Partielle Differentialgleichungen

Publikationen

Monografien

• D. Peschka, M. Thomas, A. Zafferi, Reference map approach to Eulerian thermomechanics using GENERIC, J. Fuhrmann, D. Hömberg, W.H. Müller, W. Weiss, eds., 238 of Advanced Structured Materials, Springer Cham, 2025, pp. 39--70, (Chapter Published), DOI 10.1007/978-3-031-93918-1_3 .
  Abstract
  An Eulerian GENERIC model for thermo-viscoelastic materials with diffusive components is derived based on a transformation framework that maps a Lagrangian formulation to corresponding Eulerian coordinates. The key quantity describing the deformation in Eulerian coordinates is the inverse of the deformation, i.e., the reference map. The Eulerian model is formally constructed, and by reducing the GENERIC system to a damped Hamiltonian system, the isothermal limit is derived. A structure-preserving weak formulation is developed. As an example, the coupling of finite strain viscoelasticity and diffusion in a multiphase system governed by Lagrangian indicator functions is demonstrated.

• P. Colli, J. Sprekels, Hyperbolic relaxation of the chemical potential in the viscous Cahn--Hilliard equation, J. Fuhrmann, D. Hömberg, W.H. Müller, W. Weiss, eds., 238 of Advanced Structured Materials, Springer Cham, 2025, pp. 529--556, (Chapter Published), DOI 10.1007/978-3-031-93918-1_18 .
  Abstract
  An Eulerian GENERIC model for thermo-viscoelastic materials with diffusive components is derived based on a transformation framework that maps a Lagrangian formulation to corresponding Eulerian coordinates. The key quantity describing the deformation in Eulerian coordinates is the inverse of the deformation, i.e., the reference map. The Eulerian model is formally constructed, and by reducing the GENERIC system to a damped Hamiltonian system, the isothermal limit is derived. A structure-preserving weak formulation is developed. As an example, the coupling of finite strain viscoelasticity and diffusion in a multiphase system governed by Lagrangian indicator functions is demonstrated.

• A. Mielke, An Eulerian formulation for dissipative materials using Lie derivatives and GENERIC, J. Fuhrmann, D. Hömberg, W.H. Müller, W. Weiss, eds., 238 of Advanced Structured Materials, Springer Cham, 2025, pp. 13--38, (Chapter Published), DOI 10.1007/978-3-031-93918-1_2 .
  Abstract
  An Eulerian GENERIC model for thermo-viscoelastic materials with diffusive components is derived based on a transformation framework that maps a Lagrangian formulation to corresponding Eulerian coordinates. The key quantity describing the deformation in Eulerian coordinates is the inverse of the deformation, i.e., the reference map. The Eulerian model is formally constructed, and by reducing the GENERIC system to a damped Hamiltonian system, the isothermal limit is derived. A structure-preserving weak formulation is developed. As an example, the coupling of finite strain viscoelasticity and diffusion in a multiphase system governed by Lagrangian indicator functions is demonstrated.

Artikel in Referierten Journalen

• M. Heida, B. Jahnel, A.D. Vu, Regularized homogenization on irregularly perforated domains, Networks and Heterogeneous Media, 20 (2025), pp. 165--212, DOI 10.3934/nhm.2025010 .
  Abstract
  We study stochastic homogenization of a quasilinear parabolic PDE with nonlinear microscopic Robin conditions on a perforated domain. The focus of our work lies on the underlying geometry that does not allow standard homogenization techniques to be applied directly. Instead we prove homogenization on a regularized geometry and demonstrate afterwards that the form of the homogenized equation is independent from the regularization. Then we pass to the regularization limit to obtain the anticipated limit equation. Furthermore, we show that Boolean models of Poisson point processes are covered by our approach.

• M. O'Donovan, R. Finn, P. Farrell, T. Streckenbach, J. Moatti, S. Schulz, Th. Koprucki, Developing a hybrid single band carrier transport model for (Al,Ga)N heterostructures, Journal of Computational Electronics, 24 (2025), pp. 114/1--114/19 (published online on 13.06.2025), DOI 10.1007/s10825-025-02333-2 .
  Abstract
  Aluminium gallium nitride (Al,Ga)N alloys and heterostructures are used in the development of UV light emitting devices, and can emit at energies extending into the UV-C spectral range. In the UV-C wavelength window and thus at high AlN content, devices exhibit poor quantum efciencies. In order to aid the development of these devices, simulation techniques which capture the essential physics of these materials and heterostructures should be used. Due to a change in band ordering in a quantum well at compositions close to Al0.75Ga0.25N, special attention should be given to the treatment of valence band states in device simulation. In this work we develop a hybrid single band efective mass model which is informed by degree of optical polarization data obtained from atomistic multi-band calculations. Overall, the hybrid single band efective mass model is benchmarked against tight-binding electronic structure calculations. To do so a confining energy landscape is extracted from the tight-binding model and used as input for the single band efective mass calculations. Moreover, the extracted tight-binding energy landscape is transferred to a drift-difusion model, allowing therefore for a multi-scale study of transport properties of a single (Al,Ga)N quantum well embedded in a p-i-n junction. Our results show that wider wells lead to a lower turn-on voltage due to a reduction of the band gap, but the internal quantum efciency of these wells is lower than in narrower wells. Alloy disorder leads to carrier localization and an uneven distribution of recombination within the quantum well plane, which gives rise to percolation currents. A comparison of results with 'pure' band simulations shows that when TE emission dominated, the heavy hole mass is a good approximation. In contrast, where band mixing was strong between heavy hole and split-of bands the mass from the split of band was very efective.

• P. Colli, G. Gilardi, A. Signori, J. Sprekels, Solvability and optimal control of a multi-species Cahn--Hilliard--Keller--Segel tumor growth model, ESAIM. Control, Optimisation and Calculus of Variations, 31 (2025), pp. 1--37, DOI 10.1051/cocv/2025070 .
  Abstract
  This paper investigates an optimal control problem associated with a two-dimensional multi-species Cahn--Hilliard--Keller--Segel tumor growth model, which incorporates complex biological processes such as species diffusion, chemotaxis, angiogenesis, and nutrient consumption, resulting in a highly nonlinear system of nonlinear partial differential equations. The modeling derivation and corresponding analysis have been addressed in a previous contribution. Building on this foundation, the scope of this study involves investigating a distributed control problem with the goal of optimizing a tracking-type cost functional. This latter aims to minimize the deviation of tumor cell location from desired target configurations while penalizing the costs associated with implementing control measures, akin to introducing a suitable medication. Under appropriate mathematical assumptions, we demonstrate that sufficiently regular solutions exhibit continuous dependence on the control variable. Furthermore, we establish the existence of optimal controls and characterize the first-order necessary optimality conditions through a suitable variational inequality.

• P. Colli, J. Sprekels, On the optimal control of viscous Cahn--Hilliard systems with hyperbolic relaxation of the chemical potential, Communications in Analysis and Mechanics, 17 (2025), pp. 683--706, DOI 10.3934/cam.2025027 .
  Abstract
  In this paper, we study an optimal control problem for a viscous Cahn--Hilliard system with zero Neumann boundary conditions in which a hyperbolic relaxation term involving the second time derivative of the chemical potential has been added to the first equation of the system. For the initial-boundary value problem of this system, results concerning well-posedness, continuous dependence and regularity are known. We show Fréchet differentiability of the associated control-to-state operator, study the associated adjoint state system, and derive first-order necessary optimality conditions. Concerning the nonlinearities driving the system, we can include the case of logarithmic potentials. In addition, we perform an asymptotic analysis of the optimal control problem as the relaxation coefficient approaches zero.

• A. Esposito, G. Heinze, A. Schlichting, Graph-to-local limit for the nonlocal interaction equation, Journal de Mathématiques Pures et Appliquées, 194 (2025), pp. 103663/1--103663/50, DOI 10.1016/j.matpur.2025.103663 .
  Abstract
  We study a class of nonlocal partial differential equations presenting a tensor-mobility, in space, obtained asymptotically from nonlocal dynamics on localizing infinite graphs. Our strategy relies on the variational structure of both equations, being a Riemannian and Finslerian gradient flow, respectively. More precisely, we prove that weak solutions of the nonlocal interaction equation on graphs converge to weak solutions of the aforementioned class of nonlocal interaction equation with a tensor-mobility in the Euclidean space. This highlights an interesting property of the graph, being a potential space-discretization for the equation under study.

• R. Finn, M. O'Donovan, Th. Koprucki, S. Schulz, Impact of carrier-density screening on Urbach-tail energies and optical polarization in (Al,Ga)N quantum well systems, Physical Review Applied, 24 (2025), pp. 044084/1--044084/17, DOI 10.1103/x5d6-w3cp .
  Abstract
  Aluminum gallium nitride [(Al,Ga)N] presents an ideal platform for designing ultraviolet (UV) light emitters across the entire UV spectral range. However, in the deep-UV spectral range (<280 nm) these emitters exhibit very low quantum efficiencies, which in part is linked to the light-polarization characteristics of (Al,Ga)N quantum wells (QWs). In this study, we provide insight into the degree of optical polarization of (Al,Ga)N QW systems operating across the UV-C spectral range by means of an atomistic multiband electronic structure model. Our model not only captures the difference in valence-band ordering in AlN and GaN but it also accounts for alloy-disorder-induced band-mixing effects originating from random alloy fluctuations in (Al,Ga)N QWs. The latter aspect is often not captured in widely employed continuum-based models. The impact of alloy disorder on the electronic structure is studied in terms of Urbach-tail energies, which reflect the broadening of the valence-band density of states due to carrier-localization effects. We find that especially in wider wells, Urbach-tail energies are reduced with increasing carrier densities in the well, highlighting that alloy-disorder-induced carrier-localization effects in (Al,Ga)N QWs are also tightly linked to electrostatic built-in fields. Our calculations show that for QWs designed to emit at the longer-wavelength end of the UV-C spectrum, carrier density and well width are of secondary importance for their light-emission properties, meaning that one observes mainly transverse electrical polarization. However, for (Al,Ga)N QWs with high Al contents, we find that both well width and carrier density will impact the degree of optical polarization. Our calculations suggest that wider wells will increase the degree of optical polarization and may therefore be an option to improve the light-extraction efficiency in deep-UV light emitters.

• P. Gelss, S. Matera, R. Klein, B. Schmidt, Quantum dynamics of coupled excitons and phonons in chain-like systems: Tensor train approaches and higher-order propagators, Journal of Chemical Physics, 162 (2025), pp. 154115/1--154115/18, DOI 10.1063/5.0258904 .
  Abstract
  We investigate the use of tensor-train approaches to the solution of the time-dependent Schrödinger equation for chain-like quantum systems with on-site and nearest-neighbor interactions only. Using the efficient SLIM representation for low-rank tensor train representations of quantum-mechanical Hamiltonians, we aim at reducing the memory consumption as well as the computation costs, in order to mitigate the curse of dimensionality as much as possible. As an example, coupled excitons and phonons modeled in terms of Fröhlich--Holstein type Hamiltonians are studied here. By comparing our tensor-train based results with semi-analytical results, we demonstrate the key role of the ranks of tensor-train representations for quantum state vectors. Both the computational effort of the propagations and the accuracy that can be reached crucially depend on the maximum number of ranks chosen. Typically, an excellent quality of the solutions is found only when the ranks exceeds a certain value. That threshold, however, is very different for excitons, phonons, and coupled systems. One class of propagation schemes used in the present work builds on splitting the Hamiltonian into two groups of interleaved nearest-neighbor interactions which commutate within each of the groups. In addition to the first order Lie--Trotter and the second order Strang--Marchuk splitting schemes, we have also implemented the 4-th order Yoshida--Neri and the 8-th order Kahan--Li symplectic compositions. Especially the latter two are demonstrated to yield very accurate results, close to machine precision. However, due to the computational costs, currently their use is restricted to rather short chains. Another class of propagators involves explicit, time-symmetrized Euler integrators. Building on the traditional second order differencing method, we have also implemented higher order methods. Especially the 4-th order variant is recommended for quantum simulations of longer chains, even though the high precision of the splitting schemes cannot be reached. Moreover, the scaling of the computational effort with the dimensions of the local Hilbert spaces is much more favorable for the differencing than for the splitting schemes.

• K. Kunisch, J. Rehberg, On non-autonomous parabolic equations with measure-valued right hand sides and applications to optimal control, ESAIM. Control, Optimisation and Calculus of Variations, 32 (2025), pp. 101/1--101/38, DOI https://doi.org/10.1051/cocv/2025084 .
  Abstract
  The main aim of this paper is to develop a theory for non-autonomous parabolic equations with time-dependent measures on the spatial domain appearing as right hand sides. Restricting these measures to ones which have their supports on 'curves' or 'surfaces' -- the latter understood in the sense of geometric measure theory -- we succeed in interpreting them as distributional objects from a (negatively indexed) Sobolev--Slobodetskii space with differentiability index close to minus one. For these indices a tailor suited parabolic theory is established, based on previous results. It is also demonstrated that the proposed frame work is well-suited for optimal control with controls acting on sub-manifolds.

• A. Mielke, M.A. Peletier, J. Zimmer, Deriving a GENERIC system from a Hamiltonian system, Archive for Rational Mechanics and Analysis, 249 (2025), pp. 62/1--62/71, DOI 10.1007/s00205-025-02119-7 .
  Abstract
  We reconsider the fundamental problem of coarse-graining infinite-dimensional Hamiltonian dynamics to obtain a macroscopic system which includes dissipative mechanisms. In particular, we study the thermodynamical implications concerning Hamiltonians, energy, and entropy and the induced geometric structures such as Poisson and Onsager brackets (symplectic and dissipative brackets). We start from a general finite-dimensional Hamiltonian system that is coupled linearly to an infinite-dimensional heat bath with linear dynamics. The latter is assumed to admit a compression to a finite-dimensional dissipative semigroup (i.e., the heat bath is a dilation of the semigroup) describing the dissipative evolution of new macroscopic variables. Already in the finite-energy case (zero-temperature heat bath) we obtain the so-called GENERIC structure (General Equations for Non-Equilibrium Reversible Irreversibe Coupling), with conserved energy, nondecreasing entropy, a new Poisson structure, and an Onsager operator describing the dissipation. However, their origin is not obvious at this stage. After extending the system in a natural way to the case of positive temperature, giving a heat bath with infinite energy, the compression property leads to an exact multivariate Ornstein--Uhlenbeck process that drives the rest of the system. Thus, we are able to identify a conserved energy, an entropy, and an Onsager operator (involving the Green-Kubo formalism) which indeed provide a GENERIC structure for the macroscopic system.

• A. Mielke, R. Rossi, A. Stephan, On time-splitting methods for gradient flows with two dissipation mechanisms, Calculus of Variations and Partial Differential Equations, 64 (2025), pp. 63/1--63/49, DOI 10.1007/s00526-024-02849-8 .
  Abstract
  We consider generalized gradient systems in Banach spaces whose evolutions are generated by the interplay between an energy functional and a dissipation potential. We focus on the case in which the dual dissipation potential is given by a sum of two functionals and show that solutions of the associated gradient-flow evolution equation with combined dissipation can be constructed by a split-step method, i.e. by solving alternately the gradient systems featuring only one of the dissipation potentials and concatenating the corresponding trajectories. Thereby the construction of solutions is provided either by semiflows, on the time-continuous level, or by using Alternating Minimizing Movements in the time-discrete setting. In both cases the convergence analysis relies on the energy-dissipation principle for gradient systems.

• K. Remini, L. Schmeller, D. Peschka, B. Wagner, R. Seemann, Exploring the gap between theory and experiment at the three-phase contact line of polystyrene droplets on soft PDMS, Scientific Reports, 15 (2025), pp. 43486/1--43486/12, DOI 10.1038/s41598-025-30195-y .
  Abstract
  The shapes of liquid polystyrene (PS) droplets on viscoelastic polydimethylsiloxane (PDMS) substrates are investigated experimentally using atomic force microscopy for a range of droplet sizes and substrate elasticities. These shapes, which comprise the PS-air, PS-PDMS, and PDMS-air interfaces as well as the three-phase contact line, are compared to theoretical predictions using axisymmetric sharp-interface models derived through energy minimization. We find that the polystyrene droplets are cloaked by a thin layer of uncrosslinked molecules migrating from the PDMS substrate. By incorporating the effects of cloaking into the surface energies in our theoretical model, we show that the global features of the experimental droplet shapes are in excellent quantitative agreement for all droplet sizes and substrate elasticities. However, our comparisons also reveal systematic discrepancies between the experimental results and the theoretical predictions in the vicinity of the three-phase contact line. Moreover, the relative importance of these discrepancies systematically increases for softer substrates and smaller droplets. We demonstrate that global variations in system parameters, such as surface tension and elastic shear moduli, cannot explain these differences but instead point to a locally larger elastocapillary length, whose possible origin is discussed thoroughly.

• A. Glitzky, M. Liero, Uniqueness and regularity of weak solutions of a drift-diffusion system for perovskite solar cells, Journal of Evolution Equations, 25 (2025), pp. 87/1--87/23, DOI 10.1007/s00028-025-01117-2 .
  Abstract
  We establish a novel uniqueness result for an instationary drift-diffusion model for perovskite solar cells. This model for vacancy-assisted charge transport uses Fermi--Dirac statistics for electrons and holes and Blakemore statistics for the mobile ionic vacancies in the perovskite. Existence of weak solutions and their boundedness was proven in a previous work. For the uniqueness proof, we establish improved integrability of the gradients of the charge-carrier densities. Based on estimates obtained in the previous paper, we consider suitably regularized continuity equations with partly frozen arguments and apply the regularity results for scalar quasilinear elliptic equations by Meinlschmidt & Rehberg, Evolution Equations and Control Theory, 2016, 5(1):147-184.

• TH. Eiter, L. Schmeller, Weak solutions to a model for phase separation coupled with finite-strain viscoelasticity subject to external distortion, Mathematical Models & Methods in Applied Sciences, 35 (2025), pp. 2425--2463, DOI 10.1142/S0218202525500435 .
  Abstract
  We study the coupling of a viscoelastic deformation governed by a Kelvin--Voigt model at equilibrium, based on the concept of second-grade nonsimple materials, with a plastic deformation due to volumetric swelling, described via a phase-field variable subject to a Cahn--Hilliard model expressed in a Lagrangian frame. Such models can be used to describe the time evolution of hydrogels in terms of phase separation within a deformable substrate. The equations are mainly coupled via a multiplicative decomposition of the deformation gradient into both contributions and via a Korteweg term in the Eulerian frame. To treat time-dependent Dirichlet conditions for the deformation, an auxiliary variable with fixed boundary values is introduced, which results in another multiplicative structure. Imposing suitable growth conditions on the elastic and viscous potentials, we construct weak solutions to this quasistatic model as the limit of time-discrete solutions to incremental minimization problems. The limit passage is possible due to additional regularity induced by the hyperelastic and viscous stresses.

• TH. Eiter, A.L. Silvestre, Representation formulas and far-field behavior of time-periodic flow past a body, NoDEA. Nonlinear Differential Equations and Applications, 32 (2025), pp. 37/1--37/34, DOI 10.1007/s00030-025-01039-5 .
  Abstract
  This paper is concerned with integral representations and asymptotic expansions of solutions to the time-periodic incompressible Navier-Stokes equations for fluid flow in the exterior of a rigid body that moves with constant velocity. Using the time-periodic Oseen fundamental solution, we derive representation formulas for solutions with suitable regularity. From these formulas, the decomposition of the velocity component of the fundamental solution into steady-state and purely periodic parts and their detailed decay rate in space, we deduce complete information on the asymptotic structure of the velocity and pressure fields.

• J. Ginster, A. Rüland, A. Tribuzio, B. Zwicknagl, On the effect of geometry on scaling laws for a class of Martensitic phase transformations, Annales de l'Institut Henri Poincare. Analyse Non Lineaire, (2025), pp. 1--40 (published online first on 01.10.2025), DOI 10.4171/AIHPC/163 .
  Abstract
  We study scaling laws for singular perturbation problems associated with a class of two-dimensional martensitic phase transformations and deduce a domain dependence of the scaling law in the singular perturbation parameter. In these settings the respective scaling laws give rise to a selection principle for specific, highly symmetric domain geometries for the associated nucleation microstructure. More precisely, firstly, we prove a general lower bound estimate illustrating that in settings in which the domain and well geometry are incompatible in the sense of the Hadamard-jump condition, then necessarily at least logarithmic losses in the singular perturbation parameter occur in the associated scaling laws. Secondly, for specific phase transformations in two-dimensional settings we prove that this gives rise to a dichotomy involving logarithmic losses in the scaling law for generic domains and optimal linear scaling laws for very specific, highly compatible polygonal domains. In these situations the scaling law thus gives important insight into optimal isoperimetric domains. We discuss both the geometrically linearized and nonlinear settings.

• J. Ginster, L. Neubauer, B. Zwicknagl, A scaling law for a model of epitaxially strained elastic films with dislocations, Archive for Rational Mechanics and Analysis, 249 (2025), pp. 59/1--59/34, DOI 10.1007/s00205-025-02117-9 .
  Abstract
  A static variational model for shape formation in heteroepitaxial crystal growth is considered. The energy functional takes into account surface energy, elastic misfit-energy and nucleation energy of dislocations. A scaling law for the infimal energy is proven. The results quantify the expectation that in certain parameter regimes, island formation or topological defects are favorable. This generalizes results in the purely elastic setting from [Goldman and Zwicknagl (2014)]. To handle dislocations in the lower bound, a new variant of a ball-construction combined with thorough local estimates is presented.

• M. Liero, A. Mielke, O. Tse, J.-J. Zhu, Evolution of Gaussians in the Hellinger--Kantorovich--Boltzmann gradient flow, Communications on Pure and Applied Analysis, (2025), pp. 1--33 (published online on 01.10.2025), DOI 10.3934/cpaa.2025105 .
  Abstract
  This study leverages the basic insight that the gradient-flow equation associated with the relative Boltzmann entropy, in relation to a Gaussian reference measure within the Hellinger--Kantorovich (HK) geometry, preserves the class of Gaussian measures. This invariance serves as the foundation for constructing a reduced gradient structure on the parameter space characterizing Gaussian densities. We derive explicit ordinary differential equations that govern the evolution of mean, covariance, and mass under the HK--Boltzmann gradient flow. The reduced structure retains the additive form of the HK metric, facilitating a comprehensive analysis of the dynamics involved. We explore the geodesic convexity of the reduced system, revealing that global convexity is confined to the pure transport scenario, while a variant of sublevel semi-convexity is observed in the general case. Furthermore, we demonstrate exponential convergence to equilibrium through Polyak--Łojasiewicz-type inequalities, applicable both globally and on sublevel sets. By monitoring the evolution of covariance eigenvalues, we refine the decay rates associated with convergence. Additionally, we extend our analysis to non-Gaussian targets exhibiting strong log-Lambda-concavity, corroborating our theoretical results with numerical experiments that encompass a Gaussian-target gradient flow and a Bayesian logistic regression application.

• A. Mielke, T. Roubíček, U. Stefanelli, A model of gravitational differentiation of compressible self-gravitating planets, Continuum Mechanics and Thermodynamics, 37 (2025), pp. 80/1--80/24, DOI 10.1007/s00161-025-01404-w .
  Abstract
  We present a dynamic model for inhomogeneous viscoelastic media at finite strains. The model features a Kelvin--Voigt rheology, and includes a self-generated gravitational field in the actual evolving configuration. In particular, a fully Eulerian approach is adopted. We specialize the model to viscoelastic (barotropic) fluids and prove existence and a certain regularity of global weak solutions by a Faedo--Galerkin semi-discretization technique. Then, an extension to multi-component chemically reacting viscoelastic fluids based on a phenomenological approach by Eckart and Prigogine, is advanced and studied. The model is inspired by planetary geophysics. In particular, it describes gravitational differentiation of inhomogeneous planets and moons, possibly undergoing volumetric phase transitions.

• J. Rehberg, Regularity for non-autonomous parabolic equations with right-hand side singular measures involved, Evolution Equations and Control Theory, pp. 1--27 (published online on 22.12.2025), DOI 10.3934/eect.2026006 .
  Abstract
  This article provides a theory for non-autonomous parabolic equations the right hand side of which includes singular measures - depending on the time parameter - on the spatial domain. In two space dimensions all bounded Radon measures are admissable as such. In higher dimensions the focus is on measures whose support is concentrated on l-sets in the sense of Jonsson and Wallin. It is shown that they may interpreted as elements from a Sobolev space W. So the right hand side is considered as an element from a W-valued Lebesgue space on the time interval. Having this at hand, previous results on maximal (non-autonomous) maximal parabolic regularity apply and show that the solution lies in the corresponding space of maximal parabolic regularity. In contrast to other work in this field we only require absolute minimal smothness for the data of the problem: the domain, the coefficients - and mixed boundary conditions are allowed. Under minimally stronger assumptions we even show the Hölder property in space and time. Overall, this work contains an interplay of geometric measure theory with advanced parabolic theory which delivers as much parabolic regularity for the solution as one can maximally expect.

• W. van Oosterhout, Linearization of finite-strain poro-visco-elasticity with degenerate mobility, NoDEA. Nonlinear Differential Equations and Applications, 32 (2025), pp. 96/1--96/30, DOI 10.1007/s00030-025-01100-3 .
  Abstract
  A quasistatic nonlinear model for finite-strain poro-visco-elasticity is considered in the Lagrangian frame using Kelvin--Voigt rheology. The model consists of a mechanical equation which is coupled to a diffusion equation with a degenerate mobility. Having shown existence of weak solutions in a previous work, the focus is first on showing boundedness of the concentration using Moser iteration. Afterwards, it is assumed that the external loading is small, and it is rigorously shown that solutions of the nonlinear, finite-strain system converge to solutions of the linear, small-strain system.

Beiträge zu Sammelwerken

• P. Colli, J. Sprekels, F. Tröltzsch, First- and second-order optimality conditions in the sparse optimal control of Cahn--Hilliard systems, in: Proceedings of the RIMS Symposium on Evolution Equations and Related Topics, T. Fukao, ed., 2324 of RIMS Kôkyûroku Bessatsu, Research Institute for Mathematical Sciences, Kyoto, 2025, pp. 7/1--7/22.
  Abstract
  This paper deals with the sparse distributed control of viscous and nonviscous Cahn--Hilliard systems. We report on results concerning first-order necessary and second-order sufficient optimality conditions that have recently established by the authors. The analysis covers both the cases when the nonlinear double well potential governing the evolution is of either regular or logarithmic type. A major difficulty originates from the sparsity-enhancing term in the cost functional which typically is nondifferentiable.

• R. Finn, M. O'Donovan, Th. Koprucki, S. Schulz, Theoretical investigation of optical polarisation in alloy disordered (Al,Ga)N quantum well systems, in: 25th International Conference on Numerical Simulation of Optoelectronic Devices (NUSOD 2025), IEEE, 2025, pp. 67--68, DOI 10.1109/NUSOD64393.2025.11199467 .
  Abstract
  Aluminium Gallium Nitride ((Al,Ga)N) is an ideal material for light emitting devices in the UV spectral range. However, these devices still suffer from low external quantum efficiencies, particularly in the deep-UV range. A contributor to the low external quantum efficiency is low light extraction efficiency (LEE), which is tightly linked to the valence band structure of (Al,Ga)N quantum wells. Theoretical studies that account for alloy disorder-induced valence band mixing effects in these structures are sparse. Here, we utilise an atomistic multiband tight-binding model to gain insight into the degree of optical polarisation in (Al,Ga)N quantum well systems. Special attention is paid to the impact of Al content, well width and carrier density in the wells.

• R. Finn, P. Farrell, T. Streckenbach, J. Moatti, S. Schulz, Th. Koprucki, M. O'Donovan, Multi-scale hybrid band simulation of (Al,Ga)N UV-C light emitting diodes, in: 25th International Conference on Numerical Simulation of Optoelectronic Devices (NUSOD 2025), IEEE, 2025, pp. 19--20, DOI 10.1109/NUSOD64393.2025.11199525 .
  Abstract
  Aluminium gallium nitride alloys are used for developing light emitting diodes operating in the UV part of the electromagnetic spectrum. These devices suffer from a low efficiency. To gain insight to this question we develop a 3-D modified drift-diffusion model which takes into account both alloy disorder effects and valence band mixing, and investigate the device efficiency. Results show that the current injection efficiency is strongly influenced by the chosen doping profile.

• B. Schembera, F. Wübbeling, H. Kleikamp, B. Schmidt, A. Shehu, M. Reidelbach, Ch. Biedinger, J. Fiedler, Th. Koprucki, D. Iglezakis, D. Göddeke, Towards a knowledge graph for models and algorithms in applied mathematics, in: Metadata and Semantics Research, M. Sfakakis, E. Garoufallou, M. Damigos, A. Salaba, Ch. Papatheodorou, eds., Communications in Computer and Information Science, Springer, Cham, 2025, pp. 95--109, DOI 10.1007/978-3-031-81974-2_8 .
  Abstract
  Mathematical models and algorithms are an essential part of mathematical research data, as they are epistemically grounding numerical data. To make this research data FAIR, we present how two previously distinct ontologies, MathAlgoDB for algorithms and MathModDB for models, were merged and extended into a living knowledge graph as the key outcome. This was achieved by connecting the ontologies through computational tasks that correspond to algorithmic tasks. Moreover, we show how models and algorithms can be enriched with subject-specific metadata, such as matrix symmetry or model linearity, essential for defining workflows and determining suitable algorithms. Additionally, we propose controlled vocabularies to be added, along with a new class that differentiates base quantities from specific use case quantities. We illustrate the capabilities of the developed knowledge graph using two detailed examples from different application areas of applied mathematics, having already integrated over 250 research assets into the knowledge graph.

• M. Thomas, Analysis of a viscoplastic Burgers equation, in: Report: Mathematical Advances in Geophysical Fluid Dynamics, A.-L. Dalibard, P. Korn, L.M. Smith, E.S. Titi, eds., 22 of Oberwolfach Reports, European Mathematical Society Publishing House, Zürich, 2025, pp. 1238--1240, DOI 10.4171/OWR/2025/24 .
  Abstract
  The workshop “Mathematical Advances in Geophysical Fluid Dynamics" addressed recent advances in modeling, analytical, computational and stochastical studies of geophysical models. In particular addressed are atmosphere-, ocean- and sea-ice models, well-posedness and analysis of relevant geophysical fluid regimes and models, including stochastically forced equations, boundary layers as well as coupled models.

• J. Ginster, Formation of microstructure and occurrence of vertices in a frustrated spin system, in: Report: Singularities in Discrete Systems, L. Scardia, U. Stefanelli, F. Theil, eds., 22 of Oberwolfach Reports, European Mathematical Society Publishing House, Zürich, 2025, pp. 1178--1179, DOI 10.4171/OWR/2025/23 .
  Abstract
  Discrete systems are ubiquitous in applications. Their analysis and simulation call for taming their inherent multiscale character, as microscopic dynamics lead to the emergence of structures across scales. This workshop brought together leading experts in the calculus of variations, discrete systems, and materials science to explore cutting-edge topics at the intersection of mathematics and physical modelling. Presentations spanned a variety of themes, including dislocation dynamics, crystallization, micromagnetics, fracture mechanics, and discrete-to-continuum transitions. Particular emphasis was placed on the rigorous analysis of singular structures, nonlocal interactions, and energy-driven pattern formation. Several talks also underscored emerging connections with data science.

Preprints, Reports, Technical Reports

• S. Zendehroud, O. Kleinjung, P. Loche, L. Bocquet, R.R. Netz, E. Ipocoana, D. Peschka, M. Thomas, Combined effects of evaporation, sedimentation and solute crystallization on the dynamics of aerosol size distributions on multiple length and time scales, Preprint no. 3256, WIAS, Berlin, 2026, DOI 10.20347/WIAS.PREPRINT.3256 .
  Abstract, PDF (1975 kByte)
  We investigate three aspects of aerosol-mediated air-borne viral infection mechanisms on different length and time scales. First, we address the evolution of the size distribution of a non-interacting ensemble of droplets that are subject to evaporation and sedimentation using a sharp droplet-air interface model. From the exact solution of the evolution equation we derive the viral load in the air and show that it depends sensitively on the relative humidity. Secondly, from Molecular Dynamics simulations we extract the molecular reflection coefficient of single water molecules from the air-water interface. This parameter determines the water condensation and evaporation rate at a liquid droplet surface and therefore the evaporation rate of aqueous droplets. We find the reflection of water to be negligible at room temperature but to rise significantly at elevated temperatures and for grazing incidence angles. Thirdly, we derive a thermodynamically consistent three-dimensional diffuse-interface model for solute-containing droplets that is formulated as a three-phase Cahn--Hilliard/Allen--Cahn system. By numerically solving the coupled system of equations, we explore representative scenarios that show that this model reproduces and generalizes features of the sharp-interface model. These interconnected studies on the dynamics of aerosol droplet evaporation are relevant in order to quantitatively assess the airborne infection risk under varying environmental conditions.

• P. Colli, G. Gilardi, A. Signori, J. Sprekels, Optimal velocity control of a Brinkman--Cahn--Hilliard system with curvature effects, Preprint no. 3255, WIAS, Berlin, 2026, DOI 10.20347/WIAS.PREPRINT.3255 .
  Abstract, PDF (387 kByte)
  We address an optimal control problem governed by a system coupling a Brinkman-type momentum equation for the velocity field with a sixth-order Cahn--Hilliard equation for the phase variable, incorporating curvature effects in the free energy. The control acts as a distributed velocity control, allowing for the manipulation of the flow field and, consequently, the phase separation dynamics. We establish the existence of optimal controls, prove the Fréchet differentiability of the control-to-state operator, and derive first-order necessary optimality conditions in terms of a variational inequality involving the adjoint state variables. We also discuss the aspect of sparsity. Beyond its analytical novelty, this work provides %the first a rigorous control framework for Brinkman--Cahn--Hilliard systems incorporating a curvature regularization, offering a foundation for applications in microfluidic design and controlled pattern formation.

• TH. Eiter, Solution concepts for a model of visco-elasto-plasticity with slight compressibility, Preprint no. 3252, WIAS, Berlin, 2025, DOI 10.20347/WIAS.PREPRINT.3252 .
  Abstract, PDF (454 kByte)
  We study a model for the deformation of a visco-elasto-plastic material that is nearly incompressible. It originates from geophysics, is given in the Eulerian description and combines a Kelvin--Voigt rheology in the spherical part with a Jeffreys-type rheology in the deviatoric part. Despite a constant density, the model allows for non-isochoric deformation and the propagation of pressure waves. An additive decomposition of the strain rate into elastic and inelastic parts leads to an evolution equation for the small elastic strain, which is coupled with an adapted momentum equation. As plasticity is modeled through a non-smooth dissipation potential, we introduce a weak formulation in terms of a variational inequality. Since the well-posedness in such a weak setting is out of reach, we study two possible modifications: the regularization in terms of stress diffusion, and the relaxation of the solvability concept by transition to energy-variational solutions. In both cases, solutions are constructed by the same time-discrete scheme, consisting of solving a saddle-point problem in each time step.

• M. Heida, M. Landstorfer, Modeling of porous battery Electrodes with multiple phase transitions -- Part I: Modeling and homogenization, Preprint no. 3251, WIAS, Berlin, 2025, DOI 10.20347/WIAS.PREPRINT.3251 .
  Abstract, PDF (1108 kByte)
  We derive a thermodynamically consistent multiscale model for a porous intercalation battery in a half-cell configuration. Starting from microscopically resolved balance equations, the model rigorously couples cation and anion transport in the electrolyte with electron transport and solid- state diffusion in the active material through intercalation reactions. The derivation is based on non-equilibrium thermodynamics and periodic homogenization. The central novelty of this work lies in the systematic incorporation of multi-well free energy functions for intercalated cations into a homogenized DFN-type porous-electrode framework. This modeling choice leads to non-monotonic chemical potentials and enables a macroscopic descrip- tion of phase separation and multiple phase transitions within the electrode. While multi-well free energies are well established at the particle scale, their integration into homogenized porous- electrode models has so far been lacking. By extending the homogenization framework to include Cahn--Hilliard-type regularizations, phase-transition effects are retained at the electrode level. The resulting model exhibits an intrinsically coupled 3D+3D structure, in which macroscopic transport in the electrolyte is coupled to fully resolved microscopic diffusion within active parti- cles. This coupling naturally induces memory effects and time lags in the macroscopic voltage response, which cannot be captured by reduced single-scale models. Although the microscopic dynamics possess an underlying gradient-flow structure, we adopt a formal asymptotic approach to obtain a tractable DFN-type model suitable for practical simulations. This paper constitutes Part I of a three-part series and is devoted to the systematic derivation and mathematical formulation of the model. Numerical analysis, discretization strategies, simula- tion studies of transient cycling behavior, and experimental validation are deferred to Parts II and III. Part II focuses on finite C-rates, while Part III addresses open-circuit voltage conditions, where the predictive capabilities of the framework are investigated in detail.

• A. Thayil, L. Ermoneit, L.R. Schreiber, Th. Koprucki, M. Kantner, Optimization of Si/SiGe heterostructures for large and robust valley splitting in silicon qubits, Preprint no. 3249, WIAS, Berlin, 2025, DOI 10.20347/WIAS.PREPRINT.3249 .
  Abstract, PDF (7243 kByte)
  The notoriously low and fluctuating valley splitting is one of the key challenges for electron spin qubits in silicon (Si), limiting the scalability of Si-based quantum processors. In silicon-germanium (SiGe) heterostructures, the problem can be addressed by the design of the epitaxial layer stack. Several heuristic strategies have been proposed to enhance the energy gap between the two nearly degenerate valley states in strained Si/SiGe quantum wells (QWs), emphe.g., sharp Si/SiGe interfaces, Ge spikes or oscillating Ge concentrations within the QW. In this work, we develop a systematic variational optimization approach to compute optimal Ge concentration profiles that boost selected properties of the intervalley coupling matrix element. Our free-shape optimization approach is augmented by a number of technological constraints to ensure feasibility of the resulting epitaxial profiles. The method is based on an effective mass type envelope function theory accounting for the effects of strain and compositional alloy disorder. Various previously proposed heterostructure designs are recovered as special cases of the constrained optimization problem. Our main result is a novel heterostructure design we refer to as the emphmodulated wiggle well, which provides a large deterministic enhancement of the valley splitting along with a reliable suppression of the disorder-induced volatility. In addition, our new design offers a wide-range tunability of the valley splitting controlled by the vertical electric field, which offers new perspectives to engineer switchable qubits with on-demand adjustable valley splitting.

• P. Knopf, A. Pešić, D. Trautwein, Curvature-driven pattern formation in biomembranes: A gradient flow approach, Preprint no. 3244, WIAS, Berlin, 2025, DOI 10.20347/WIAS.PREPRINT.3244 .
  Abstract, PDF (7300 kByte)
  In this work, we study a phase-field model for curvature-driven pattern formation in biomembranes. The model is derived as a gradient flow of an energy functional that approximates the two-phase Canham--Helfrich energy. This leads to a Cahn--Hilliard-type equation with cross diffusion for the relative chemical concentration of one lipid phase, coupled to a fourth-order reaction-diffusion equation describing the height profile of the membrane. We first prove the existence of weak solutions for the case of regular double-well potentials, using a minimizing movement scheme to construct approximate solutions. The analysis is then extended to singular potentials, e.g., the Flory--Huggins potential, by approximating them with a Moreau--Yosida regularization. For both cases, we establish higher regularity, continuous dependence on the initial data, and consequently the uniqueness of weak solutions. Finally, we propose a well-posed finite element discretization of the model and present numerical experiments illustrating the effect of different physical parameters on the resulting membrane patterns. Depending on the parameter regime, we observe purely striped, dotted, or snake-like structures.

• A. Glitzky, M. Liero, Drift-diffusion models with nonlinear boundary conditions modeling Schottky contacts at metal-semiconductor interfaces, Preprint no. 3242, WIAS, Berlin, 2025, DOI 10.20347/WIAS.PREPRINT.3242 .
  Abstract, PDF (345 kByte)
  The paper deals with drift-diffusion models for semiconductor heterostructures with Schottky contacts at all metal-semiconductor interfaces. Our analytical investigations allow for Boltzmann as well as Fermi--Dirac statistics for the charge-carrier densities. We verify the existence and boundedness of weak solutions of the instationary van Roosbroeck system in this context. Moreover, under additional assumptions the uniqueness and the higher regularity of the solution are demonstrated. Here, higher regularity results for scalar quasilinear parabolic PDEs are used.

• N. Ciroth, A. Sala, R. Xue, L. Ermoneit, Th. Koprucki, M. Kantner, L.R. Schreiber, Numerical simulation of coherent spin-shuttling in a QuBus with charged defects, Preprint no. 3241, WIAS, Berlin, 2025, DOI 10.20347/WIAS.PREPRINT.3241 .
  Abstract, PDF (874 kByte)
  Recent advances in coherent conveyor-mode spin qubit shuttling are paving the way for large scale quantum computing platforms with qubit connectivity achieved by spin qubit shuttles. We developed a simulation tool to investigate numerically the impact of device imperfections on the spin-coherence of conveyor-mode shuttling in Si/SiGe. We simulate the quantum evolution of a mobile electron spin-qubit under the influence of sparse and singly charged point defects placed in the Si/SiGe heterostructure in close proximity to the shuttle lane. We consider different locations of a single charge defect with respect to the center of the shuttle lane, multiple orbital states of the electron in the shuttle with g-factor differences between the orbital levels, and orbital relaxation induced by electron-phonon interaction. With this simulation framework, we identify the critical defect density of charged point defects in the heterostructure for conveyor-mode spin qubit shuttle devices and quantify the impact of a single defect on the coherence of a qubit.

• H. Meinlschmidt, J. Rehberg, Sharp angle estimates for second order divergence operators, Preprint no. 3240, WIAS, Berlin, 2025, DOI 10.20347/WIAS.PREPRINT.3240 .
  Abstract, PDF (389 kByte)
  This article is about the (minimal) sector containing the numerical range of the principal part of a linear second-order elliptic differential operator defined by a form on closed subspaces V of the first-order Sobolev space W^1,2(Ω) incorporating mixed boundary conditions. We collect a comprehensive array of results on the angle of sectoriality and the H^∞-angle attached to realizations of the elliptic operator. We thereby consider the operator in several scales of Banach spaces: the Lebesgue space, the negative Sobolev space, and their interpolation scale. For the latter two types of spaces, we rely on recent results regarding the Kato square root property. We focus on minimal assumptions on geometry, and we consider both real and complex coefficients. Not all results presented are new, but we strive for a streamlined and comprehensive overall picture from several branches of operator theory, and we complement the existing results with several new ones, in particular aiming at explicit estimates built on readily accessible problem data. This concerns for example a new estimate on the angle of the sector containing the numerical range of a linear, continuous and coercive Hilbert space operator, but also an explicit estimate for the angle of sectoriality for the elliptic operator on L^p( Ω) with complex coefficients without any assumptions on geometry and a general transfer principle for the Crouzeix--Delyon theorem from bounded operators to sectorial ones, keeping the explicit constant.

• P. Dondl, M. Heida, S. Hermann, Non-local homogenization limits of discrete elastic spring network models with random coefficients, Preprint no. 3238, WIAS, Berlin, 2025, DOI 10.20347/WIAS.PREPRINT.3238 .
  Abstract, PDF (276 kByte)
  This work examines a discrete elastic energy system with local interactions described by a discrete second-order functional in the symmetric gradient and additional non-local random long-range interactions. We analyze the asymptotic behavior of this model as the grid size tends to zero. Assuming that the occurrence of long-range interactions is Bernoulli distributed and depends only on the distance between the considered grid points, we derive -- in an appropriate scaling regime -- a fractional p-Laplace-type term as the long-range interactions' homogenized limit. A specific feature of the presented homogenization process is that the random weights of the p-Laplace-type term are non-stationary, thus making the use of standard ergodic theorems impossible. For the entire discrete energy system, we derive a non-local fractional p-Laplace-type term and a local second-order functional in the symmetric gradient. Our model can be used to describe the elastic energy of standard, homogeneous, materials that are reinforced with long-range stiff fibers.

• W.J.M. van Oosterhout, M. Liero, Modeling and analysis of finite-strain visco-elastic materials with electrostatic interaction, Preprint no. 3237, WIAS, Berlin, 2025, DOI 10.20347/WIAS.PREPRINT.3237 .
  Abstract, PDF (404 kByte)
  We develop a thermodynamically consistent model for the viscoelastic deformation of electrically charged bodies in the Lagrangian frame, incorporating a Jeffreys-type rheology and flow of free charge-carriers within the framework of the General Equations for Non-Equilibrium Reversible?Irreversible Coupling (GENERIC). The formulation couples mechanical, electrostatic, and dissipative effects in a structure that ensures compatibility with the principles of nonequilibrium thermodynamics. Furthermore, in the isothermal and mechanically quasistatic regime, i.e., where inertial effects are neglected, we establish the existence of weak solutions to a reduced version of the governing system. The proof relies on a Galerkin approximation combined with suitable regularizations of the degenerate mobilities of the free charge carriers and of the free energy. A typical application is the description of conductive hydrogels used in biomedicine.

• P. Colli, E. Rocca, J. Sprekels, On the hyperbolic relaxation of the chemical potential in a phase field tumor growth model, Preprint no. 3234, WIAS, Berlin, 2025, DOI 10.20347/WIAS.PREPRINT.3234 .
  Abstract, PDF (307 kByte)
  In this paper, we study a phase field model for a tumor growth model of Cahn--Hilliard type in which the often assumed parabolic relaxation of the chemical potential is replaced by a hyperbolic one. We show that the resulting initial-boundary value problem is well posed and that its solutions depend continuously on two given functions: one appearing in the mass balance equation and one in the nutrient equation, representing, respectively, sources of drugs (e.g. chemotherapy) and antiangiogenic therapy. We also discuss regularity properties of the solutions. Moreover, in the case of a constant proliferation function, we rigorously analyze the asymptotic behavior as the coefficient of the inertial term tends to zero, establishing convergence to the corresponding viscous Cahn--Hilliard tumor growth model. Our results apply to a broad class of double-well potentials, including nonsmooth ones.

• E. Schrohe, J. Rehberg, Optimal Sobolev regularity for second order divergence elliptic operators on domains with buried boundary parts, Preprint no. 3232, WIAS, Berlin, 2025, DOI 10.20347/WIAS.PREPRINT.3232 .
  Abstract, PDF (330 kByte)
  We study the regularity of solutions of elliptic second order boundary value problems on a bounded domain $Omega$ in $mathbb R^3$. The coefficients are not necessarily continuous and the boundary conditions may be mixed, i.e. Dirichlet on one part $D$ of the boundary and Neumann on the complementing part. The peculiarity is that $D$ is partly `buried' in $Omega$ in the sense that the topological interior of $Omega cup D$ properly contains $Omega$. The main result is that the singularity of the solution along the border of the buried contact behaves exactly as the singularity for the solution of a mixed boundary value problem along the border between the Dirichlet and the Neumann boundary part.

• V. Bach, A.F.M. TER Elst, J. Rehberg, The Birman--Solomyak theorem revisited: A novel elementary proof, generalisation, and applications, Preprint no. 3231, WIAS, Berlin, 2025, DOI 10.20347/WIAS.PREPRINT.3231 .
  Abstract, PDF (289 kByte)
  We provide a new short proof for the Birman--Solomyak theorem for Hilbert--Schmidt operators and give an application to a Schrödinger--Poisson system.

• K. Buryachenko, A. Glitzky, M. Liero, B. Zwicknagl, Dimension reduction for a coupled electro-elastic saddle-point problem at finite strains, Preprint no. 3230, WIAS, Berlin, 2025, DOI 10.20347/WIAS.PREPRINT.3230 .
  Abstract, PDF (394 kByte)
  We study the finite deformation of a thin, elastically heterogeneous sheet subject to electrostatic coupling. The interaction between mechanics and electrostatics is formulated as a saddle-point problem involving the deformation and the electrostatic potential. Starting from a three-dimensional electro-elastic model with prestrain in the elastic energy, we rigorously derive a reduced plate model in the bending regime. To perform the dimension reduction, that is, to derive the energy of a thin object by taking a suitable limit as its thickness tends to zero, we apply Gamma-convergence-type methods to the underlying saddle-point problem. In the case of bivariate functionals, this convergence is understood in an adapted epi/hypo-convergence sense. In this concept, we demonstrate the convergence of the rescaled electro-elastic problems to an effective two-dimensional bending model coupled to electric effects. We verify that cluster points of saddle points are saddle points for the limit.

• J. Ginster, On the formation of microstructure and the occurrence of vortices in a singularly perturbed energy related to helimagnetism: A scaling law result, Preprint no. 3227, WIAS, Berlin, 2025, DOI 10.20347/WIAS.PREPRINT.3227 .
  Abstract, PDF (449 kByte)
  In this work, singularly perturbed energies arising from discrete spin models are studied. The energies under consideration consist of a non-convex bulk term and a higher-order regularizing term and are subject to incompatible boundary conditions. In contrast to existing results in the literature, in this work, admissible fields are not necessarily gradient fields, instead their curl is linked to topological singularities, so-called vortices, in the discrete spin model. The main result of this work is a scaling law for the minimal energy with respect to three parameters: one measuring the incompatibility of the boundary conditions, the second measuring the strength of the regularizing term, and the third being related to the interatomic distance in the discrete model. The shown result implies in particular that in certain parameter regimes, minimizers necessarily develop vortices. A key tool in the analysis is a careful modification of the celebrated ball-construction technique that, due to a lack of rigidity, considers simultaneously both the bulk energy and the regularizing term.

• A. Mielke, Some notes on the Hellinger distance and various Fisher--Rao distances, Preprint no. 3222, WIAS, Berlin, 2025, DOI 10.20347/WIAS.PREPRINT.3222 .
  Abstract, PDF (380 kByte)
  These expository notes introduce the Hellinger distance on the set of all measures and the induced Fisher-Rao distances for subsets of measures, such as probability measures or Gaussian measures. The historical background is highlighted and the relations and the distinct features of the two distances are discussed. Moreover, we provide a dynamic characterization of absolutely continuous curves in the Hellinger spaces in terms of the growth equation, which replaces the continuity equation in the theory of optimal transport.

• A. Mielke, A. Schlichting, A. Stephan, Derivation of the fourth--order DLSS equation with nonlinear mobility via chemical reactions, Preprint no. 3221, WIAS, Berlin, 2025, DOI 10.20347/WIAS.PREPRINT.3221 .
  Abstract, PDF (1482 kByte)
  We provide a derivation of the fourth-order DLSS equation based on an interpretation as a chemical reaction network. We consider the rate equation on the discretized circle for a process in which pairs of particles occupying the same site simultaneously jump to the two neighboring sites; the reverse process involves pairs of particles at adjacent sites simultaneously jumping back to the site located between them. Depending on the rates, in the vanishing-mesh-size limit we obtain either the classical DLSS equation or a variant with nonlinear mobility of power type. Via EDP convergence, we identify the limiting gradient structure to be driven by entropy with respect to a generalization of diffusive transport with nonlinear mobility. Interestingly, the DLSS equation with power-type mobility shares qualitative similarities with the fast diffusion and porous medium equation, since we find traveling wave solutions with algebraic tails or compactly supported polynomials, respectively.

• P. Colli, G. Gilardi, A. Signori, J. Sprekels, On Brinkman flows with curvature-induced phase separation in binary mixtures, Preprint no. 3218, WIAS, Berlin, 2025, DOI 10.20347/WIAS.PREPRINT.3218 .
  Abstract, PDF (333 kByte)
  The mathematical analysis of diffuse-interface models for multiphase flows has attracted significant attention due to their ability to capture complex interfacial dynamics, including curvature effects, within a unified, energetically consistent framework. In this work, we study a novel Brinkman--Cahn--Hilliard system, coupling a sixth-order phase-field evolution with a Brinkman-type momentum equation featuring variable shear viscosity. The Cahn--Hilliard equation includes a nonconservative source term accounting for mass exchange, and the velocity equation contains a non divergence-free forcing term. We establish the existence of weak solutions in a divergence-free variational framework, and, in the case of constant mobility and shear viscosity, prove uniqueness and continuous dependence on the forcing. Additionally, we analyze the Darcy limit, providing existence results for the corresponding reduced system.

• T. Fastovska, J. Ginster, B. Zwicknagl, Derivation of the Reissner--Mindlin model from nonlinear elasticity, Preprint no. 3216, WIAS, Berlin, 2025, DOI 10.20347/WIAS.PREPRINT.3216 .
  Abstract, PDF (351 kByte)
  We discuss how the Reissner--Mindlin plate model can be derived from three-dimensional finite elasticity in terms of Gamma-convergence. The presence of transverse shear effects in the Reissner--Mindlin model requires to scale different components of the three-dimensional elastic strain differently. A main technical tool is then the combination of rigidity estimates for the deformation and suitably averaged versions.

• A. Acharya, J. Ginster, A convex variational principle for the necessary conditions of classical optimal control, Preprint no. 3215, WIAS, Berlin, 2025, DOI 10.20347/WIAS.PREPRINT.3215 .
  Abstract, PDF (288 kByte)
  A scheme for generating a family of convex variational principles is developed, the Euler--Lagrange equations of each member of the family formally corresponding to the necessary conditions of optimal control of a given system of ordinary differential equations (ODE) in a well-defined sense. The scheme is applied to the Quadratic-Quadratic Regulator problem for which an explicit form of the functional is derived, and existence of minimizers of the variational principle is rigorously shown. It is shown that the Linear-Quadratic Regulator problem with time-dependent forcing can be solved within the formalism without requiring any nonlinear considerations, in contrast to the use of a Riccati system in the classical methodology. Our work demonstrates a pathway for solving nonlinear control problems via convex optimization.

• D. Peschka, A. Zafferi, Variational modelling of porosity waves, Preprint no. 3210, WIAS, Berlin, 2025, DOI 10.20347/WIAS.PREPRINT.3210 .
  Abstract, PDF (694 kByte)
  Mathematical models for finite-strain poroelasticity in an Eulerian formulation are studied by constructing their energy-variational structure, which gives rise to a class of saddle-point problems. This problem is discretised using an incremental time-stepping scheme and a mixed finite element approach, resulting in a monolithic, structure-preserving discretisation. The Eulerian formulation is based on the inverse deformation, the so-called emphreference map. We present examples from geophysical applications, where elasticity and diffusive fluid flow are fully coupled and can be used to describe porosity waves, i.e., localised ascending fluid waves driven by gravitational forces.

• M.I. Gau, M. Liero, Derivation of a thermo-visco-elastic plate model at small strains, Preprint no. 3209, WIAS, Berlin, 2025, DOI 10.20347/WIAS.PREPRINT.3209 .
  Abstract, PDF (339 kByte)
  We investigate a three-dimensional thermo-visco-elastic model with Kelvin--Voigt rheology under small strains confined to a thin domain. The model comprises a quasistatic linear momentum equation, with viscous stresses adhering to a Kelvin--Voigt viscosity law, coupled with a nonlinear heat equation governing temperature. The heat equation incorporates source terms arising from viscous dissipation and adiabatic heat sources due to thermal expansion. The model ensures thermodynamic consistency, maintaining energy conservation, positive temperature, and entropy production. We analyze the asymptotic behavior of solutions as the domain thickness approaches zero, deriving an effective two-dimensional model. This derivation involves rescaling the domain to a fixed thickness and establishing uniform a priori estimates relative to the plate's thickness. In the limit, the temperature becomes vertically constant, and displacement are of Kirchhoff--Love type, enabling meaningful interpretation of the limiting objects within the plate's two-dimensional cross-section. The mechanical equations consist of two parabolic equations, one for the membrane part and one for the bending part. Notably, the viscosity law in the limiting model departs from the Kelvin--Voigt form, reflecting nontrivial kinematic constraints on the rescaled out-of-plane strains. The bending of the plate does not depend on the temperature in the limit.

• TH. Eiter, S. Schindler, Time-asymptotic self-similarity of the damped compressible Euler equations in parabolic scaling variables, Preprint no. 3207, WIAS, Berlin, 2025, DOI 10.20347/WIAS.PREPRINT.3207 .
  Abstract, PDF (355 kByte)
  We study the long-time behavior of solutions to the compressible Euler equations with frictional damping in the whole space, where we prescribe direction-dependent values for the density at spatial infinity. To this end, we transform the system into parabolic scaling variables and derive a relative entropy inequality, which allows to conclude the convergence of the density towards a self-similar solution to the porous medium equation while the associated limit momentum is governed by Darcy's law. Moreover, we obtain convergence rates that explicitly depend on the flatness of the limit profile. While we focus on weak solutions in the one-dimensional case, we extend our results to energy-variational solutions in the multi-dimensional setting.

• TH. Eiter, A.L. Silvestre, Approximation of time-periodic flow past a translating body by flows in bounded domains, Preprint no. 3206, WIAS, Berlin, 2025, DOI 10.20347/WIAS.PREPRINT.3206 .
  Abstract, PDF (380 kByte)
  We consider a time-periodic incompressible three-dimensional Navier-Stokes flow past a translating rigid body. In the first part of the paper, we establish the existence and uniqueness of strong solutions in the exterior domain that satisfy pointwise estimates for both the velocity and pressure. The fundamental solution of the time-periodic Oseen equations plays a central role in obtaining these estimates. The second part focuses on approximating this exterior flow within truncated domains, incorporating appropriate artificial boundary conditions. For these bounded domain problems, we prove the existence and uniqueness of weak solutions. Finally, we estimate the error in the velocity component as a function of the truncation radius, showing that, as the latter passes to infinity, the velocities of the truncated problems converge, in an appropriate norm, to the velocity of the exterior flow.

• D.W. Boutros, X. Liu, M. Thomas, E.S. Titi, Global well-posedness of the elastic-viscous-plastic sea-ice model with the inviscid Voigt-regularisation, Preprint no. 3202, WIAS, Berlin, 2025, DOI 10.20347/WIAS.PREPRINT.3202 .
  Abstract, PDF (303 kByte)
  In this paper, we initiate the rigorous mathematical analysis of the elastic-viscous-plastic (EVP) sea-ice model, which was introduced in E. C. Hunke and J. K. Dukowicz, J. Phys. Oceanogr., 27, 9 (1997), 1849--1867. The EVP model is one of the standard and most commonly used dynamical sea-ice models. We study a regularised version of this model. In particular, we prove the global well-posedness of the EVP model with the inviscid Voigt-regularisation of the evolution equation for the stress tensor. Due to the elastic relaxation and the Voigt regularisation, we are able to handle the case of viscosity coefficients without cutoff, which has been a major issue and a setback in the computational study and analysis of the related Hibler sea-ice model, which was originally introduced in W. D. Hibler, J. Phys. Oceanogr., 9, 4 (1979), 815--846. The EVP model shares some structural characteristics with the Oldroyd-B model and related models for viscoelastic non-Newtonian complex fluids.

• Z. Amer, A. Avdzhieva, M. Bongarti, P. Dvurechensky, P. Farrell, U. Gotzes, F.M. Hante, A. Karsai, S. Kater, M. Landstorfer, M. Liero, D. Peschka, L. Plato, K. Spreckelsen, J. Taraz, B. Wagner, Modeling hydrogen embrittlement for pricing degradation in gas pipelines, Preprint no. 3201, WIAS, Berlin, 2025, DOI 10.20347/WIAS.PREPRINT.3201 .
  Abstract, PDF (12 MByte)
  This paper addresses aspects of the critical challenge of hydrogen embrittlement in the context of Germany's transition to a sustainable, hydrogen-inclusive energy system. As hydrogen infrastructure expands, estimating and pricing embrittlement become paramount due to safety, operational, and economic concerns. We present a twofold contribution: We discuss hydrogen embrittlement modeling using both continuum models and simplified approximations. Based on these models, we propose optimization-based pricing schemes for market makers, considering simplified cyclic loading and more complex digital twin models. Our approaches leverage widely-used subcritical crack growth models in steel pipelines, with parameters derived from experiments. The study highlights the challenges and potential solutions for incorporating hydrogen embrittlement into gas transportation planning and pricing, ultimately aiming to enhance the safety and economic viability of Germany's future energy infrastructure.

• M. Heida, On the parallelized efficient computation of high dimensional Voronoi diagrams on bounded, unbounded, spherical and periodic domains, Preprint no. 3197, WIAS, Berlin, 2025, DOI 10.20347/WIAS.PREPRINT.3197 .
  Abstract, PDF (636 kByte)
  We investigate a recently implemented new algorithm for the computation of a Voronoi diagram in high dimensions and generalize it to N nodes in general or non-general position using a geometric characterization of edges and vertices. The algorithm consist of local computations, is well suited for parallelization and can be applied to the Euclidean geometry or on the sphere.
  We provide a mathematical proof that the algorithm is exact, convergent and has computational costs of O(E NN (N))$, where E is the number of edges and NN (N) is the computational cost to calculate the nearest neighbor among N points. We also provide data from performance tests in the recently developed Julia package „HighVoronoi.jl” and compare it to the quickhull algorithm.
  It turns out that the new approach is particularly well suited for bounded domains, periodic domains and parallelization of computations.

• G. Heinze, A. Mielke, A. Stephan, Discrete-to-continuum limit for nonlinear reaction-diffusion systems via EDP convergence for gradient systems, Preprint no. 3194, WIAS, Berlin, 2025, DOI 10.20347/WIAS.PREPRINT.3194 .
  Abstract, PDF (460 kByte)
  We investigate the convergence of spatial discretizations for reaction-diffusion systems with mass-action law satisfying a detailed balance condition. Considering systems on the d-dimensional torus, we construct appropriate space-discrete processes and show convergence not only on the level of solutions, but also on the level of the gradient systems governing the evolutions. As an important step, we prove chain rule inequalities for the reaction-diffusion systems as well as their discretizations, featuring a non-convex dissipation functional. The convergence is then obtained with variational methods by building on the recently introduced notion of gradient systems in continuity equation format.

• A. Mielke, An Eulerian formulation for dissipative materials using Lie derivatives and GENERIC, Preprint no. 3180, WIAS, Berlin, 2025, DOI 10.20347/WIAS.PREPRINT.3180 .
  Abstract, PDF (342 kByte)
  We recall the systematic formulation of Eulerian mechanics in terms of Lie derivatives along the vector field of the material points. Using the abstract properties of Lie derivatives we show that the transport via Lie derivatives generates in a natural way a Poisson structure on the chosen phase space. The evolution equations for thermo-viscoelastic-viscoplastic materials in the Eulerian setting is formulated in the abstract framework of GENERIC (General Equations for Non-Equilibrium Reversible Irreversible Coupling). The equations may not be new, but the systematic splitting between reversible Hamiltonian and dissipative effects allows us to see the equations in a new light that is especially useful for future generalizing of the system, e.g.for adding new effects like reactive species.

• D. Peschka, M. Thomas, A. Zafferi, Reference map approach to Eulerian thermomechanics using GENERIC, Preprint no. 3178, WIAS, Berlin, 2025, DOI 10.20347/WIAS.PREPRINT.3178 .
  Abstract, PDF (7829 kByte)
  An Eulerian GENERIC model for thermo-viscoelastic materials with diffusive components is derived based on a transformation framework that maps a Lagrangian formulation to corresponding Eulerian coordi- nates. The key quantity describing the deformation in Eulerian coordinates is the inverse of the deformation, i.e. the reference map. The Eulerian model is formally constructed, and by reducing the GENERIC system to a damped Hamiltonian system, the isothermal limit is derived. A structure-preserving weak formulation is developed. As an example, the coupling of finite strain viscoelasticity and diffusion in a multiphase system governed by Lagrangian indicator functions is demonstrated.

• A. Mielke, J.-J. Zhu, Hellinger--Kantorovich gradient flows: Global exponential decay of entropy functionals, Preprint no. 3176, WIAS, Berlin, 2025, DOI 10.20347/WIAS.PREPRINT.3176 .
  Abstract, PDF (508 kByte)
  We investigate a family of gradient flows of positive and probability measures, focusing on the Hellinger--Kantorovich (HK) geometry, which unifies transport mechanism of Otto--Wasserstein, and the birth-death mechanism of Hellinger (or Fisher--Rao). A central contribution is a complete characterization of global exponential decay behaviors of entropy functionals under Otto--Wasserstein and Hellinger-type gradient flows. In particular, for the more challenging analysis of HK gradient flows on positive measures---where the typical log-Sobolev arguments fail---we develop a specialized shape-mass decomposition that enables new analysis results. Our approach also leverages the Polyak--Łojasiewicz-type functional inequalities and a careful extension of classical dissipation estimates. These findings provide a unified and complete theoretical framework for gradient flows and underpin applications in computational algorithms for statistical inference, optimization, and machine learning.

• G. Heinze, J.-F. Pietschmann, A. Schlichting, Gradient flows on metric graphs with reservoirs: Microscopic derivation and multiscale limits, Preprint no. 3161, WIAS, Berlin, 2025, DOI 10.20347/WIAS.PREPRINT.3161 .
  Abstract, PDF (1430 kByte)
  We study evolution equations on metric graphs with reservoirs, that is graphs where a one-dimensional interval is associated to each edge and, in addition, the vertices are able to store and exchange mass with these intervals. Focusing on the case where the dynamics are driven by an entropy functional defined both on the metric edges and vertices, we provide a rigorous understanding of such systems of coupled ordinary and partial differential equations as (generalized) gradient flows in continuity equation format. Approximating the edges by a sequence of vertices, which yields a fully discrete system, we are able to establish existence of solutions in this formalism. Furthermore, we study several scaling limits using the recently developed framework of EDP convergence with embeddings to rigorously show convergence to gradient flows on reduced metric and combinatorial graphs. Finally, numerical studies confirm our theoretical findings and provide additional insights into the dynamics under rescaling.

Vorträge, Poster

• J. Rehberg, A mathematical analysis of the Schrödinger--Poisson system, Institutskolloquium, Universität Kassel, Mathematik und Naturwissenschaften, January 19, 2026.

• S. Schindler, On asymptotically self-similar behavior in reaction-diffusion systems, 95th Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM 2025), Section 14.04 ``Applied Analysis'', April 7 - 11, 2025, Poznan University of Technology, Poland, April 10, 2025.

• M. Heida, Upscaling battery models: Connecting microscopic dynamics with macroscopic behavior, 24th GAMM Seminar on Microstructures, January 30 - 31, 2025, Humboldt-Universität zu Berlin, January 31, 2025.

• M. O'Donovan, Developing a multi-scale drift-diffusion simulation framework for UV-C emitting quantum well systems, Analysis of Robust Numerical Solvers for Innovative Semiconductors in View of Energy Transition (ARISE 2025), November 4 - 5, 2025, WIAS Berlin, November 4, 2025.

• M. O'Donovan, Multi-scale hybrid band simulation of (Al,Ga)N UV-C light emitting diodes, International Conference on Numerical Simulation of Optoelectronic Devices (NUSOD 2025), September 14 - 18, 2025, Łódź University of Technology, Poland, September 15, 2025.

• M. O'Donovan, Simulation of (Al,Ga)N-based UV LEDs including effects from disorder, 15th International Conference on Nitride Semiconductors (ICNS 15), Sweden, July 6 - 11, 2025.

• D. Peschka, Fluid-structure interaction and wetting of soft polymer substrates, Leibniz MMS Days 2025, March 26 - 28, 2025, Leibniz-Institut für Ostseeforschung Warnemünde, March 28, 2025.

• D. Peschka, Thin-film free boundary problems with moving contact lines - modeling, numerics, and model hierarchies, Thematic Program on Free Boundary Problems, October 6 - 10, 2025, Universtität Wien, Erwin Schrödinger International Institute for Mathematics and Physics, Austria, October 10, 2025.

• D. Peschka, Wetting of soft deformable substrates - phase fields for fluid structure interaction with moving contact lines, Institute of Thermomechanics Seminar, Czech Academy of Sciences, Prague, Czech Republic, June 4, 2025.

• B. Schmidt, FAIR representation of mathematical research data: MathModDB and MathAlgoDB as knowledge graphs for mathematical models and numerical algorithms, Conference on Research Data Infrastructure (CoRDI), August 26 - 28, 2025, Rheinisch-Westfälische Technische Hochschule Aachen, August 28, 2025.

• B. Schmidt, MathModDB and MathAlgoDB: Knowledge graphs for mathematical models and numerical algorithms, NFDI4DS Conference, November 25 - 26, 2025, Fraunhofer Institut für Offene Kommunikationssysteme, Berlin, November 25, 2025.

• B. Schmidt, MathModDB and MathAlgoDB: Knowledge graphs for mathematical models and numerical algorithms, Kickoff Meeting of the GAMM Activity Group on Research Software Engineering and Research Data Management in Mathematics & Mechanics, December 4 - 5, 2025, Technische Universität Braunschweig, December 5, 2025.

• B. Schmidt, MathModDB: An ontology and knowledge graph for mathematical models, FAIR Data in Plasma Science (FDPS-IV), May 12 - 13, 2025, Leibniz-Institut für Plasmaforschung und Technologie, Greifswald, May 12, 2025.

• B. Schmidt, Towards a knowledge graph for mathematical models and algorithms: Application to surface hopping trajectories, 61st Symposium on Theoretical Chemistry, September 22 - 26, 2025.

• A. Mielke, An L^p approach to chain rules for gradient systems, Department of Mathematics, Technische Universität München, November 6, 2025.

• A. Mielke, Analysis of evolutionary Gamma convergence for gradient systems, Summer School on Mathematical Analysis and Applications, June 9 - 13, 2025, Lake Como School of Advanced Studies, Villa del Grumello, Italy.

• A. Mielke, Modeling and analysis of multiscale problems in geodynamics, 25th GAMM Seminar on Microstructures, November 27 - 28, 2025, Technische Universität Dortmund, November 27, 2025.

• A. Mielke, Thermodynamical and mathematical principles for energy-electro-reaction diffusion systems, Current Research at the Interface of Continuum Physics and Applied Mathematics, October 8 - December 10, 2025, WIAS Berlin, October 9, 2025.

• J. Sprekels, Optimal control of the viscous Cahn--Hilliard system with hyperbolic relaxation of the chemical potential, Seminari di Matematica Applicata, Università degli Studi di Pavia, Dipartimento di Matematica, Italy, May 6, 2025.

• A. Glitzky, M. Liero, Strain engineering for functional heterostructures: Aspects of elasticity, MATH+ Day 2025, Berlin, November 17, 2025.

• A. Glitzky, A uniqueness result for a drift-diffusion model for perovskite solar cells, Analysis of Robust Numerical Solvers for Innovative Semiconductors in View of Energy Transition (ARISE 2025), November 4 - 5, 2025, WIAS Berlin, November 4, 2025.

• A. Maltsi, Modeling thermoporoelasticity in photoacoustics, 19th Panhellenic Conference in Mathematical Analysis, December 18 - 20, 2025, National Technical University of Athens, Greece, December 19, 2025.

• A. Pešić, From scaling laws to gradient flows: Analysis of pattern formation in biomembranes, ÖMG-DMV Annual Meeting 2025, Minisymposium 19 ``Variational Methods for PDEs in Materials Science and Biology'', September 1 - 5, 2025, Johannes Kepler Universität Linz, Austria, September 3, 2025.

• A. Pešić, Nonlinear interpolation inequalities with fractional Sobolev norms and pattern formation in biomembranes, 95th Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM 2025), Poland, April 7 - 11, 2025.

• A. Pešić, Pattern formation in biomembranes: From interpolation inequalities to a scaling law result, 95th Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM 2025), Young Researchers' Minisymposium 4 ``Mulit-scale Phenomena in Magnetic and Elastic Materials'', April 7 - 11, 2025, Poznan University of Technology, Poland, April 7, 2025.

• A. Pešić, Variational approach to pattern formation in biomembranes, Calculus of Variations at the Orangery, October 29 - 31, 2025, Friedrich-Alexander-Universität Erlangen-Nürnberg, October 29, 2025.

• S. Schindler, On asymptotically self-similar patterns in coupled systems, Mathematics of Wave Phenomena, Minisymposium 01 ``Dissipative Patterns and Waves'', February 24 - 28, 2025, Karlsruhe Institute of Technology (KIT), February 26, 2025.

• M. Thomas, Analysis of a dynamic phase-field fracture model and how spaghettis break, Colloquium in Memory of Prof. Anna-Margarete Sändig, March 27, 2025, Universität Stuttgart.

• M. Thomas, Analysis of a viscoplastic Burgers equation, 95th Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM 2025), Section 14.04 ``Applied Analysis'', April 7 - 11, 2025, Poznan University of Technology, Poland, April 8, 2025.

• M. Thomas, Analysis of a viscoplastic Burgers equation, Mathematical Advances in Geophysical Fluid Dynamics, May 11 - 16, 2025, Mathematisches Forschungsinstitut Oberwolfach, May 13, 2025.

• M. Thomas, Analysis of non-smooth PDEs in materials modeling - fractures, faults and sea ice, BMS Student Conference 2025, February 19 - 21, 2025, Berlin Mathematical School, February 20, 2025.

• M. Thomas, First-order formulation for dynamic phase-field fracture in viscoelastic materials, Seminar on Nonlinear Partial Differential Equations, Texas A&M University, Department of Mathematics, College Station, USA, March 25, 2025.

• TH. Eiter, Energy-variational solutions in the context of hyperbolic conservation laws, Oberseminar der AG ``Mathematische Modellierung", Technische Universität Clausthal, Institut für Mathematik, May 26, 2025.

• TH. Eiter, Existence results for fluid flow around a periodically deforming body, Frankenstein 25 - Maximal Regularity Methods in Mathematical Fluid Mechanics, March 31 - April 4, 2025, Rheinland-Pfälzische Technische Universität Kaiserslautern-Landau, Frankenstein, April 1, 2025.

• TH. Eiter, Long-time asymptotics of the damped Euler equations by parabolic scaling, 95th Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM 2025), Section 14.01 ``Applied Analysis'', April 7 - 11, 2025, Poznan University of Technology, Poland, April 8, 2025.

• TH. Eiter, Long-time behavior of the damped Euler equations with direction dependent spatial limits, Hydrodynamic Models and Multi-scale Analysis in PDEs, September 14 - 17, 2025, Polish Academy of Sciences, Warsaw, Poland, September 17, 2025.

• TH. Eiter, MathGarage: Variations, On the concept of energy-variational solutions, June 23 - 24, 2025, University of Warsaw, Poland, June 24, 2025.

• TH. Eiter, On a compatibility condition for oscillating flow past a rotating body, Summer School on Rotation and Fluids, August 25 - 29, 2025, Czech Academy of Sciences, Prague, Czech Republic, August 27, 2025.

• TH. Eiter, Regularizations and energy-variational solutions for a visco-elasto-plastic semicompressible fluid model, SCCS Days 2025 of the Collaborative Research Center -- CRC 1114 ``Scaling Cascades in Complex Systems'', November 5 - 6, 2025, Zuse-Institut Berlin, November 5, 2025.

• TH. Eiter, The asymptotic far field of time-periodic flow past an obstacle, Seminar Series on PDEs and Applications, Uppsala University, Department of Mathematics, Sweden, May 13, 2025.

• TH. Eiter, Viscous flow around an obstacle with oscillating boundary, Mathematics with Applications, June 2 - 6, 2025, University of Madeira, Funchal, Portugal, June 2, 2025.

• J. Ginster, A scaling law for a model of epitaxially strained elastic films with dislocations, 24th GAMM Seminar on Microstructures, January 30 - 31, 2025, Humboldt-Universität zu Berlin, January 31, 2025.

• J. Ginster, Formation of microstructure and occurrence of vertices in a frustrated spin system, Singularities in Discrete Systems, May 5 - 8, 2025, Mathematisches Forschungsinstitut Oberwolfach, May 6, 2025.

• J. Ginster, Variational models for pattern formation in biomembranes, Vito Volterra Meeting in Calculus of Variations 2025, June 16 - 20, 2025, (Università degli Studi di Roma``La Sapienza'', Italy, June 18, 2025.

• J. Ginster, Variational models for pattern formation in biomembranes, Analysis-Seminar Augsburg-München, Universität Augsburg, Institut für Mathematik, June 26, 2025.

• M. Heida, Modeling intercalation processes in batteries, Mixtures: Modeling, Analysis and Computing, February 5 - 7, 2025, Charles University, Prague, Czech Republic, February 6, 2025.

• G. Heinze, Discrete-to-continuum limit for reaction-diffusion systems via variational convergence of gradient systems, 95th Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM 2025), Section 14.04 ``Applied Analysis'', April 7 - 11, 2025, Poznan University of Technology, Poland, April 10, 2025.

• G. Heinze, Gradient flow methods for reaction-diffusion systems, 95th Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM 2025), Poland, April 7 - 11, 2025.

• G. Heinze, Gradient flows on metric graphs with reservoirs, Networked MathFlows 2025, September 7 - 13, 2025, Institute of Mathematics at the Polish Academy of Sciences, Będlewo, Poland, September 9, 2025.

• G. Heinze, Gradient flows on metric graphs with reservoirs, Analysis of Robust Numerical Solvers for Innovative Semiconductors in View of Energy Transition (ARISE 2025), November 4 - 5, 2025, WIAS Berlin, November 5, 2025.

• G. Heinze, Gradient flows on metric graphs with reservoirs: Microscopic derivation and multiscale limits, ÖMG-DMV Annual Meeting 2025, Minisymposium S09 ``Partial Differential Equations", September 1 - 5, 2025, Johannes Kepler Universität Linz, Austria, September 5, 2025.

• G. Heinze, Gradient flows on metric graphs with reservoirs: Microscopic derivation and multiscale limits, Research Seminar ``Numerical Analysis of Stochastic and Deterministic Partial Differential Equations'', Freie Universität Berlin, January 16, 2025.

• G. Heinze, Two examples of gradient flows in continuity equation format, Gradient Flows Face-to-Face 5, September 16 - 19, 2025, Universidad de Granada, Spain, September 18, 2025.

• TH. Koprucki, FAIR representation of mathematical research data: MathModDB and MathAlgoDB as knowledge graphs for mathematical models and numerical algorithms, DiHMa.Lab Workshop, October 14 - 15, 2025, Freie Universität Berlin, October 15, 2025.

• TH. Koprucki, Making tabular data FAIR: Applying CSV on the web (CSVW) for semantic interoperability in computational science and engineering, Kickoff Meeting of the GAMM Activity Group on Research Software Engineering and Research Data Management in Mathematics & Mechanics, December 4 - 5, 2025, Technische Universität Braunschweig, December 5, 2025.

• TH. Koprucki, Semiconductor modeling and simulation: Bridging mathematics, physics, and engineering, Award Ceremony for IHP's Junior Research Group, Leibniz-Institut für innovative Mikroelektronik, Frankfurt (Oder), June 3, 2025.

• M. Landstorfer, M. Heida, Ch. Pohl, Modeling lithium-ion batteries with phase separation using non-equilibrium thermodynamics and homogenization theory, Oxford Battery Modelling Symposium (OBMS), Oxford, UK, July 24 - 25, 2025.

• M. Liero, EDP convergence for evolutionary systems with gradient flow structure, Calculus of Variations & Applications, May 16, 2025, Università degli Studi di Firenze, Italy.

• M. Liero, Generalized gradient systems for thermodynamically consistent modeling including temperature coupling, 11th International Conference on Engineering of Chemical Complexity (ECC11), July 29 - 1, 2025, University of Tokyo, Japan, July 30, 2025.

• M. Liero, Optimal transport meets rough analysis, Retreat of the Collaborative Research Center TRR 388 ``Rough Analysis, Stochastic Dynamics & Related Fields", September 11 - 13, 2025, Technische Universität Berlin, Templin, September 12, 2025.

• M. Liero, The Hellinger--Kantorovich distance: Properties and applications in machine learning, Research Seminar of the Institute of Industrial Science, University of Tokyo, Japan, August 6, 2025.

• M. Liero, Transportation cost inequalities on Heisenberg path space, Internal Workshop of the CRC/TRR 388 ``Rough Analysis, Stochastic Dynamics and Related Fields", July 7, 2025, Max-Planck-Institut für Mathematik in den Naturwissenschaften, Leipzig.

• J. Rehberg, A marriage between geometric measure theory and advanced parabolic theory, Forschungsseminar Angewandte Mathematik, Technische Universität Darmstadt, May 6, 2025.

• J. Rehberg, Maximal parabolic regularity for the treatment of real world problems, Mathematisches Kolloquium, Technische Universität Darmstadt, May 7, 2025.

Preprints im Fremdverlag

• R. Finn, M. O'Donovan, Th. Koprucki, S. Schulz, Theoretical study of the impact of carrier density screening on Urbach tail energies and optical polarization in (Al,Ga)N quantum well systems, Preprint no. arXiv:2501.16808, Cornell University, 2025, DOI 10.48550/arXiv.2501.16808 .
  Abstract
  Aluminium Gallium Nitride ((Al,Ga)N) presents an ideal platform for designing ultra-violet (UV) light emitters across the entire UV spectral range. However, in the deep-UV spectral range (<280 nm) these emitters exhibit very low quantum efficiencies, which in part is linked to the light polarization characteristics of (Al,Ga)N quantum wells (QWs). In this study we provide insight into the degree of optical polarization of (Al,Ga)N QW systems operating across the UV-C spectral range by means of an atomistic, multi-band electronic structure model. Our model not only captures the difference in valence band ordering in AlN and GaN, it accounts also for alloy disorder induced band mixing effects originating from random alloy fluctuations in (Al,Ga)N QWs. The latter aspect is not captured in widely employed continuum based models. The impact of alloy disorder on the electronic structure is studied in terms of Urbach tail energies, which reflect the broadening of the valence band density of states due to carrier localization effects. We find that especially in wider wells, Urbach tail energies are reduced with increasing carrier densities in the well, highlighting that alloy disorder induced carrier localization effects in (Al,Ga)N QWs are also tightly linked to electrostatic built-in fields. Our calculations show that for QWs designed to emit at the longer wavelength end of the UV-C spectrum, carrier density and well width are of secondary importance for their light emission properties, meaning that one observes mainly transverse electrical polarization. However, for (Al,Ga)N QWs with high Al contents, we find that both well width and carrier density will impact the degree of optical polarization. Our calculations suggest that wider wells will increase the degree of optical polarization and may therefore be a viable option to improve the light extraction efficiency in deep UV light emitters.