Seminar "Material Modeling"

This interdisciplinary seminar is dedicated to the mathematical modeling of different phases of matter and their transitions, covering microscopic and macroscopic scales and using both discrete and continuum descriptions. Topics include both stationary and evolutionary processes. 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, Martin Heida, Elena Magnanini, Dirk Peschka, Marita Thomas, Barbara Wagner

Upcoming and recent talks


Title: A posteriori error estimates for systems of hyperbolic conservation laws modeling compressible flows.
Speaker: Jan Giesselmann (Department of Mathematics, TU Darmstadt) [link]
Time: Thursday, 18.07.2024, 15:00
Location: WIAS-406/Online (link on request from peschka{at}wias-berlin.de)

Hyperbolic conservation laws are a class of PDEs that have many applications, most notably in compressible fluid flows when viscosity is neglected. While these equations are successfully used by engineers in simulations, there are many open questions regarding their mathematical study. These are mostly driven by to the non-uniqueness of entropy solutions in multiple space dimensions but even in one space dimensions stability of solutions is challenging if one is to go beyond initial data that are small in BV.

The challenges in the mathematical analysis have lead to a situation where a variety of sophisticated numerical schemes exists and is successfully used in practice but the mathematical foundations of these methods are not as substantial as one would hope. This issue has been addressed by several authors in recent years and we plan plan to present what has been achieved in the field of a posteriori error estimates, i.e. explicit bounds for the error of the numerical solution that can be computed from the numerical solution.

A fundamental building block of a posteriori error estimates are stability theories that allow to relate certain norms of residuals, i.e. quantities measuring by how much an approximate solution fails to satisfy the PDE, to certain norms of the error, i.e. the difference between numerical and exact solution. Examples of such stability theories include the classical relative entropy framework, the theory of shifts developed by Vasseur and coworkers and recent results by Bressan and coworkers.

We will describe these stability results and discuss how they have been used to derive a posteriori error estimates for hyperbolic conservation laws.


Title: Axisymmetric capillary water waves with vorticity and swirl.
Speaker: Jörg Weber (Universität Wien) [link]
Time: Thursday, 04.07.2024, 15:00
Location: WIAS-406/Online (link on request from peschka{at}wias-berlin.de)

While the research on axisymmetric capillary water waves has a long history, surprisingly little has been done when one wants to allow for vorticity (local spinning) and swirl (angular momentum). After introducing the problem and presenting a well-known formulation in terms of the Stokes stream function, we will explain the main analytical ingredients in order to rigorously construct travelling wave solutions with a free boundary. Then, two solution curves are constructed: First, we start at perfectly cylindrical jets, where we derive the dispersion relation and investigate it in detail in certain cases. Also, we will point out inherent connections to the famous Rayleigh instability observed in everyday life, e.g. when a tap drips. Second, we start at static configurations with constant mean curvature surfaces, so-called unduloids. There, as an interesting interplay between water waves, geometry, and elliptic integrals, we show rigorously that to any such configuration there connects a curve of non-static configurations, which confirms previous numerical observations. The talk is based on joint work with André Erhardt (WIAS), Anna-Mariya Otsetova (Aalto), and Erik Wahlén (Lund).


Title: Mixed-dimensional Coupled Finite Elements in FEniCS(x).
Speaker: Cécile Daversin-Catty (Simula Research Laboratory, (Oslo, Norway)) [link]
Time: Tuesday, 09.04.2024, 13:30
Location: Online (link on request)

Mixed-dimensional partial differential equations (PDEs) are equations coupling fields defined over distinct domains that may differ in topological dimension. Such PDEs naturally arise in a wide range of fields including geology, bio-medicine, and fracture mechanics. Mixed-dimensional models are also used to impose non-standard conditions through Lagrange multipliers. Finite element discretizations of such PDEs involve nested meshes of possibly heterogeneous topological dimension. The assembly of such systems is non-standard and non-trivial, and requires the design of both generic high level software abstractions and lower level algorithms. The FEniCS project aims at automating the numerical solution of PDE-based models using finite element methods. A core feature is a high-level domain-specific language for finite element spaces and variational forms, close to mathematical syntax. Lately, FEniCS gave way to its successor FEniCSx, including major improvements over the legacy library. An automated framework was developed in core FEniCS legacy libraries to address the challenges characterizing mixed-dimensional problems. These concepts were recently ported to FEniCSx, taking advantage of the underlying upgrades in the library features and design. This talk gives an overview of the abstractions and algorithms involved, and their implementation in the FEniCS project core libraries. The introduced features are illustrated by concrete applications in biomedicine.


Title: Microscopic and mesoscopic simulations of fluid interfaces.
Speaker: Marcello Sega (University College London, UK) [link]
Time: Tuesday, 13.02.2024, 13:30
Location: WIAS-406/Online (link on request)

I will present recent advancements in analyzing fluid interfaces from the microscopic to the mesoscopic scales. Beginning with the classical atomistic description of fluids in molecular dynamics simulations, I will discuss techniques for extracting surface information in the presence of thermal capillary waves. These modern numerical methods allow resolving the interface properties on a molecular layer basis, revealing a high degree of heterogeneity in their structure and transport coefficients. I will conclude by introducing a novel approach that bridges the microscopic and hydrodynamic scales, offering a more comprehensive understanding of droplet wetting dynamics at the mesoscopic level.

Past talks

  • 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, Martin Slowik (TU Berlin), Random conductance model in a degenerate ergodic environment.
  • 09.05.2017, Mathias Schäffner (TU Dresden), Stochastic homogenization of discrete energies with degenerate growth.
  • 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.