified for the associated planar traveling fronts. We provide existence of suitably defined weak and very weak solutions. After providing a thermodynamically motivated gradient structure we also establish convergence into steady state for bounded domains and provide a conjecture on the asymptotically self-similar behavior of the solutions in Rd for large times.

  • M. Heida, Stochastic homogenization on perforated domains III -- General estimates for stationary ergodic random connected Lipschitz domains, Preprint no. 2932, WIAS, Berlin, 2022, DOI 10.20347/WIAS.PREPRINT.2932 .
    Abstract, PDF (394 kByte)
    This is Part III of a series on the existence of uniformly bounded extension operators on randomly perforated domains in the context of homogenization theory. Recalling that randomly perforated domains are typically not John and hence extension is possible only from W 1,p to W 1,r, r < p, we will show that the existence of such extension operators can be guarantied if the weighted expectations of four geometric characterizing parameters are bounded: The local Lipschitz constant M, the local Lipschitz radius Δ , the mesoscopic Voronoi diameter ∂ and the local connectivity radius R.

  • TH. Eiter, M. Kyed, Y. Shibata, Periodic Lp estimates by R-boundedness: Applications to the Navier--Stokes equations, Preprint no. 2931, WIAS, Berlin, 2022, DOI 10.20347/WIAS.PREPRINT.2931 .
    Abstract, PDF (400 kByte)
    General evolution equations in Banach spaces are investigated. Based on an operator-valued version of de Leeuw's transference principle, time-periodic Lp estimates of maximal regularity type are established from R-bounds of the family of solution operators (R-solvers) to the corresponding resolvent problems. With this method, existence of time-periodic solutions to the Navier--Stokes equations is shown for two configurations: in a periodically moving bounded domain and in an exterior domain, subject to prescribed time-periodic forcing and boundary data.

  • P.-É. Druet, Incompressible limit for a fluid mixture, Preprint no. 2930, WIAS, Berlin, 2022, DOI 10.20347/WIAS.PREPRINT.2930 .
    Abstract, PDF (627 kByte)
    In this paper we discuss the incompressible limit for multicomponent fluids in the isothermal ideal case. Both a direct limit-passage in the equation of state and the low Mach-number limit in rescaled PDEs are investigated. Using the relative energy inequality, we obtain convergence results for the densities and the velocity-field under the condition that the incompressible model possesses a sufficiently smooth solution, which is granted at least for a short time. Moreover, in comparison to single-component flows, uniform estimates and the convergence of the pressure are needed in the multicomponent case because the incompressible velocity field is not divergence-free. We show that certain constellations of the mobility tensor allow to control gradients of the entropic variables and yield the convergence of the pressure in L1.

  • M. Heida, A. Sikorski, M. Weber, Consistency and order 1 convergence of cell-centered finite volume discretizations of degenerate elliptic problems in any space dimension, Preprint no. 2913, WIAS, Berlin, 2022, DOI 10.20347/WIAS.PREPRINT.2913 .
    Abstract, PDF (601 kByte)
    We study consistency of cell-centered finite difference methods for elliptic equations with degenerate coefficients in any space dimension $dgeq2$. This results in order of convergence estimates in the natural weighted energy norm and in the weighted discrete $L^2$-norm on admissible meshes. The cells of meshes under consideration may be very irregular in size. We particularly allow the size of certain cells to remain bounded from below even in the asymptotic limit. For uniform meshes we show that the order of convergence is at least 1 in the energy semi-norm, provided the discrete and continuous solutions exist and the continuous solution has $H^2$ regularity.

Talks, Poster

  • K. Hopf, The Cauchy problem for multi-component systems with strong cross-diffusion, Johannes Gutenberg-Universität Mainz, Fachbereich Physik, Mathematik und Informatik, January 11, 2023.

  • TH. Koprucki, MaRDI - The Mathematical Research Data Initiative within the German National Research Data Infrastructure (NFDI), Kolloquium der AG ``Modellierung, Numerik, Differentialgleichungen'', Technische Universität Berlin, January 31, 2023.

  • M. Liero, On the geometry of the Hellinger--Kantorovich space (hybrid talk), Seminar ``Modern Methods in Applied Stochastics and Nonparametric Statistics'', WIAS Berlin, January 31, 2023.

  • A. Mielke, Asymptotic self-similar behavior in reaction-diffusion systems on the real line, Minisymposium ``Interacting Particle Systems and Variational Methods", Einhoven University of Technology, Department of Mathematics and Computer Science, Netherlands, February 3, 2023.

  • A. Maltsi, Symmetries in TEM images of strained crystals, ``European Women in Mathematics'' General Meeting 2022, Finland, August 22 - 26, 2022.

  • A. Maltsi, Symmetries in TEM images of strained crystals, BMS-BGSMath Junior Meeting, September 5 - 7, 2022, Universidad de Barcelona, Spain, September 6, 2022.

  • S. Schindler, Convergence to self-similar profiles for a coupled reaction-diffusion system on the real line, CRC 910: Workshop on Control of Self-Organizing Nonlinear Systems, September 26 - 28, 2022.

  • S. Schindler, Energy approach for a coupled reaction-diffusion system on the real line (online talk), SFB 910 Symposium ``Pattern formation and coherent structure in dissipative systems'' (Online Event), Technische Universität Berlin, January 14, 2022.

  • S. Schindler, Entropy method for a coupled reaction-diffusion system on the real line, Annual Workshop of the GAMM Activity Group ``Analysis of PDEs" 2022, October 5 - 7, 2022, Institute of Science and Technology Austria (ISTA), Klosterneuburg, October 5, 2022.

  • S. Schindler, On asymptotic self-similar behavior of solutions to parabolic systems (hybrid talk), SFB910: International Conference on Control of Self-Organizing Nonlinear Systems (Hybrid Event), November 23 - 26, 2022, Technische Universität Berlin, Potsdam, November 25, 2022.

  • Y. Hadjimichael, O. Marquardt, Ch. Merdon, P. Farrell, Band structures in highly strained 3D nanowires, 22th International Conference on Numerical Simulation of Optoelectronic Devices (NUSOD) (Online Event, Italy, September 12 - 16, 2022.

  • M. Heida, Convergence of the infinite range SQRA operator, 92th Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM 2022), Session 14 ``Applied Analysis'', August 15 - 19, 2022, Rheinisch-Westfälische Technische Hochschule Aachen, August 17, 2022.

  • M. Heida, Elasticity on randomly perforated domains, Jahrestreffen des SPP 2256, September 28 - 30, 2022, Universität Regensburg, September 29, 2022.

  • M. Heida, Homogenization on locally Lipschitz random domains (online talk), SIAM Conference on Analysis of Partial Differential Equations, Minisymposium ``Disordered Media and Homogenization" (Online Event), March 14 - 18, 2022, Society for Industrial and Applied Mathematics, March 15, 2022.

  • M. Heida, Homogenization on randomly perforated domains, Block Course ``Multiscale Problems and Homogenization'' at Freie Universität Berlin, November 10 - December 15, 2022, Berlin Mathematical School & Berlin Mathematics Research Center MATH+, November 17, 2022.

  • M. Heida, Upscaling of intercalation electrodes featuring Cahn--Hilliard to Allen--Cahn transitions (online talk), 21st GAMM Seminar on Microstructures (Online Event), Technische Universität Wien, Austria, January 28, 2022.

  • O. Marquardt, Simulating the electronic properties of semiconductor nanostructures, 5th Leibniz MMS Days, April 25 - 27, 2022, Potsdam-Institut für Klimafolgenforschung (PIK), April 26, 2022.

  • O. Marquardt, SPHInX-Tutorial 2022 (Hybrid Event), March 14 - April 11, 2022, WIAS Berlin.

  • P. Pelech, Balanced-viscosity solutions for a Penrose--Fife model with rate-independent friction (hybrid talk), Oberseminar ``Mathematik in den Naturwissenschaften'', Julius-Maximilians-Universität Würzburg, December 8, 2022.

  • P. Pelech, Penrose--Fife model as a gradient flow - interplay between signed measures and functionals on Sobolev spaces, DMV Annual Meeting 2022, Section 09 ``Applied Analysis and Partial Differential Equations", September 12 - 16, 2022, Freie Universität Berlin, September 13, 2022.

  • P. Pelech, Penrose--Fife model as a gradient flow - interplay between signed measures and functionals on Sobolev spaces, Annual Workshop of the GAMM Activity Group ``Analysis of PDEs" 2022, October 5 - 7, 2022, Institute of Science and Technology Austria (ISTA), Klosterneuburg, October 7, 2022.

  • P. Pelech, Penrose--Fife model with activated phase transformation - existence and effective model for slowloading regimes, 92th Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM 2022), Session 08 ``Multiscales and Homogenization'', August 15 - 19, 2022, Rheinisch-Westfälische Technische Hochschule Aachen, August 18, 2022.

  • A. Stephan, EDP-convergence for a linear reaction-diffusion systems with fast reversible reaction (online talk), SIAM Conference on Analysis of Partial Differential Equations (Online Event), March 14 - 18, 2022, Society for Industrial and Applied Mathematics, March 14, 2022.

  • P. Vágner, Capacitance of the blocking YSZ I Au electrode, 18th Symposium on Modeling and Experimental Validation of Electrochemical Energy Technologies, March 14 - 16, 2022, DLR Institut für Technische Thermodynamik, Hohenkammer, March 16, 2022.

  • M. Kniely, Degenerate random elliptic operators: Regularity aspects and stochastic homogenization, Annual Workshop of the GAMM Activity Group ``Analysis of PDEs" 2022, October 5 - 7, 2022, Institute of Science and Technology Austria (ISTA), Klosterneuburg, Austria, October 6, 2022.

  • M. Kniely, Global renormalized solutions and equilibration of reaction-diffusion systems with nonlinear diffusion (online talk), SIAM Conference on Analysis of Partial Differential Equations, Minisymposium ``Bridging Gradient Flows, Hypocoercivity and Reaction-Diffusion Systems" (Online Event), March 14 - 18, 2022, Society for Industrial and Applied Mathematics, March 14, 2022.

  • M. Kniely, Global solutions to a class of energy-reaction-diffusion systems, Conference on Differential Equations and Their Applications (EQUADIFF 15), Minisymposium NAA-03 ``Evolution Differential Equations with Application to Physics and Biology II'', July 11 - 15, 2022, Masaryk University, Brno, Czech Republic, July 12, 2022.

  • J. Sprekels, Deep quench approach and sparsity in the optimal control of a phase field model for tumor growth, PHAse field MEthods in applied sciences (PHAME 2022), May 23 - 27, 2022, Istituto Nazionale di Alta Matematica, Roma, Italy, May 27, 2022.

  • A. Glitzky, A drift-diffusion based electrothermal model for organic thin-film devices including electrical and thermal environment, DMV Annual Meeting 2022, Section 09 ``Applied Analysis and Partial Differential Equations", September 12 - 16, 2022, Freie Universität Berlin, September 14, 2022.

  • K. Hopf, Relative entropies and stability in strongly coupled parabolic systems (online talk), SIAM Conference on Analysis of Partial Differential Equations, Minisymposium ``Variational Evolution: Analysis and Multi-Scale Aspects" (Online Event), March 14 - 18, 2022, Society for Industrial and Applied Mathematics, March 16, 2022.

  • K. Hopf, The Cauchy problem for a cross-diffusion system with incomplete diffusion, Annual Workshop of the GAMM Activity Group ``Analysis of PDEs" 2022, October 5 - 7, 2022, Institute of Science and Technology Austria (ISTA), Klosterneuburg, October 5, 2022.

  • P.-É. Druet, Global existence and weak-strong uniqueness for isothermal ideal multicomponent flows, Against the flow, October 18 - 22, 2022, Polish Academy of Sciences, Będlewo, Poland, October 19, 2022.

  • TH. Eiter, Energy-variational solutions for a viscoelastoplastic fluid model (online talk), SIAM Conference on Analysis of Partial Differential Equations, Minisymposium ``Generalized Solvability Concepts for Evolutionary PDEs and their Properties" (Online Event), March 14 - 18, 2022, Society for Industrial and Applied Mathematics, March 16, 2022.

  • TH. Eiter, Existence of time-periodic flows in domains with oscillating boundaries, International Workshop on Multiphase Flows: Analysis, Modelling and Numerics, December 5 - 9, 2022, Waseda University, Tokyo, Japan, December 6, 2022.

  • TH. Eiter, Junior Richard von Mises Lecture: On time-periodic viscous flow around a moving body, Richard von Mises Lecture 2022, Humboldt-Universität zu Berlin, June 17, 2022.

  • TH. Eiter, On the resolvent problem associated with flow outside a rotating body, 92th Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM 2022), Session 14 ``Applied Analysis'', August 15 - 19, 2022, Rheinisch-Westfälische Technische Hochschule Aachen, August 16, 2022.

  • TH. Eiter, On the resolvent problems associated with rotating viscous flow, DMV Annual Meeting 2022, Section 09 ``Applied Analysis and Partial Differential Equations", September 12 - 16, 2022, Freie Universität Berlin, September 14, 2022.

  • TH. Eiter, On the time-periodic viscous flow outside a rotating body (online talk), SIAM Conference on Analysis of Partial Differential Equations, Minisymposium ``Recent Developments in the Mathematical Analysis of Viscous Fluids" (Online Event), March 14 - 18, 2022, Society for Industrial and Applied Mathematics, March 15, 2022.

  • TH. Eiter, On time-periodic Navier--Stokes flow around a rotating body (online talk), EDP non linéaires en dynamique des fluides (Hybrid Event), May 9 - 13, 2022, Centre International de Rencontres Mathématiques, Marseille, France, May 9, 2022.

  • TH. Eiter, On uniform resolvent estimates associated with time-periodic rotating viscous flow, Mathematical Fluid Mechanics in 2022 (Hybrid Event), August 22 - 26, 2022, Czech Academy of Sciences, Prague, Czech Republic, August 24, 2022.

  • TH. Eiter, On uniformity of the resolvent estimates associated with time-periodic flow past a rotating body, Germany-Japan Workshop on Free and Singular Boundaries in Fluid Dynamics and Related Topics (Hybrid Event), August 10 - 12, 2022, Heinrich-Heine-Universität Düsseldorf, August 10, 2022.

  • TH. Eiter, Resolvent estimates for the flow past a rotating body and existence of time-periodic solutions, CEMAT Seminar, July 24 - 30, 2022, University of Lisbon, Center for Computational and Stochastic Mathematics, Portugal, July 27, 2022.

  • TH. Eiter, The Navier--Stokes equations in domains with oscillating boundaries, Against the flow, October 18 - 22, 2022, Polish Academy of Sciences, Będlewo, Poland, October 20, 2022.

  • TH. Eiter, Time-periodic maximal Lp regularity by R-boundedness in the context of incompressible viscous flows, Research Seminar Function Spaces, Friedrich-Schiller-Universität Jena, November 4, 2022.

  • TH. Koprucki, K. Tabelow, HackMD (online talk), E-Coffee-Lecture (Online Event), WIAS Berlin, March 25, 2022.

  • TH. Koprucki, MaRDI - The Mathematical Research Data Initiative within the German National Research Data Infrastructure (NFDI), 1st MaRDI Workshop on Scientific Computing, October 26 - 28, 2022, Westfälische Wilhelms-Universität Münster, October 26, 2022.

  • M. Landstorfer, A. Selahi, M. Heida, M. Eigel, Recovery of battery ageing dynamics with multiple timescales, MATH+-Day 2022, Technische Universität Berlin, November 18, 2022.

  • M. Liero, Analysis of an electrothermal drift-diffusion model for organic semiconductor devices, PHAse field MEthods in applied sciences (PHAME 2022), May 23 - 27, 2022, Istituto Nazionale di Alta Matematica, Roma, Italy, May 24, 2022.

  • M. Liero, Automated building and testing of software projects using the WIAS Gitlab server (online talk), E-Coffee-Lecture (Online Event), WIAS Berlin, January 21, 2022.

  • M. Liero, EDP-convergence for evolutionary systems with gradient flow structure, 92th Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM 2022), Minisymposium 4 ``Evolution Equations with Gradient Flow Structure'', August 15 - 19, 2022, Rheinisch-Westfälische Technische Hochschule Aachen, August 16, 2022.

  • M. Liero, From diffusion to reaction-diffusion in thin structures via EDP-convergence (online talk), SIAM Conference on Analysis of Partial Differential Equations, Minisymposium ``Bridging Gradient Flows, Hypocoercivity and Reaction-Diffusion Systems" (Online Event), March 14 - 18, 2022, Society for Industrial and Applied Mathematics, March 14, 2022.

  • M. Liero, Modeling, analysis, and simulation of electrothermal feedback in organic devices, Audit 2022, September 22 - 23, 2022, Weierstraß-Institut Berlin, September 22, 2022.

  • M. Liero, The impact of modeling, analysis, and simulation on organic semiconductor development (online talk), ERCOM Meeting 2022 (Hybrid Event), March 25 - 26, 2022, European Research Centers on Mathematics, Bilbao, Spain, March 26, 2022.

  • M. Liero, Viscoelastodynamics of solids at large strains coupled to diffusion processes, Jahrestreffen des SPP 2256, September 28 - 30, 2022, Universität Regensburg, September 29, 2022.

  • A. Mielke, Convergence of a split-step scheme for gradient flows with a sum of two dual dissipation potentials, Nonlinear evolutionary equations and applications 2022, September 6 - 9, 2022, Technische Universität Chemnitz, September 8, 2022.

  • A. Mielke, Convergence to thermodynamic equilibrium in a degenerate parabolic system, DMV Annual Meeting 2022, Section 09 ``Applied Analysis and Partial Differential Equations", September 12 - 16, 2022, Freie Universität Berlin, September 13, 2022.

  • A. Mielke, Existence and longtime behavior of solutions to a degenerate parabolic system, Journées Équations aux Dérivées Partielles 2022, May 30 - June 3, 2022, Centre national de la recherche scientifique, Obernai, France, May 31, 2022.

  • A. Mielke, Gamma convergence for evolutionary problems: using EDP convergence for deriving nontrivial kinetic relations, Calculus of Variations, May 16 - 20, 2022, Università degli Studi di Roma ``Tor Vergata'', Tunis, Tunisia, May 18, 2022.

  • A. Mielke, Gradient flows in the Hellinger--Kantorovich space, 92th Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM 2022), Minisymposium 4 ``Evolution Equations with Gradient Flow Structure'', August 15 - 19, 2022, Rheinisch-Westfälische Technische Hochschule Aachen, August 16, 2022.

  • A. Mielke, Gradient flows: existence and Gamma-convergence via the energy-dissipation principle, Horizons in non-linear PDEs, September 26 - 30, 2022, Universität Ulm.

  • A. Mielke, On the existence and longtime behavior of solutions to a degenerate parabolic system (online talk), SIAM Conference on Analysis of Partial Differential Equations (Online Event), March 14 - 18, 2022, Society for Industrial and Applied Mathematics, March 16, 2022.

  • A. Mielke, On the longtime behavior of solutions to a coupled degenerate parabolic system motivated by thermodynamics (online talk), Nonlinear Waves and Coherent Structures Webinar Series (Online Event), University of Massachusetts, Amherst, USA, January 25, 2022.

  • A. Mielke, On time-splitting methods for gradient flows with two dissipation mechanisms, Annual Workshop of the GAMM Activity Group ``Analysis of PDEs" 2022, October 5 - 7, 2022, Institute of Science and Technology Austria (ISTA), Klosterneuburg, October 7, 2022.

  • J. Rehberg, Explicit Lp-estimates for second-order divergence operators, Oberseminar Analysis und Angewandte Mathematik, Universität Kassel, June 9, 2022.

  • J. Rehberg, On non-autonomous and quasilinear parabolic equations, Oberseminar AG Analysis, Technische Universität Darmstadt, December 8, 2022.

  • A. Stephan, EDP-convergence for a linear reaction-diffusion system with fast reversible reaction, Mathematical Models for Biological Multiscale Systems (Hybrid Event), September 12 - 14, 2022, WIAS Berlin, September 12, 2022.

  • A. Stephan, EDP-convergence for gradient systems and applications to fast-slow chemical reaction systems, Block Course ``Multiscale Problems and Homogenization'' at Freie Universität Berlin, November 10 - December 15, 2022, Berlin Mathematical School & Berlin Mathematics Research Center MATH+, November 24, 2022.

  • W. van Oosterhout, Analysis of a poro-visco-elastic material model, Mathematical models for bio-medical sciences, Como, Italy, June 20 - 24, 2022.

External Preprints

  • T. Boege, R. Fritze, Ch. Görgen, J. Hanselman, D. Iglezakis, L. Kastner, Th. Koprucki, T. Krause, Ch. Lehrenfeld, S. Polla, M. Reidelbach, Ch. Riedel, J. Saak, B. Schembera, K. Tabelow, M. Weber, Research-data management planning in the german mathematical community, Preprint no. arXiv:2211.12071, Cornell University, 2022.
    Abstract
    In this paper we discuss the notion of research data for the field of mathematics and report on the status quo of research-data management and planning. A number of decentralized approaches are presented and compared to needs and challenges faced in three use cases from different mathematical subdisciplines. We highlight the importance of tailoring research-data management plans to mathematicians' research processes and discuss their usage all along the data life cycle.

  • M. O'Donovan, P. Farrell, J. Moatti, T. Streckenbach, Th. Koprucki, S. Schulz, Impact of random alloy fluctuations on the carrier distribution in multi-color (In,Ga)N/GaN quantum well systems, Preprint no. arXiv.2209.11657, Cornell University Library, arXiv.org, 2022, DOI 10.48550/arXiv.2209.11657 .
    Abstract
    In this work, we study the impact that random alloy fluctuations have on the distribution of electrons and holes across the active region of a (In,Ga)N/GaN multi-quantum well based light emitting diode (LED). To do so, an atomistic tight-binding model is employed to account for alloy fluctuations on a microscopic level and the resulting tight-binding energy landscape forms input to a drift-diffusion model. Here, quantum corrections are introduced via localization landscape theory and we show that when neglecting alloy disorder our theoretical framework yields results similar to commercial software packages that employ a self-consistent Schroedinger-Poisson-drift-diffusion solver. Similar to experimental studies in the literature, we have focused on a multi-quantum well system where two of the three wells have the same In content while the third well differs in In content. By changing the order of wells in this multicolor quantum well structure and looking at the relative radiative recombination rates of the different emitted wavelengths, we (i) gain insight into the distribution of carriers in such a system and (ii) can compare our findings to trends observed in experiment. Our results indicate that the distribution of carriers depends significantly on the treatment of the quantum well microstructure. When including random alloy fluctuations and quantum corrections in the simulations, the calculated trends in the relative radiative recombination rates as a function of the well ordering are consistent with previous experimental studies. The results from the widely employed virtual crystal approximation contradict the experimental data. Overall, our work highlights the importance of a careful and detailed theoretical description of the carrier transport in an (In,Ga)N/GaN multi-quantum well system to ultimately guide the design of the active region of III-N-based LED structures.

  • M. Oliva, T. Flissikowsky, M. Góra, J. Lähnemann, J. Herranz, R. Lewis, O. Marquardt, M. Ramsteiner, L. Geelhaar, O. Brandt, Carrier recombination in highly uniform and phase-pure GaAs/(Al,Ga)As core/shell nanowire arrays on Si(111): Mott transition and internal quantum efficiency, Preprint no. arXiv:2211.17167v1, Cornell University Library, arXiv.org, 2022, DOI 10.48550/arXiv.2211.17167 .
    Abstract
    GaAs-based nanowires are among the most promising candidates for realizing a monolithical integration of III-V optoelectronics on the Si platform. To realize their full potential for applications as light absorbers and emitters, it is crucial to understand their interaction with light governing the absorption and extraction efficiency, as well as the carrier recombination dynamics determining the radiative efficiency. Here, we study the spontaneous emission of zincblende GaAs/(Al,Ga)As core/shell nanowire arrays by μ -photoluminescence spectroscopy. These ordered arrays are synthesized on patterned Si(111) substrates using molecular beam epitaxy, and exhibit an exceptionally low degree of polytypism for interwire separations exceeding a critical value. We record emission spectra over more than five orders of excitation density for both steady-state and pulsed excitation to identify the nature of the recombination channels. An abrupt Mott transition from excitonic to electron-hole-plasma recombination is observed, and the corresponding Mott density is derived. Combining these experiments with simulations and additional direct measurements of the external quantum efficiency using a perfect diffuse reflector as reference, we are able to extract the internal quantum efficiency as a function of carrier density and temperature as well as the extraction efficiency of the nanowire array. The results vividly document the high potential of GaAs/(Al,Ga)As core/shell nanowires for efficient light emitters integrated on the Si platform. Furthermore, the methodology established in this work can be applied to nanowires of any other materials system of interest for optoelectronic applications.