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Seminar "Material Modeling"

This interdisciplinary seminar covers a wide range of scientific topics, primarily focusing on advanced theoretical and computational methods in physics, engineering, and applied mathematics using both discrete and continuum descriptions. Key themes include modeling and simulation of complex systems (e.g., biological flows, material degradation, and charge transport), machine learning applications, and the development of new mathematical frameworks for understanding dynamic processes and stochastic particle systems in various physical and biological contexts. In particular, macroscopic properties that arise from these systems, such as condensation, percolation or crystallization, are investigated, together with rescaling limits. Additionally, the seminar is dedicated to the mathematical modeling of different phases of matter and their transitions, encompassing both microscopic and macroscopic scales. Topics include both stationary and evolutionary processes. Mathematical techniques include, among others, adaptive computational methods, asymptotic analysis, mathematical physics, non-smooth differential equations, stochastics, thermodynamic modeling, and variational methods.

Place: Weierstrass-Institute for Applied Analysis and Stochastics
Mohrenstraße 39, 10117 Berlin
Organizers: Thomas Eiter, Manuel Landstorfer, Elena Magnanini, Dirk Peschka, Barbara Wagner

Upcoming and recent talks


Title: From Equations to Materials: The Logic of Modeling Thin Film Growth.
Speaker: Nadire Nayir (Paul-Drude-Institut für Festkörperelektronik) [link]
Time: Thursday, 19.06.2025, 14:00
Location: WIAS-405

The synthesis of technologically vital thin films presents complex, multiscale challenges that lie at the intersection of physics, chemistry, and increasingly, mathematics. As materials science progresses toward predictive design and precise control of growth processes, mathematical modeling has become indispensable for understanding how microscopic rules shape macroscopic behavior.

With a particular emphasis on simulation techniques rooted in quantum mechanics and Newtonian mechanics, in this talk, I will explain how atomic interactions are described mathematically -- starting from basic concepts like interatomic forces and potential energy surfaces, and moving toward how these are used in time-evolution schemes to simulate atomic motion. These elements form the foundation of computational models that help us understand key processes in thin film growth, such as how nuclei form, how domains align and grow, and how defects emerge and evolve on a substrate [1-5]. To connect further these atomic-scale models with experimentally observable behavior, we will then turn to multiscale modeling, which provides a systematic way to combine different levels of description. I will show how we link atomistic simulations with continuum methods -- including phase-field models which describe morphological evolution and domain coarsening, and computational fluid dynamics, which captures macroscopic transport phenomena in the growth environment (as in chemical vapor deposition or hybrid molecular beam epitaxy). At this stage, I will walk through how they are coupled together to form an integrated, multiscale modeling framework [6-7].

By grounding simulation techniques in their mathematical origins, this talk aims to provide a deeper understanding of how theoretical models mirror real-world materials behavior. Ultimately, I hope to show how mathematics not only powers atomistic simulations but also serves as a conceptual bridge between fundamental physics and the technological development of advanced materials.

Key highlights:

  1. Matter, Volume 7, Issue 10, 3672-3687 (2024) 10.1016/j.matt.2024.08.006
  2. Small, 20, 2306554 (2024) 10.1002/smll.202306554
  3. Nat. Nanotechnol. 18, 1295-1302 (2023). 10.1038/s41565-023-01456-6
  4. ACS Nano, 17, 13, 12140-12150 (2023) 10.1021/acsnano.2c12621
  5. 2D Mater. 10 032002 (2023) 10.1088/2053-1583/acd7fd
  6. npj Computational Materials 8(1):240, (2022) 10.1038/s41524-022-00936-y
  7. Journal of Crystal Growth 527, 125247 (2019) 10.1016/j.jcrysgro.2019.125247

Title: Universality of the band-gap density - from periodic graphs to laminates.
Speaker: Ram Band (Department of Mathematics Technion – Israel Institute of Technology) [link]
Time: Thursday, 22.05.2025, 14:00
Location: WIAS-ESH

The spectrum of periodic objects has a band-gap structure. We show that such a spectrum can be described in terms of a linear flow on a torus. This characterization is valid for various periodic structures, from quantum graphs to wave propagation in elastic laminates. Using this approach allows us to prove universal properties of the band-gap density and obtain many useful spectral characteristics.

The talk is based on joint works with Lior Alon, Gregory Berkolaiko and Gal Shmuel.

Title: Optimal Control for the Generalized Navier-Stokes Equations With a Directional Do Nothing Boundary Condition.
Speaker: Pedro Nogueira (Department of Mathematics and CEMAT, Instituto Superior Técnico, Universidade de Lisboa, Portugal) [link]
Time: Thursday, 06.03.2025, 14:00
Location: WIAS-406

Motivated by the works [3, 2, 1], which introduce an artificial boundary condition known as the directional-do-nothing (DDN) condition, we investigate its use and advantages in both distributed and boundary control problems within the context of stationary generalized Newtonian fluids. It is well known that the DDN condition enhances both theoretical and numerical stability of the Navier-Stokes equations - stationary and unsteady regimes - when compared to the classical do-nothing (CDN) boundary condition [1, 5].

While the DDN condition, compared to the CDN boundary condition, enhances well-posedness results and provides numerical stability, it also introduces differentiability issues in control problems due to the absence of a Hadamard derivative for the control-to-state operator. This derivative is crucial in classical approaches for deriving the KKT system. To overcome this challenge, we adopt alternative techniques, such as a limiting process, following the approach in [4]. In this framework, we construct a family of smooth approximating problems that converge, in a suitable sense, to the generalized Navier-Stokes-DDN problem. By leveraging this convergence and employing precise analytical techniques, we establish the KKT system for the associated control problem.

This is joint work with Ana Leonor Silvestre, my PhD supervisor.

References:

[1] M. Braack and P. B. Mucha. Directional do-nothing condition for the Navier-Stokes equations. Journal of Computational Mathematics, pages 507–521, 2014.

[2] C.-H. Bruneau. Boundary conditions on artificial frontiers for incompressible and compressible Navier-Stokes equations. ESAIM: Mathematical Modelling and Numerical Analysis, 34(2):303–314, 2000.

[3] C.-H. Bruneau and P. Fabrie. New efficient boundary conditions for incompressible navier-stokes equations: a well-posedness result. ESAIM: Mathematical Modelling and Numerical Analysis, 30(7):815–840, 1996.

[4] C. Christof, C. Clason, C. Meyer, and S. Walther. Optimal control of a non-smooth semilinear elliptic equation. arXiv preprint arXiv:1705.00939, 2017.

[5] V. John. Finite element methods for incompressible flow problems, volume 51. Springer, 2016.

Title: Kirchhoff Graphs and their Role as Circuit Diagrams for Reaction Networks.
Speaker: Joseph Fehribach (Worcester Polytechnic Institute, Massachusetts, USA) [link]
Time: Tuesday, 04.03.2025, 15:00
Location: WIAS-HVP11A, video conference room

Kirchhoff graphs are vector graphs (graphs whose edges are vectors) where all vertex cuts are orthogonal to every cycle. When developed based on the stoichiometry of a chemical or electrochemical reaction network, such a graph can be viewed as a circuit diagram for that network. The orthogonality condition means that the Kirchhoff graph satisfies the Kirchhoff laws, the current law at the vertices and the voltage/potential law for the cycle. This presentation will discuss some of the stoichiometric implications for the reaction networks that can be obtained from these graphs, then some of the properties of Kirchhoff graphs and how such graphs can be constructed.

Title: Large Stochastic Differential Equations, Viscoelastic Stress and the Role of Fluctuations in Complex Materials.
Speaker: Arturo Winters (ETH Zürich, Department of Materials, Laboratory for Soft Materials) [link]
Time: Tuesday, 25.02.2025, 14:00
Location: WIAS-HVP11A, video conference room

When exploring the world of viscoelasticity, one of the first equations we encounter is the constitutive relation for linear viscoelasticity,

$\tau = \int_0^t G(t-t') \dot{\gamma} \, dt',$

where $\tau,G(t)$ and $\dot{\gamma}$ are the stress tensor, the relaxation modulus and the symmetrized velocity gradient. A key feature that emerges from this fundamental equation for complex fluids is the presence of a memory integral. The interpretation of this memory effect in terms of underlying microscopic dynamics has been a central theme in rheology for the past fifty years, leading to the widespread use of Stochastic Differential Equations to describe the relationship between stochastic processes in polymeric fluids and their macroscopic stress response [1,2]. This talk will summarize this coarse-grained connection and extend the discussion from stochastic fluctuations in such models to fluctuations in more macroscopic observables, as measured through light scattering techniques [3] or microrheological experiments [4].

Our last work [5] presents novel insights into the interpretation of these stochastic phenomena in flowing viscoelastic materials. We illustrate the limits of the classical Gaussian approximation and show how, in the context of a local field theory, the most fundamental viscoelastic model, the Upper Convected Maxwell (UCM), exhibits different fluctuations depending on the underlying microscopic dynamics. Both the Temporary Network Model (TNM) and the Dumbell Model (DM), which constitute model systems for two groups of microscopic models, reproduce the Maxwellian behavior. Until now, literature pointed out the equality of the two models with respect to stress evolution. We now quantify differences when taking into account fluctuations and suggest techniques to measure them.

[1] H. C. Öttinger. Stochastic Processes in Polymeric Fluids. Springer, Berlin, 1996.

[2] Robert Byron Bird, Charles F Curtiss, Robert C Armstrong, and Ole Hassager. Dynamics of polymeric liquids, volume 2: Kinetic theory. Wiley, 1987.

[3] J.M.O. Zárate and J.V. Sengers. Hydrodynamic Fluctuations in Fluids and Fluid Mixtures. Elsevier, 01 2006.

[4] T.G. Mason and D.A. Weitz. Optical measurements of frequency-dependent linear viscoelastic moduli of complex fluids. Phys. Rev. Lett., 74:1250, 1995.

[5] A. Winters, H. C. Öttinger, and J. Vermant. Comparative analysis of fluctuations in viscoelastic stress: A comparison of the temporary network and dumbbell models. J. Chem. Phys., 161(1):014901, 07 2024.

Past talks

  • 19.11.2024, Angeliki Koutsimpela (University of Augsburg, Faculty of Mathematics, Natural Sciences and Technology), Mean-field limits for interacting particle systems.
  • 07.11.2024, Tomáš Bodnár (Czech Technical University in Prague, Faculty of Mechanical Engineering, Department of Technical Mathematics), On the use of viscoelastic fluids flows models in hemolysis prediction.
  • 05.09.2024, Georgy Kitavtsev (Middle East Technical University, Northern Cyprus Campus), Composite solutions to a liquid bilayer model.
  • 08.08.2024, Ferran Brosa Planella (University of Warwick), Asymptotic methods for lithium-ion battery models.
  • 18.07.2024, Jan Giesselmann (Department of Mathematics, TU Darmstadt), A posteriori error estimates for systems of hyperbolic conservation laws modeling compressible flows.
  • 04.07.2024, Jörg Weber (Universität Wien), Axisymmetric capillary water waves with vorticity and swirl.
  • 09.04.2024, Cécile Daversin-Catty (Simula Research Laboratory, (Oslo, Norway)), Mixed-dimensional Coupled Finite Elements in FEniCS(x).
  • 13.02.2024, Marcello Sega (University College London, UK), Microscopic and mesoscopic simulations of fluid interfaces.
  • 21.11.2023, Jan Grebik (University of California Los Angeles), Large deviation principles for graphon sampling.
  • 09.11.2023, Rupert Klein (Freie Universitaet Berlin), Thoughts on Machine Learning.
  • 25.09.2023, Leonardo Araujo (TU Munich), Beyond the Born-Oppenheimer Approximation by Surface Hopping Trajectories Methods.
  • 16.05.2023, Amit Acharya (Carnegie Mellon University), Slow time-scale behavior of fast microscopic dynamics.
  • 06.04.2023, Markus Mittnenzweig (Weizmann Institute ), From an egg to an embryo - inferring the temporal dynamics of cells during embryonic development.
  • 21.02.2023, Alberto Salvadori (University of Brescia), Modeling and simulations towards the design of high performance batteries.
  • 08.11.2022, Leonid Berlyand (Pennsylvania State University), Asymptotic stability in a free boundary PDE model of active matter.
  • 29.09.2022, Bob Eisenberg (Rush University, Chicago), From Maxwell to Mitochondria.
  • 19.09.2022, Robert Jack (University of Cambridge), Examples of hydrodynamic behaviour in two-species exclusion processes.
  • 12.07.2022, Steinar Evje (University of Stavanger, Norway), A cell-fluid-matrix model to understand how aggressive cancer cell behavior possibly is linked to elevated fluid pressure.
  • 23.06.2022, Giovanni Ligorio (Humboldt-Universität zu Berlin), Neuromorphic device development: from modification of surfaces to modification of functions.
  • 31.05.2022, Eric Sonnendrücker (Max Planck Institute for Plasma Physics), Geometric Numerical Methods for Models from Plasma Physics.
  • 26.04.2022, Alessia Nota (Universitá degli studi dell'Aquila), Stationary non-equilibrium solutions for coagulation equations.
  • 23.11.2021, Silvia Budday (Friedrich-Alexander-Universität (FAU), Erlangen), Brain mechanics across scales.
  • 21.04.2020, Alfonso Caiazzo (WIAS), Modeling of biological flows and tissues.
  • 03.12.2019, Michal Pavelka (Charles University, Prague), Symmetric Hyperbolic Thermodynamically Compatible (SHTC) equations within GENERIC.
  • 25.07.2019, Robert Style (ETH Zürich), Arresting phase separation with polymer networks.
  • 09.07.2019, Carsten Graeser (Freie Universität Berlin), Truncated nonsmooth Newton multigrid for nonsmooth minimization problems.
  • 25.06.2019, Luca Heltai (SISSA mathLab, Trieste), Unconventional frameworks for the simulation of coupled bulk-interface problems.
  • 18.06.2019, Amit Acharya (Carnegie Mellon University Pittsburgh), Line Defect dynamics and solid mechanics.
  • 04.06.2019, Giselle Monteiro (Czech Academy of Sciences , Prague), On the convergence of viscous approximation for rate-independent processes with regulated inputs.
  • 14.05.2019, Mirjam Walloth (TU Darmstadt), Reliable, efficient and robust a posteriori estimators for the variational inequality in fracture phase-field models.
  • 07.05.2019, Rainer Falkenberg (Bundesanstalt für Materialforschung und -prüfung BAM), Aspects on the modelling of material degradation.
  • 23.04.2019, Marijo Milicevic (Uni. Freiburg), The alternating direction method of multipliers with variable step sizes for the iterative solution of nonsmooth minimization problems and application to BV-damage evolution.
  • 28.02.2019, Uwe Thiele (Westfälische Wilhelms-Universität Münster), Gradient dynamics models for films of complex fluids and beyond - dewetting, line deposition and biofilms.
  • 29.01.2019, Vittorio Romano (University of Catania), Charge and phonon transport in graphene.
  • 13.11.2018, Alex Christoph Goeßmann (Fritz Haber Institute of the Max Planck Society), Representing crystals for kernel-based learning of their properties.
  • 16.10.2018, Arik Yochelis (Ben-Gurion University of the Negev, Israel), From solvent free to dilute electrolytes: A unified continuum approach.
  • 16.10.2018, Ch. Kuhn and A. Schlüter (Technische Universität Kaiserslautern), Phase field modelling of fracture -- From a mechanics point of view.
  • 08.05.2018, Simon Praetorius (TU Dresden), From individual motion to collective cell migration.
  • 27.03.2018, Esteban Meca (Agronomy Department, University of Cordoba, Spain), Localized Instabilities in Phase-Changing Systems: The Effect of Elasticity.
  • 07.03.2018, Matthias Liero (WIAS), Modeling and simulation of charge transport in organic semiconductors via kinetic and drift-diffusion models.
  • 21.02.2018, Marco Morandotti (TU München), Dimension reduction in the context of structured deformations.
  • 23.01.2018, Jan Giesselmann (RWTH Aachen), Modelling error estimates and model adaptation in compressible flows.
  • 14.12.2017, Bartlomiej Matejczyk (University of Warwick), Macroscopic models for ion transport in nanoscale pores.
  • 16.11.2017, Andreas Münch (University of Oxford), Asymptotic analysis of models involving surface diffusion.
  • 24.10.2017, Anna Zubkova (Karl-Franzens-Universität Graz), Homogenization of the generalized Poisson-Nernst-Planck system with nonlinear interface conditions.
  • 12.07.2017, Rodica Toader (SISSA, Trieste), Existence for dynamic Griffith fracture with a weak maximal dissipation condition.
  • 30.05.2017, Ciro Visone (University of Sannio, Benevento), The applicative challenges of Smart Materials: from Sensing to Harvesting.
  • 17.05.2017, Riccarda Rossi (University of Brescia), In Between Energetic and Balanced Viscosity solutions of rate-independent systems: the Visco-Energetic concept, with some applications to solid mechanics.
  • 09.05.2017, Mathias Schäffner (TU Dresden), Stochastic homogenization of discrete energies with degenerate growth.
  • 09.05.2017, Martin Slowik (TU Berlin), Random conductance model in a degenerate ergodic environment.
  • 25.04.2017, Ian Thompson (University of Bath, Department of Physics), Modelling Device Charge Dynamics on the Microscopic Scale.
  • 11.04.2017, Luca Heltai (SISSA mathLab, Trieste), A numerical framework for optimal locomotion at low Reynolds numbers.