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: 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.

Title: Large deviation principles for graphon sampling.
Speaker: Jan Grebik (University of California Los Angeles) [link]
Time: Tuesday, 21.11.2023, 17:00
Location: Online

Let $G(n,p)$ be the random graph on $[n]$ vertices, where each edge is added independently with probability $p$. Using the theory of dense graph limits, so-called graphons, Chatterjee and Varadhan established a large deviation principle (LDP) for this model, which they used to investigate properties of a typical graph under the assumption that a rare event has occurred.

In this talk I will discuss LDP for general graphon sampling with particular emphasis on block graphons. Here the setup is as follows; a graphon $W:[0,1]^2\to [0,1]$ is a symmetric Lebesgue measurable function and $G(n,W)$ is the random graph on $[n]$ vertices, where we first sample $x_1,\dots, x_n\in [0,1]$ independently according to the Lebesgue measure and then add the edge between vertices $k,\ell\in [n]$ independently with probability $W(x_k,x_{\ell})$. We describe a LDP for $G(n,W)$ in the case when $W$ is a so-called step graphon, and hint on why finding LDP for sampling from a general graphon seems to be a difficult problem.

Time permitting, we compare our work with a recent result by Borgs, Chayes, Gaudio, Petti and Sen on LDP for block models.

This is a joint work with O.Pikhurko.

Title: Thoughts on Machine Learning.
Speaker: Rupert Klein (Freie Universitaet Berlin) [link]
Time: Thursday, 09.11.2023, 15:30
Location: WIAS-406/Online

Techniques of machine learning (ML) find a rapidly increasing range of applications touching upon social, economic, and technological aspects of everyday life. They are also being used with great enthusiasm to fill in gaps in our scientific knowledge by data-based modelling approaches. I have followed these developments for a while with interest, concern, and mounting disappointment. When these technologies are employed to take over decisive functionality in safety-critical applications, we would like to exactly know how to guarantee their compliance with pre-defined guardrails and limitations. Moreover, when they are utilized as building blocks in scientific research, it would violate scientific standards -- in my opinion -- if these building blocks were used without a throrough understanding of their functionality, including inaccuracies, uncertainties, and other pitfalls. In this context, I will juxtapose (a subset of) deep neural network methods with the family of entropy-optimal Sparse Probabilistic Approximation (sSPA) techniques developed recently by Illia Horenko and colleagues.

Title: Beyond the Born-Oppenheimer Approximation by Surface Hopping Trajectories Methods.
Speaker: Leonardo Araujo (TU Munich)
Time: Monday, 25.09.2023, 10:00
Location: WIAS-ESH

In molecular dynamics, the Born-Oppenheimer approximation is a fundamental concept, assuming the decoupling of electronic and nuclear motions due to the significant mass difference between them. This implies that, from the perspective of the nuclei, the electrons effectively reside in an eigenstate. While this approximation is widely employed in quantum chemistry to expedite molecular wavefunction calculations, it encounters limitations, especially in scenarios involving light atoms and high-energy systems.

In the first part of this presentation, we confront this limitation by going beyond the Born-Oppenheimer approximation and adding multiple electronic eigenstates into the approximation. We will discuss the theory of this approach and present the resulting equations of motion for the nuclei.

Moving on to the second part, we explore computationally efficient methods for simulating such dynamics by considering a class of quantum-classical methods: the Surface Hopping Trajectories. These methods entail an ensemble of trajectories, sampled from the initial nuclear configuration, performing classical dynamics on the eigensurface of an electronic eigenstate. They further allow each trajectory to undergo transitions to different eigenstates guided by hopping probabilities. We present two famous versions of Surface Hopping: the Fewest-Switches Surface Hopping (FSSH) and the Single Switch Surface Hopping (SSSH), also recognised as Landau-Zener Surface Hopping.

To culminate, we illustrate the use of these methods through a practical example using WavePacket, a Matlab software package for quantum-mechanical and quantum-classical simulations.

Title: Slow time-scale behavior of fast microscopic dynamics.
Speaker: Amit Acharya (Carnegie Mellon University) [link]
Time: Tuesday, 16.05.2023, 15:15
Location: WIAS-ESH/Online

This talk aims to understand and exploit the slow time-scale behavior of rapidly evolving microscopic dynamics posed in terms of systems of nonlinear ordinary differential equations, not necessarily containing an a priori split into fast and slow variables. Such a question arises naturally and ubiquitously in efforts to understand macroscopic dynamics, on engineering time-scales, of well-accepted models of microscopic dynamics that, however, are not amenable to practical computing over the much, much larger macroscopic time-scales of interest. This is because there is a vast separation of time scales involved between the dynamics of the macroscopic variables of interest and the microscopic dynamics, and evolving the microscopic dynamics directly fails to address the question of the macroscopic dynamics. The methodology employed involves a computational scheme based on fundamental mathematical theory that a) defines appropriate `coarse' variables corresponding to the microscopic dynamics that evolve in a stable manner on the coarse time scale; b) determines the equation of evolution for such variables; and c) defines a practically useful strategy for accurately initializing short bursts of microscopic runs for the evolution of the slow variables, without special requirements on the nature of the microscopic dynamics.

We will illustrate the theory with examples that violate ergodicity and include both conservative and dissipative behavior. A first step towards coarse graining of discrete dislocation dynamics to a pde-based plasticity model without relying on constitutive assumptions will also be demonstrated.

This is joint work with Sabyasachi Chatterjee, Zvi Artstein, Giacomo Po, Xiaohan Zhang, and Nasr Ghoniem.

Title: From an egg to an embryo - inferring the temporal dynamics of cells during embryonic development.
Speaker: Markus Mittnenzweig (Weizmann Institute )
Time: Thursday, 06.04.2023, 11:00
Location: WIAS-ESH/Online

Novel single-genomics technologies allow probing biological tissues and entire embryos at unprecedented molecular resolution. In the context of developmental biology, these technologies allow measuring in a very quantitative way the emergence of spatial and molecular complexity that characterizes early embryonic development. Mouse embryonic development is a canonical model for studying mammalian cell fate acquisition. Recently, we introduced a temporal flow model for early mouse development, consisting of data from 153 individually sampled embryos spanning 36 hours of molecular diversification. Using a convex optimization framework and precise timing of embryos we infer the differentiation dynamics of individual cells along the continuum of embryonic cellular states. In the second part, I will show how to use this time-resolved model to assess the function of epigenetic regulators and intercellular signals involved in early embryonic development.

Title: Modeling and simulations towards the design of high performance batteries.
Speaker: Alberto Salvadori (University of Brescia) [link]
Time: Tuesday, 21.02.2023, 13:30
Location: WIAS-406/Online

The upcoming request of renewable energy requires high performance energy storage and power delivery systems. The conventional batteries rely on liquid electrolytes, which is still the state of art due to their high ionic conductivity. These systems, though, show safety concerns in view of the flammability of toxic organic solvents. Therefore, there is a great effort to introduce novel electrolyte materials with excellent transport properties, low interfacial resistance, good mechanical strength, and safer behavior. Solid-state electrolytes are promising candidates. Upon combining with Li or Na metal anodes they have the potential to deliver higher energy densities with enhanced safety compared to liquid electrolyte batteries. However, upon charging such cells at current densities greater than a critical value, "dendrites" nucleate and grow from the metal electrode and result in short-circuiting the cell. Furthermore, SSE present contact problem with the porous electrode interfaces.

For this reason, gel polymer electrolytes (GPE) can be seen as a valid alternative. It is composed by a polymer network with solvent filling the interstitial spaces, the confined liquid into the polymer matrix can boost the conductivity and can provide better adhesion at the electrode interfaces. It is well known that low ionic diffusivities cause high concentration and potential polarization across thick, porous cathodes at high current rates. Furthermore, the rapid depletion of Li+ ions at the reaction surface limits the rate capability of thick electrode-based Li-ion batteries.

In a series of different research endeavours, modelling and simulations have been carried out at the m4lab towards the design of the next generation of electrochemical storage systems. In this talk, a brief overview will be presented at first, concerning dendritic growth and a multiscale compatible approach in electrolytes. Eventually, a detailed investigation of gel polymer electrolytes, optimal electrode design, and the influence of ionic additives in the porous carbon-binder network will be presented and validated against experimental evidence.

see pdf file

Past talks

  • 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, Ch. Kuhn and A. Schlüter (Technische Universität Kaiserslautern), Phase field modelling of fracture -- From a mechanics point of view.
  • 16.10.2018, Arik Yochelis (Ben-Gurion University of the Negev, Israel)), From solvent free to dilute electrolytes: A unified continuum approach.
  • 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.