Publications
Monographs

A.H. Erhardt, K. TsanevaAtanasova, G.T. Lines, E.A. Martens, eds., Dynamical Systems, PDEs and Networks for Biomedical Applications: Mathematical Modeling, Analysis and Simulations, Special Edition, articles published in Frontiers of Physics, Frontiers in Applied Mathematics and Statistics, and Frontiers in Physiology, Frontiers Media SA, Lausanne, Switzerland, 2023, 207 pages, (Collection Published), DOI 10.3389/9782832514580 .

B. Wagner, M. Timme, eds., Special Issue ``The Mathematics in Renewable Energy'', 34 of European Journal of Applied Mathematics, Springer Nature, Heidelberg et al., 2023, 190 pages, (Collection Published), DOI 10.1017/S0956792523000013 .
Articles in Refereed Journals

L. Schmeller, D. Peschka, Sharpinterface limits of CahnHilliard models and mechanics with moving contact lines, , 22 (2024), pp. 869890, DOI 10.1137/23M1546592 .
Abstract
We construct gradient structures for free boundary problems with moving capillary interfaces with nonlinear (hyper)elasticity and study the impact of moving contact lines. In this context, we numerically analyze how phasefield models converge to certain sharpinterface models when the interface thickness tends to zero. In particular, we study the scaling of the CahnHilliard mobility with certain powers of the interfacial thickness. In the presence of interfaces, it is known that the intended sharpinterface limit holds only for a particular range of powers However, in the presence of moving contact lines we show that some scalings that are valid for interfaces produce significant errors and the effective range of valid powers of the interfacial thickness in the mobility reduces. 
A. Erhardt, D. Peschka, Ch. Dazzi, L. Schmeller, A. Petersen, S. Checa, A. Münch, B. Wagner, Modeling cellular selforganization in strainstiffening hydrogels, Computational Mechanics, published online on 31.08.2024, DOI 10.1007/s00466024025367 .
Abstract
We develop a threedimensional mathematical model framework for the collective evolution of cell populations by an agentbased model (ABM) that mechanically interacts with the surrounding extracellular matrix (ECM) modeled as a hydrogel. We derive effective twodimensional models for the geometrical setup of a thin hydrogel sheet to study cellcell and cellhydrogel mechanical interactions for a range of external conditions and intrinsic material properties. We show that without any stretching of the hydrogel sheets, cells show the wellknown tendency to form long chains with varying orientations. Our results further show that external stretching of the sheet produces the expected nonlinear strainsoftening or stiffening response, with, however, little qualitative variation of the overall cell dynamics for all the materials considered. The behavior is remarkably different when solvent is entering or leaving from strain softening or stiffening hydrogels, respectively. 
M. Heida, M. Landstorfer, M. Liero, Homogenization of a porous intercalation electrode with phase separation, Multiscale Modeling & Simulation. A SIAM Interdisciplinary Journal, 22 (2024), pp. 10681096, DOI 10.1137/21M1466189 .
Abstract
In this work, we derive a new model framework for a porous intercalation electrode with a phase separating active material upon lithium intercalation. We start from a microscopic model consisting of transport equations for lithium ions in an electrolyte phase and intercalated lithium in a solid active phase. Both are coupled through a Neumannboundary condition modeling the lithium intercalation reaction. The active material phase is considered to be phase separating upon lithium intercalation. We assume that the porous material is a given periodic microstructure and perform analytical homogenization. Effectively, the microscopic model consists of a diffusion and a CahnHilliard equation, whereas the limit model consists of a diffusion and an AllenCahn equation. Thus we observe a CahnHilliard to AllenCahn transition during the upscaling process. In the sense of gradient flows, the transition goes in hand with a change in the underlying metric structure of the PDE system. 
L. Schmeller, D. Peschka, Gradient flows for coupling order parameters and mechanics, SIAM Journal on Applied Mathematics, 83 (2023), pp. 225253, DOI 10.1137/22M148478X .
Abstract
We construct a formal gradient flow structure for phasefield evolution coupled to mechanics in Lagrangian coordinates, present common ways to couple the evolution and provide an incremental minimization strategy. While the usual presentation of continuum mechanics is intentionally very brief, the focus of this paper is on an extensible functional analytical framework and a discretization approach that preserves an appropriate variational structure as much as possible. As examples, we first present phase separation and swelling of gels and then the approach of stationary states of multiphase systems with surface tension and show the robustness of the general approach. 
R. Müller, M. Landstorfer, Galilean bulksurface electrothermodynamics and applications to electrochemistry, Entropy. An International and Interdisciplinary Journal of Entropy and Information Studies, 25 (2023), pp. 416/1416/27, DOI 10.3390/e25030416 .
Abstract
In this work, the balance equations of nonequilibrium thermodynamics are coupled to Galilean limit systems of the Maxwell equations, i.e. either to (i) the quasielectrostatic limit or (ii) the quasimagnetostatic limit. We explicitly consider a volume $Omega$ which is divided into $Omega^+$ and $Omega^$ by a possibly moving singular surface S, where a charged reacting mixture of a viscous medium can be present on each geometrical entity ($Omega$^+, S, $Omega^$). By the restriction to Galilean limits of the Maxwell equations, we achieve that only subsystems of equations for matter and electric field are coupled that share identical transformation properties with respect to observer transformations. Moreover, the application of an entropy principle becomes more straightforward and finally it helps to estimate the limitations of the more general approach based the full set of Maxwell equations. Constitutive relations are provided based on an entropy principle and particular care is taken for the analysis of the stress tensor and the momentum balance in the general case of nonconstant scalar susceptibility. Finally, we summarize the application of the derived model framework to an electrochemical system with surface reactions 
A.K. Barua, R. Chew, L. Shuwang, J. Lowengrub, A. Münch, B. Wagner, Sharpinterface problem of the OhtaKawasaki model for symmetric diblock copolymers, Journal of Computational Physics, 481 (2023), pp. 112032/1112032/23, DOI 10.1016/j.jcp.2023.112032 .
Abstract
The OhtaKawasaki model for diblockcopolymers is well known to the scientific community of diffuseinterface methods. To accurately capture the longtime evolution of the moving interfaces, we present a derivation of the corresponding sharpinterface limit using matched asymptotic expansions, and show that the limiting process leads to a HeleShaw type moving interface problem. The numerical treatment of the sharpinterface limit is more complicated due to the stiffness of the equations. To address this problem, we present a boundary integral formulation corresponding to a sharp interface limit of the OhtaKawasaki model. Starting with the governing equations defined on separate phase domains, we develop boundary integral equations valid for multiconnected domains in a 2D plane. For numerical simplicity we assume our problem is driven by a uniform Dirichlet condition on a circular farfield boundary. The integral formulation of the problem involves both double and singlelayer potentials due to the modified boundary condition. In particular, our formulation allows one to compute the nonlinear dynamics of a nonequilibrium system and pattern formation of an equilibrating system. Numerical tests on an evolving slightly perturbed circular interface (separating the two phases) are in excellent agreement with the linear analysis, demonstrating that the method is stable, efficient and spectrally accurate in space. 
A.C. Moore, M.G. Hennessy, L.P. Nogueira, S.J. Franks, M. Taffetani, H. Seong , Y.K. Kang, W.S. Tan, G. Miklosic, R. El Laham, K. Zhou, L. Zharova, J.R. King , B. Wagner, H.J. Haugen, A. Münch, M.M. Stevens, Fiber reinforced hydrated networks recapitulate the poroelastic mechanics of articular cartilage, Acta Biomaterialia, 167 (2023), pp. 6982, DOI 10.1016/j.actbio.2023.06.015 .

R. Shiri, L. Schmeller, R. Seemann, D. Peschka, B. Wagner, Impact of noise on spinodal dewetting of liquidliquid films, communications physics, 6 (2023), pp. 109/1109/11, DOI 10.1038/s4200502301208x .
Abstract
We investigate the spinodal dewetting of a thin liquid polystyrene (PS) film on a liquid polymethylmethacrylate (PMMA) subtrate. Following the evolution of the corrugations of the PS film via in situ measurements by atomic force microscopy (AFM) and those of the PSPMMA interface via ex situ imaging, we provide a direct and detailed comparison of the experimentally determined spinodal wavelengths with the predictions from linear stability analysis of a thinfilm continuum model for the bilayer system. The impact of rough interfaces and fluctuations is studied theoretically by investigating the impact of different choices of initial data on the unstable wavelength and on the rupture time. The key factor is the mode selection by initial data perturbed with correlated colored noise in the linearly unstable regime, which becomes relevant only for liquid bilayers to such an extent. By numerically solving the mathematical model, we further address the impact of nonlinear effects on rupture times and on the morphological evolution of the interfaces in comparison with experimental results. 
G.L. Celora, R. Blossey, A. Münch, B. Wagner, Counterioncontrolled phase equilibria in a chargeregulated polymer solution, Journal of Chemical Physics, 159 (2023), pp. 184902/1184902/17, DOI 10.1063/5.0169610 .
Abstract
We study phase equilibria in a minimal model of chargeregulated polymer solutions. Our model consists of a single polymer species whose charge state arises from protonationdeproto nation processes in the presence of a dissolved acid, whose anions serve as screening counteri ons. We explicitly account for variability in the polymers' charge states. Homogeneous equilibria in this model system are characterised by the total concentration of polymers, the concentration of counterions and the charge distributions of polymers which can be computed with the help of analytical approximations. We use these analytical results to characterise how parameter values and solution acidity influence equilibrium charge distributions and identify for which regimes uni modal and multimodal charge distributions arise. We then study the interplay between charge regulation, solution acidity and phase separation. We find that charge regulation has a significant impact on polymer solubility and allows for nonlinear responses to the solution acidity: reentrant phase behaviour is possible in response to increasing solution acidity. Moreover, we show that phase separation can yield to the coexistence of local environments characterised by different charge distributions and mixture com 
G.L. Celora, M.G. Hennessy, A. Münch, B. Wagner, S.L. Waters, The dynamics of a collapsing polyelectrolyte gel, SIAM Journal on Applied Mathematics, 83 (2023), pp. 11461171, DOI 10.1137/21M1419726 .

M.G. Hennessy, G.L. Celora, S.L. Waters, A. Münch, B. Wagner, Breakdown of electroneutrality in polyelectrolyte gels, European Journal of Applied Mathematics, published online on 06.09.2023, DOI 10.1017/S0956792523000244 .

E. Meca, A.W. Fritsch, J. IglesiasArtola, S. Reber, B. Wagner, Predicting disordered regions driving phase separation of proteins under variable salt concentration, Frontiers in Physics, section Biophysics, 11 (2023), pp. 1213304/11213304/13, DOI 10.3389/fphy.2023.1213304 .
Abstract
We determine the intrinsically disordered regions (IDRs) of phase separating proteins and investigate their impact on liquidliquid phase separation (LLPS) with a randomphase approx imation (RPA) that accounts for variable salt concentration. We focus on two proteins, PGL3 and FUS, known to undergo LLPS. For PGL3 we predict that an IDR near the Cterminus pro motes LLPS, which we validate through direct comparison with in vitro experimental results. For the structurally more complex protein FUS the role of the low complexity (LC) domain in LLPS is not as well understood. Apart from the LC domain we here identify two IDRs, one near the Nterminus and another near the Cterminus. Our RPA analysis of these domains predict that, surprisingly, the IDR at the Nterminus (aa 1285) and not the LC domain promotes LLPS of FUS by comparison to in vitro experiments under physiological temperature and salt conditions. 
O. Klein, On forward and inverse uncertainty quantification for a model for a magneto mechanical device involving a hysteresis operator, Applications of Mathematics, 68 (2023), pp. 795828, DOI 10.21136/AM.2023.008023 .
Abstract
Modeling real world objects and processes one may has to deal with hysteresis effects but also with uncertainties. Following D. Davino, P. Krejčí, and C. Visone: Fully coupled modeling of magnetomechanical hysteresis through `thermodynamic' compatibility. Smart Mater. Struct., 22(9), (2013) 0950099, a model for a magnetostrictive material involving a generalized Prandtl Ishlinskiĭoperator is considered here. Using results of measurements, some parameters in the model are determined and inverse Uncertainty Quantification (UQ) is used to determine random densities to describe the remaining parameters and their uncertainties. Afterwards, the results are used do perform forward UQ and to compare the results with measured data. This extends some of the results from O. Klein, D. Davino, and C. Visone. On forward and inverse uncertainty quantification for models involving hysteresis operators. Math. Model. Nat. Phenom. 15 (2020) 53.
Contributions to Collected Editions

A.H. Erhardt, K. TsanevaAtanasova, G.T. Lines, E.A. Martens, Editorial: Dynamical systems, PDEs and networks for biomedical applications: Mathematical modeling, analysis and simulations, 10 of Front. Phys., Sec. Statistical and Computational Physics, Frontiers, Lausanne, Switzerland, 2023, pp. 0103, DOI 10.3389/fphy.2022.1101756 .

B. Wagner, M. Timme, Editorial Announcement, in: Special Issue of EJAM: The Mathematics in Renewable Energies, B. Wagner, M. Timme, eds., 34 of European Journal of Applied Mathematics, Cambridge University Press, 2023, pp. 425428, DOI 10.1017/S0956792523000013 .

J. Fuhrmann, B. Gaudeul, Ch. Keller, Two entropic finite volume schemes for a NernstPlanckPoisson system with ion volume constraints, in: Finite Volumes for Complex Applications X  Volume 1, Elliptic and Parabolic Problems: FVCA10, Strasbourg, France, October 30, 2023  November 03, 2023, Invited Contributions, E. Franck , J. Fuhrmann, V. MichelDansac, L. Navoret, eds., Springer Proceedings in Mathematics & Statistics, Springer International Publishing, Cham, 2023, pp. 285294, DOI 10.1007/9783031408649_23 .

O. Klein, On forward and inverse uncertainty quantification for a model for a magneto mechanical device involving a hysteresis operator, in: Proceedings of the Murphys 2022 Conference, V. Dolejší, ed., 6 of Applications of Mathematics (Special Issue), Czech Academy of Sciences, Prague, 2023, pp. 795828, DOI 10.21136/AM.2023.008023 .
Abstract
Modeling real world objects and processes one may has to deal with hysteresis effects but also with uncertainties. Following D. Davino, P. Krejčí, and C. Visone: Fully coupled modeling of magnetomechanical hysteresis through `thermodynamic' compatibility. Smart Mater. Struct., 22(9), (2013) 0950099, a model for a magnetostrictive material involving a generalized Prandtl Ishlinskiĭoperator is considered here. Using results of measurements, some parameters in the model are determined and inverse Uncertainty Quantification (UQ) is used to determine random densities to describe the remaining parameters and their uncertainties. Afterwards, the results are used do perform forward UQ and to compare the results with measured data. This extends some of the results from O. Klein, D. Davino, and C. Visone. On forward and inverse uncertainty quantification for models involving hysteresis operators. Math. Model. Nat. Phenom. 15 (2020) 53. 
M. Landstorfer, M. Heida, Energie effizienter speichern, Spektrum der Wissenschaft, Spektrum der Wissenschaft Verlagsgesellschaft mbH, Heidelberg, 2023, pp. 7279.
Preprints, Reports, Technical Reports

CH. Keller, J. Fuhrmann, M. Landstorfer, B. Wagner, A model framework for ion channels with selectivity filters based on continuum nonequilibrium thermodynamics, Preprint no. 3072, WIAS, Berlin, 2023, DOI 10.20347/WIAS.PREPRINT.3072 .
Abstract, PDF (7287 kByte)
A mathematical model framework to describe ion transport in nanopores is presented. The model is based on nonequilibrium thermodynamics and considers finite size effects, solvation phenomena as well as the electrical charges of membrane surfaces and channel proteins. Par ticular emphasis is placed on the consistent modelling of the selectivity filter in the pore. It is treated as an embedded domain in which the constituents can change their chemical properties. The diffusion process through the filter is governed by an independent diffusion coefficient and at the interfaces, de and resolvation reactions are introduced as Neumann interface conditions. The evolution of the molar densities is described by driftdiffusion equations, where the fluxes depend on the gradient of the chemical potentials and the electric force. The chemical potentials depend on the molar fractions and on the pressure in the electrolyte and accounts for solvation effects. The framework allows the calculation of currentvoltage relations for a variety of chan nel properties and ion concentrations. We compare our model framework to experimental results for calciumselective ion channels and show the general validity of our approach. Our parameter studies show that calcium and sodium currents are proportional to the surface charge in the se lectivity filter and to the diffusion coefficients of the ions. Moreover, they show that the negative charges inside the pore have a decisive influence on the selectivity of divalent over monovalent ions.
Talks, Poster

CH. Keller, A driftdiffusion model to describe ion channel dynamics, Applied Mathematics and Simulation for Semiconductor Devices (AMaSiS 2024), Berlin, September 10  13, 2024.

CH. Keller, A model framework for calcium ion channels: Consistent modeling of selectivity filters, The European Conference on Mathematical and Theoretical Biology (ECMTB 2024), July 22  26, 2024, University of Castilla La Mancha, Toledo, Spain, July 25, 2024.

T. Dörffel, Modeling a hurricane boundary layer through matched asymptotics, 36th Conference on Hurricanes and Tropical Meteorology, Session 16C Tropical Cyclones  Observing and Simulating the Boundary Layer, May 6  10, 2024, Long Beach, USA, May 9, 2024.

T. Dörffel, Modeling a hurricane boundary layer through matched asymptotics, Workshop ``Model Hierarchies in Atmosphere, Ocean, and Climate Sciences'', June 30  July 5, 2024, Mathematisches Forschungsinstitut Oberwolfach, July 2, 2024.

A. Erhardt, Mathematical modeling of cellhydrogel interactions, The XXIII Symposium on Trends in Applications of Mathematics to Mechanics (STAMM), April 3  5, 2024, Universität Würzburg, April 3, 2024.

O. Klein, A model for a magneto mechanical device: Forward and inverse uncertainty quantization, Leibniz MMS Days 2024, Kaiserslautern, April 10  12, 2024.

O. Klein, On a model for a magneto mechanical device: forward and inverse uncertainty quantification, 2nd Workshop des MATH+Thematic Einstein Semester ``Mathematics of Small Data Analysis'', Berlin, January 17  19, 2024.

M. Landstorfer, T. Dörffel, Mathematical modeling of intercalation batteries with nonequilibrium thermodynamics and homogenization theory, Oxford Battery Modelling Symposium 2024, UK, April 15  17, 2024.

M. Landstorfer, Thermodynamic modeling of aqueous and aprotic electrodeelectrolyte interfaces and their and double layer capacitance, 75th Annual Meeting of the International Society of Electrochemistry, Symposium S13  Double layer reloaded: Theory meets experiments, August 18  23, 2024, Montréal, Canada, August 23, 2024.

CH. Keller, Continuumbased modeling of biological ion channels, Energetic Methods for MultiComponent Reactive Mixtures Modelling, Stability, and Asymptotic Analysis (EMRM 2023), Berlin, September 13  15, 2023.

CH. Keller, Continuumbased modeling of calciumselective ion channels, Conference on Mathematical Life Sciences, April 17  20, 2023, Universität Bonn, April 20, 2023.

CH. Keller, Development of an ion channel modelframework, 10th International Congress on Industrial and Applied Mathematics (ICIAM 2023), August 20  25, 2023, Waseda University, Tokyo, Japan, August 23, 2023.

CH. Keller, Mathematical modeling of biological ion channels, 93rd Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM), May 29  June 2, 2023, Technische Universität Dresden, May 31, 2023.

CH. Keller, Numerical simulation of biological ion channels, Third Conference of Young Applied Mathematicians (YAMC23), September 18  22, 2023, Siena, Italy, September 21, 2023.

L. Schmeller, Dynamic wetting and dewetting of viscous liquid droplets/films on viscoelastic substrates, SPP 2171 Workshop ''Wetting of Flexible, Adaptive, and Switchable Substrates" 2023, December 4  7, 2023, Technische Universität Berlin.

L. Schmeller, Gel models for phase separation at finite strains, 93rd Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM), May 29  June 2, 2023, Technische Universität Dresden, June 2, 2023.

L. Schmeller, Gel models for phase separation at finite strains, Conference ``Calculus of Variations and Applications'', June 19  21, 2023, Université ParisCité (Campus des Grands Moulins), France, June 19, 2023.

L. Schmeller, Gradient flows and moving contact lines, Seminar Prof. Sebastian Aland, Technische Universität Bergakademie Freiberg, Institut für Numerische Mathematik und Optimierung, February 8, 2023.

L. Schmeller, Phasefield systems coupled with large deformations, 10th International Congress on Industrial and Applied Mathematics (ICIAM 2023), August 20  25, 2023, Waseda University, Tokyo, Japan, August 25, 2023.

A.H. Erhardt, Bifurcation analysis for axisymmetric capillary water waves, 29th Nordic Congress of Mathematicians with EMS, July 3  7, 2023, Aalborg University, Department of Mathematical Sciences, Denmark, July 4, 2023.

A.H. Erhardt, Mathematical modelling and simulation of cellhydrogel interactions, Leibniz MMS Days 2023, April 17  19, 2023, LeibnizInstitut für Agrartechnik und Bioökonomie (ATB), Potsdam, April 19, 2023.

A. Selahi, A finiteelementsolver for coupled domains in rust, SIAM Conference on Computational Science and Engineering (CSE23), Amsterdam, Netherlands, February 26  March 3, 2023.

A. Selahi, Recovering battery ageing dynamics with invertible neuronal networks, 10th International Congress on Industrial and Applied Mathematics (ICIAM 2023), August 20  25, 2023, Waseda University, Tokyo, Japan, August 23, 2023.

A. Selahi, Recovery of battery ageing dynamics using Bayesian inference, 93rd Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM), May 29  June 2, 2023, Technische Universität Dresden, June 1, 2023.

B. Wagner, On disordered regions driving phase separation of proteins under variable salt concentration, Cellular Matters Conference 2023, Ascona, Switzerland, June 4  7, 2023.

B. Wagner, On disordered regions driving phase separation of proteins under variable salt concentration, Cellular Matters Conference 2023, June 4  7, 2023, Ascona, Switzerland.

CH. Bayer, D. Kreher, M. Landstorfer, W. Kenmoe Nzali, Volatile electricity markets and battery storage: A modelbased approach for optimal control, MATH+ Day, HumboldtUniversität zu Berlin, October 20, 2023.

M. Eigel, M. Heida, M. Landstorfer, A. Selahi, Recovery of battery ageing dynamics with multiple timescales, MATH+ Day, HumboldtUniversität zu Berlin, October 20, 2023.

J. Fuhrmann, Ch. Keller, M. Landstorfer, B. Wagner, Development of an ionchannel modelframework for invitro assisted interpretation of current voltage relations, MATH+ Day, HumboldtUniversität zu Berlin, October 20, 2023.

O. Klein, On a model for a magneto mechanical device: Forward and inverse uncertainty quantification, 13th International Symposium on Hysteresis Modeling and Micromagnetics (HMM 2023), June 5  7, 2023, Technische Universität Wien, Austria, June 6, 2023.

M. Landstorfer, A model framework for Lithiumion intercalation cells, 10th International Congress on Industrial and Applied Mathematics (ICIAM 2023), Minisymposium 01140 ``Modelling and simulation of electrochemomechanical processes in batteries and fuel cells'', August 20  25, 2023, Waseda University, Tokyo, Japan, August 25, 2023.

M. Landstorfer, Modeling and validation of material and transport models for electrolytes, Energetic Methods for MultiComponent Reactive Mixtures Modelling, Stability, and Asymptotic Analysis (EMRM 2023), September 13  15, 2023, WIAS, Berlin, September 15, 2023.

M. Landstorfer, Thermodynamic modeling of the electrodeelectrolyte interface  Doublelayer capacitance, solvation number, validation, Van Marum Colloquia, Leiden University, Institute of Chemistry, Netherlands, November 14, 2023.

M. Landstorfer, Thermodynamic modelling of aqueous and aprotic electrodeelectrolyte interfaces and their and double layer capacitance, BunsenTagung 2023  Physical Chemistry of the Energy Transition, 122nd Annual Conference of the German Bunsen Society for Physical Chemistry, June 5  7, 2023, Berlin, June 7, 2023.
Research Groups
 Partial Differential Equations
 Laser Dynamics
 Numerical Mathematics and Scientific Computing
 Nonlinear Optimization and Inverse Problems
 Interacting Random Systems
 Stochastic Algorithms and Nonparametric Statistics
 Thermodynamic Modeling and Analysis of Phase Transitions
 Nonsmooth Variational Problems and Operator Equations