Some of the current members of the research group "Thermodynamic Modeling and Analysis of Phase Transitions" were members of a former group or of RG 1 respectively. Therefore, the corresponding publications can found on the web pages of these groups:

  • former Young Scientists' Group "Modeling of Damage Processes"
  • former Leibniz Group "Mathematical Models for Lithium-Ion Batteries"
  • Research group 1 "Partial Differential Equations"
    • Articles in Refereed Journals

      • A.H. Erhardt, S. Solem, Bifurcation analysis of a modified cardiac cell model., SIAM Journal on Applied Dynamical Systems, 21 (2022), pp. 231--247, DOI 10.1137/21M1425359 .

      • G.L. Celora, M.G. Hennessy, A. Münch, B. Wagner, S.L. Waters, A kinetic model of a polyelectrolyte gel undergoing phase separation, Journal of the Mechanics and Physics of Solids, 160 (2022), 104771, DOI 10.1016/j.jmps.2021.104771 .
        In this study we use non-equilibrium thermodynamics to systematically derive a phase-field model of a polyelectrolyte gel coupled to a thermodynamically consistent model for the salt solution surrounding the gel. The governing equations for the gel account for the free energy of the internal interfaces which form upon phase separation, as well as finite elasticity and multi-component transport. The fully time-dependent model describes the evolution of small changes in the mobile ion concentrations and follows their impact on the large-scale solvent flux and the emergence of long-time pattern formation in the gel. We observe a strong acceleration of the evolution of the free surface when the volume phase transition sets in, as well as the triggering of spinodal decomposition that leads to strong inhomogeneities in the lateral stresses, potentially leading to experimentally visible patterns.

      • G. Shanmugasundaram, G. Arumugam, A.H. Erhardt, N. Nagarajan, Global existence of solutions to a two-species predator-prey parabolic chemotaxis system, International Journal of Biomathematics, published online on 21.05.2022, DOI 10.1142/S1793524522500541 .

      • A.H. Erhardt, S. Solem, On complex dynamics in a Purkinje and a ventricular cardiac cell model, Communications in Nonlinear Science and Numerical Simulation, 93 (2021), pp. 105511/1--105511/21, DOI 10.1016/j.cnsns.2020.105511 .

      • A.H. Erhardt, Stability of weak solutions to parabolic problems with nonstandard growth and cross-diffusion, Axioms, 10 (2021), pp. 14/1--14/7, DOI 10.3390/axioms10010014 .

      • A.S. Shatla, M. Landstorfer, H. Baltruschat, On the differential capacitance and potential of zero charge of Au(111) in some aprotic solvents, ChemElectroChem, 8 (2021), pp. 1817--1835, DOI 10.1002/celc.202100316 .
        A combined experimental and theoretical investigation on various aprotic solvents and their electrochemical behaviors at gold surfaces is presented. The potential of zero charge was determined for all the solvents and the differential capacity was measured and simulated for various salts. Conclusions about the adsorption behavior and solvent-specific solvation number could be drawn from this combined study.

      Preprints, Reports, Technical Reports

      • L. Schmeller, D. Peschka, Gradient flows for coupling order parameters and mechanics, Preprint no. 2909, WIAS, Berlin, 2022, DOI 10.20347/WIAS.PREPRINT.2909 .
        Abstract, PDF (7667 kByte)
        We construct a formal gradient flow structure for phase-field 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.

      • M. Landstorfer, R. Müller, Thermodynamic models for a concentration and electric field dependent susceptibility in liquid electrolytes, Preprint no. 2906, WIAS, Berlin, 2021, DOI 10.20347/WIAS.PREPRINT.2906 .
        Abstract, PDF (1920 kByte)
        The dielectric susceptibility $chi$ is an elementary quantity of the electrochemical double layer and the associated Poisson equation. While most often $chi$ is treated as a material constant, its dependency on the salt concentration in liquid electrolytes is demonstrated by various bulk electrolyte experiments. This is usually referred to as dielectric decrement. Further, it is theoretically well accepted that the susceptibility declines for large electric fields. This effect is frequently termed dielectric saturation. We analyze the impact of a variable susceptibility in terms of species concentrations and electric fields based on non-equilibrium thermodynamics. This reveals some non-obvious generalizations compared to the case of a constant susceptibility. In particular the consistent coupling of the Poisson equation, the momentum balance and the chemical potentials functions are of ultimate importance. In a numerical study, we systematically analyze the effects of a concentration and field dependent susceptibility on the double layer of a planar electrode electrolyte interface. We compute the differential capacitance and the spatial structure of the electric potential, solvent concentration and ionic distribution for various non-constant models of $chi$.

      • M. Heida, M. Landstorfer, M. Liero, Homogenization of a porous intercalation electrode with phase separation, Preprint no. 2905, WIAS, Berlin, 2021, DOI 10.20347/WIAS.PREPRINT.2905 .
        Abstract, PDF (1704 kByte)
        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 Neumann--boundary 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 Cahn--Hilliard equation, whereas the limit model consists of a diffusion and an Allen--Cahn equation. Thus we observe a Cahn--Hilliard to Allen--Cahn 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.

      • M. Landstorfer, M. Ohlberger, S. Rave, M. Tacke, A modeling framework for efficient reduced order simulations of parametrized lithium-ion battery cells, Preprint no. 2882, WIAS, Berlin, 2021, DOI 10.20347/WIAS.PREPRINT.2882 .
        Abstract, PDF (3767 kByte)
        In this contribution we present a new modeling and simulation framework for parametrized Lithium-ion battery cells. We first derive a new continuum model for a rather general intercalation battery cell on the basis of non-equilibrium thermodynamics. In order to efficiently evaluate the resulting parameterized non-linear system of partial differential equations the reduced basis method is employed. The reduced basis method is a model order reduction technique on the basis of an incremental hierarchical approximate proper orthogonal decomposition approach and empirical operator interpolation. The modeling framework is particularly well suited to investigate and quantify degradation effects of battery cells. Several numerical experiments are given to demonstrate the scope and efficiency of the modeling framework.

      • E. Meca, A.W. Fritsch, J. Iglesias--Artola, S. Reber, B. Wagner, Predicting disordered regions driving phase separation of proteins under variable salt concentration, Preprint no. 2875, WIAS, Berlin, 2021, DOI 10.20347/WIAS.PREPRINT.2875 .
        Abstract, PDF (5499 kByte)
        We determine the intrinsically disordered regions (IDRs) of phase separating proteins and investigate their impact on liquid-liquid phase separation (LLPS) with a random-phase approx- imation (RPA) that accounts for variable salt concentration. We focus on two proteins, PGL-3 and FUS, known to undergo LLPS. For PGL-3 we predict that an IDR near the C-terminus 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 N-terminus and another near the C-terminus. Our RPA analysis of these domains predict that, surprisingly, the IDR at the N-terminus (aa 1-285) and not the LC domain promotes LLPS of FUS by comparison to in vitro experiments under physiological temperature and salt conditions.

      • R. Shiri, L. Schmeller, R. Seemann, D. Peschka, B. Wagner, On the spinodal dewetting of thin liquid bilayers, Preprint no. 2861, WIAS, Berlin, 2021, DOI 10.20347/WIAS.PREPRINT.2861 .
        Abstract, PDF (12 MByte)
        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 PS-PMMA 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 thin-film 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.

      • A.K. Barua, R. Chew, L. Shuwang, J. Lowengrub, A. Münch, B. Wagner, Sharp-interface problem of the Ohta--Kawasaki model for symmetric diblock copolymers, Preprint no. 2855, WIAS, Berlin, 2021, DOI 10.20347/WIAS.PREPRINT.2855 .
        Abstract, PDF (1087 kByte)
        The Ohta-Kawasaki model for diblock-copolymers is well known to the scientific community of diffuse-interface methods. To accurately capture the long-time evolution of the moving interfaces, we present a derivation of the corresponding sharp-interface limit using matched asymptotic expansions, and show that the limiting process leads to a Hele-Shaw type moving interface problem. The numerical treatment of the sharp-interface 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 Ohta-Kawasaki model. Starting with the governing equations defined on separate phase domains, we develop boundary integral equations valid for multi-connected domains in a 2D plane. For numerical simplicity we assume our problem is driven by a uniform Dirichlet condition on a circular far-field boundary. The integral formulation of the problem involves both double- and single-layer potentials due to the modified boundary condition. In particular, our formulation allows one to compute the nonlinear dynamics of a non-equilibrium 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.H. Erhardt, S. Solem, Analysis and simulation of a modified cardiac cell model gives accurate predictions of the dynamics of the original one, Preprint no. 2848, WIAS, Berlin, 2021, DOI 10.20347/WIAS.PREPRINT.2848 .
        Abstract, PDF (4937 kByte)
        The 19-dimensional TP06 cardiac muscle cell model is reduced to a 17-dimensional version, which satisfies the required conditions for performing an analysis of its dynamics by means of bifurcation theory. The reformulated model is shown to be a good approximation of the original one. As a consequence, one can extract fairly precise predictions of the behaviour of the original model from the bifurcation analysis of the modified model. Thus, the findings of bifurcations linked to complex dynamics in the modified model - like early afterdepolarisations (EADs), which can be precursors to cardiac death - predicts the occurrence of the same dynamics in the original model. It is shown that bifurcations linked to EADs in the modified model accurately predicts EADs in the original model at the single cell level. Finally, these bifurcations are linked to wave break-up leading to cardiac death at the tissue level.

      • G. Arumgam, A.K. Dond, A.H. Erhardt, Global existence of solutions to Keller--Segel chemotaxis system with heterogeneous logistic source and nonlinear secretion, Preprint no. 2847, WIAS, Berlin, 2021, DOI 10.20347/WIAS.PREPRINT.2847 .
        Abstract, PDF (219 kByte)
        We study the following Keller-Segel chemotaxis system with logistic source and nonlinear secretion. For this system, we prove the global existence of solutions under suitable assumptions.

      Talks, Poster

      • R. Müller, Non-equilibrium thermodynamics modeling of polycrystalline electrode liquid electrolyte interface, 31st Topical Meeting of the International Society of Electrochemistry, Meeting topic: ``Theory and Computation in Electrochemistry: Seeking Synergies in Methods, Materials and Systems'', Session 2: ``Theory and Computation of Interfacial and Nanoscale Phenomena'', May 15 - 19, 2022, Rheinisch-Westfälische Technische Hochschule Aachen, May 17, 2022.

      • L. Schmeller, K. Remini, Liquid dewetting from liquid and soft substrates (online talk), Colloquium of the SPP 2171 (Online Event), May 21, 2021.

      • L. Schmeller, B. Wagner, Dynamic wetting and dewetting of viscous liquid droplets films on viscoelastic substrates, Conference ``Dynamic Wetting of Flexible, Adaptive, and Switchable Substrates'' of the SPP 2171, Freiburg, November 8 - 10, 2021.

      • L. Schmeller, Multi-phase dynamic systems at finite strain elasticity: Mathematical modeling, existence theory and numerical solutions (online talk), Workshop: Young Women in PDEs and Applications (Online Event), September 20 - 22, 2021, Bonn, September 22, 2021.

      • L. Schmeller, Phase field model with nonlinear elasticity (online talk), Workshop on Dynamic Wetting of Flexible, Adaptive, and Switchable Substrates (SPP 2171) (Online Event), June 28 - July 1, 2021, Universität Münster, June 29, 2021.

      • A. Erhardt, Modelling and analysis of cardiac dynamics (online talk), Applied Analysis Group Seminar (Online Event), Universität Bremen, June 1, 2021.

      • A.H. Erhardt, S. Checa, A. Petersen, B. Wagner, AA1-12: Mathematical modelling of cellular self-organization on stimuli responsive extracellular matrix (online poster), MATH+ Day 2021 (Online Event), Technische Universität Berlin, November 5, 2021.

      • M.H. Farshbaf Shaker, D. Peschka , M. Thomas, B. Wagner, Variational methods for viscoelastic flows and gelation, MATH+ Day 2021 (Online Event), Technische Universität Berlin, November 5, 2021.

      • M. Landstorfer, Modeling electrochemical systems with continuum thermodynamics -- From fundamental electrochemistry to porous intercalation electrodes (online talk), Stochastic & Multiscale Modeling and Computation Seminar (Online Event), Illinois Institute of Technology, Chicago, USA, October 28, 2021.

      • M. Landstorfer, Modeling of concentration and electric field dependent susceptibilities in electrolytes (online talk), AA2 -- Materials, Light, Devices, Freie Universität Berlin, Humboldt-Universität zu Berlin, WIAS Berlin, February 26, 2021.

      • R. Müller, Concentration. and field dependent suspeptibiliy of electrolytes (online talk), MODVAL 17, EPFL Valais Walis, Online, April 20 - July 22, 2021, Switzerland, April 22, 2021.

      • R. Müller, Modeling and simulation of concentration and field dependent susceptibility of liquid electrolytes (online talk), 72nd Annual Meeting of the International Society of Electrochemistry (ISE) (Online Event), August 29 - September 3, 2021, Jeju Island, Korea (Republic of), September 1, 2021.

      • R. Müller, Modeling electrode-electrolyte interfaces: The differential capacitance of polycrystalline surfaces and non-constant susceptibility (online talk), ESEE (12th European Symposium on Electrochemical Engineering (Online Event), June 14 - 17, 2021, Leeuwarden, Netherlands, June 16, 2021.

      • R. Müller, Modeling of complex polycristalline electrodes and numerical study (online talk), DMV--ÖMG Annual Meeting 2021 (Online Event), Minisymposium 8: ``PDE Models Describing Interfaces and Complex Structures'', September 27 - October 1, 2021, Universität Passau, September 30, 2021.

      • R. Müller, Modeling of ion transport by a Maxwell--Stefan approach and numerical results (online talk), 8th European Congress of Mathematics (8ECM), Minisymposium ``Multicomponent Diffusion in Porous Media'', June 20 - 26, 2021, Portorož, Slovenia, June 22, 2021.

      • R. Müller, Modeling polycrystalline electrode-electrolyte interfaces: The differential capacitance (online talk), 14th Virtual Congress WCCM & ECCOMAS 2020, January 11 - 15, 2021, January 11, 2021.

      • A. Selahi, M. Landstorfer, The double layer capacity of non-ideal electrolyte solutions -- A numerical study (online poster), 240th ECS meeting (Online Event), October 10 - 14, 2021.

      • A. Selahi, The double layer capacity of non-ideal electrolyte solutions - A numerical study (online talk available during the whole conference), 240th ECS Meeting (Online Event), October 10 - 14, 2021.

      • K. Remini, L. Schmeller, Liquid dewetting from visco-elastic substrates, Conference ``Dynamic Wetting of Flexible, Adaptive, and Switchable Substrates'' of the SPP 2171, November 8 - 10, 2021, Universität Freiburg, November 9, 2021.

      • B. Wagner, R. Seemann, Liquid dewetting from liquid and soft substrates (online talk), SPP2171 Kolloquium, May 27, 2021.

      • P.-É. Druet, The free energy of incompressible fluid mixtures: An asymptotic study (online talk), TES-Seminar on Energy-based Mathematical Methods and Thermodynamics, Thematic Einstein Semester on Energy-based Mathematical Methods for Reactive Multiphase Flows, Technische Universität Berlin, WIAS Berlin, January 21, 2021.

      • M. Landstorfer, M. Eigel, M. Heida, A. Selahi, Recovery of battery ageing dynamics with multiple timescales (online poster), MATH+ Day 2021 (Online Event), Technische Universität Berlin, November 5, 2021.

      External Preprints

      • A. Erhardt, E. Wahlén, J. Weber, Bifurcation analysis for axisymmetric water waves, Preprint no. arXiv:2202.01754, arXiv, Cornell University, 2022, DOI .
        We study steady axisymmetric water waves with general vorticity and swirl, subject to the influence of surface tension. This can be formulated as an elliptic free boundary problem in terms of Stokes' stream function. A change of variables allows us to overcome the generic coordinate-induced singularities and to cast the problem in the form "identity plus compact", which is amenable to Rabinowitz' global bifurcation theorem, while no restrictions regarding the absence of stagnation points in the flow have to be made. Within the scope of this new formulation, local and global solution curves, bifurcating from laminar flows with a flat surface, are constructed.