Seminar "Material Modeling"

This seminar is dedicated to the mathematical modelling of different phases of matter and their transitions, covering microscopic and macroscopic scales and utilising discrete and continuum descriptions. The topics cover stationary and evolutionary processes. Techniques include among others adaptive computational methods, asymptotic analysis, mathematical physics, nonsmooth differential equations, numerics, stochastics, thermodynamical modeling, and variational methods.

23.01.2018 Jan Giesselmann (RWTH Aachen)

Title: Modelling error estimates and model adaptation in compressible flows

Abstract: Compressible fluid flows may be described by different models having different levels of complexity. One example are the compressible Euler equations which are the limit of the Navier-Stokes-Fourier (NSF) equations when heat conduction and viscosity vanish. Arguably the NSF system provides a more accurate description of the flow since viscous effects which are neglected in Euler's equation play a dominant role in certain flow regimes, e.g. thin regions near obstacles. However, viscous effects are negligible in large parts of the computational domain where convective effects dominate. Thus, it is desirable to avoid the effort of handling the viscous terms in these parts of the domain, that is, to use the NSF system only where needed and simpler models, on the rest of the computational domain. To this end we derive an a posteriori estimator for the modelling error which is based on the relative entropy stability framework and reconstructions of the numerical solution. This is a crucial step in the construction of numerical schemes handling model adaptation in an automated manner.


14.12.2017, 14:00

Bartlomiej Matejczyk (University of Warwick )

Erhard-Schmidt lecture room

Title: Macroscopic models for ion transport in nanoscale pores

Abstract: During this talk, we discuss ionic transport through confined geometries. Our problem concerns modeling ionic flow through nanopores and ion channels. We present different methods of engineering the pores together with its characteristics. Next, we comment on the challenges in simulating the flow efficiently.
In the second part, we present a derivation of 1D asymptotic reduction of the Poisson-Nernst-Planck model applied to long and narrow pores. We discuss numerical schema and compare the results the solution of the two-dimensional system of equations.

16.11.2017 Andreas Münch (University of Oxford)

HVP 11a, room 4.01

Title: Asymptotic analysis of models involving surface diffusion

Abstract: We study the evolution of solid surfaces and pattern formation by surface diffusion. Phase field models with degenerate mobilities are frequently used to model such phenomena, and are validated by investigating their sharp interface limits. We demonstrate by a careful asymptotic analysis involving the matching of exponential terms that a certain combination of degenerate mobility and a double well potential leads to a combination of surface and nonlinear bulk diffusion to leading order. We also present a stability analysis for the sharp interface model of an evolving non-homogeneous base state and show how to correctly determine the dominant mode, which is not the one predicted by a frozen mode eigenvalue analysis.

24.10.2017 Anna Zubkova (Karl-Franzens-Universität Graz)

starts at 1:45 PM

Title: Homogenization of the generalized Poisson-Nernst-Planck system with nonlinear interface conditions

Abstract: We consider the generalized system of nonlinear Poisson-Nernst-Planck equations, which describes concentrations of multiple charged particles with the overall electrostatic potential. It is modeled in terms of the Fickian multiphase diffusion law coupled with thermodynamic principles. The generalized model is supplied by volume and positivity constraints and quasi-Fermi electrochemical potentials depending on the pressure. The model describes a plenty of electrokinetic phenomena in physical and biological sciences. We examine nonlinear inhomogeneous transmission conditions describing electro-chemical reactions on the interface in a periodic two-phase medium. We aim at a proper variational modeling, well-posedness, and asymptotic analysis as well as homogenization of the model.

12.07.2017 joint seminar with Langenbach Seminar

Rodica Toader (SISSA, Trieste)

Title: Existence for dynamic Griffith fracture with a weak maximal dissipation condition

Abstract: The study of dynamic fracture is based on the dynamic energy-dissipation balance. This condition is always satisfied by a stationary crack together with a displacement satisfying the system of elastodynamics. Therefore to predict crack growth a further principle is needed. We introduce a weak maximal dissipation condition that, together with elastodynamics and energy balance, provides a model for dynamic fracture, at least within a certain class of possible crack evolutions. In particular, we prove the existence of dynamic fracture evolutions satisfying this condition, subject to smoothness constraints, and exhibit an explicit example to show that maximal dissipation can indeed rule out stationary cracks.
These results are obtained in collaboration with G. Dal Maso (SISSA) and C. Larsen (WPI).

30.05.2017 Ciro Visone (University of Sannio, Benevento)

HVP 11a, room 4.01

Title: The applicative challenges of Smart Materials: from Sensing to Harvesting

Abstract: The talk would provide a view on functional materials observed and employed at the macro-scale. Starting from the most known Multi-Functional materials, a common modeling approach, based on the definition of constitutive relationships, is discussed.
Examples on the effectiveness of the constitutive equations in the analysis and design problems in engineering is illustrated, along with the basic challenges arising when these materials are of concern.
Further, the statement of consistent constitutive relationships when rate-independent memory processes (hysteresis) are considered is also carried out, through the definition of models for multi-input/multi-output systems that formally satisfy the Duhem inequality. Practical examples and specific applications are also proposed.


starts at 3:15 PM
Erhard-Schmidt lecture room

joint seminar with Langenbach Seminar

Riccarda Rossi (University of Brescia)

Title: In Between Energetic and Balanced Viscosity solutions of rate-independent systems: the Visco-Energetic concept, with some applications to solid mechanics

Abstract: This talk focuses on weak solvability concepts for rate-independent systems. Visco-Energetic solutions have been recently obtained by passing to the time- continuous limit in a time-incremental scheme, akin to that for Energetic solutions, but perturbed by a "viscous" correction term, as in the case of Balanced Viscosity solutions. However, for Visco-Energetic solutions this viscous correction is tuned by a fixed parameter. The resulting solution notion is characterized by a stability condition and an energy balance analogous to those for Energetic solutions, but, in addition, it provides a fine description of the system behavior at jumps as Balanced Viscosity solutions do. Visco-Energetic evolution can be thus thought as "in-between" Energetic and Balanced Viscosity evolution.
We will explore these aspects in a general metric framework. We will then illustrate the application of the Visco-Energetic concept to models for damage and finite-strain plasticity.
Joint work with Giuseppe Savaré.

09.05.2017 Martin Slowik (TU Berlin)

starts at 1:00 PM

Title: Random conductance model in a degenerate ergodic environment

Abstract: Consider a continuous time random walk on the Euclidean lattice ℤ in an environment of random conductances taking values in [0, ∞). The law of the environment is assumed to be ergodic with respect to space shifts and satisfies some moment conditions. In this talk, I will review old and discuss recent results on quenched invariance principles (an instance of stochastic homogenization in path space), local limit theorems as well as heat kernel estimates for this Markov process.
This is joint work with Sebastian Andres (Univ. Cambridge), Jean-Dominique Deuschel (TU Berlin) and Tuan Ahn Nguyen (TU Berlin).

09.05.2017 Mathias Schäffner (TU Dresden)

Title: Stochastic homogenization of discrete energies with degenerate growth

Abstract: We present a discrete-to-continuum analysis for lattice systems with random interactions. In particular, we assume that the interaction potentials satisfy polynomial growth conditions which degenerate and are given in terms of certain weight functions. Under suitable moment conditions on the weight functions and stationarity/ergodicity assumptions for the interaction potentials, we prove that the discrete energy Gamma-converges almost surely to a deterministic, homogeneous and non-degenerate integral functional.
This is joint work with S. Neukamm (TU Dresden) and A. Schlömerkemper (U Würzburg)

25.4.2017 Dr. Ian Thompson (University of Bath, Department of Physics)

Title: Modelling Device Charge Dynamics on the Microscopic Scale

Abstract: We attempt to predict the properties of organic semiconductor (OSC) materials using a microscopic ab initio approach. Charge transport through organic semiconductors (OSCs) is qualitatively different from metallic semiconductors, charges hop between molecules discretely. Marcus theory describes the microscopic hopping mechanism, quantum chemistry methods can calculate the parameters and kinetic Monte Carlo methods can be used to model charge motion. We also need to describe realistic configurations of a set of given molecules. To combine all of these approaches into a single multi-scale model is the goal of the EXTMOS project. We present simulations of charge carrier motion in a system of discotic molecules with high levels of shape anisotropy; using explicitly calculated parameters we are able to capture and quantify the effect on charge transport anisotropy. We also consider the use of network models to describe collective behaviour.

11.04.2017 Luca Heltai (SISSA mathLab, Trieste)

Title: A numerical framework for optimal locomotion at low Reynolds numbers

Abstract: Swimming (advancing in a fluid in the absence of external propulsive forces by performing cyclic shape changes) is particularly demanding at low Reynolds numbers. This is the regime of interest for microorganisms and micro- or nano-robots, where hydrodynamics is governed by Stokes equations, and swimming is complicated by the fact that viscosity dominates over all participating forces. We exploit a formulation of the swimming problem in the context of Control Theory, and we present a numerical approximation scheme based on Boundary Element Methods (BEM) and reduced space Successive Quadratic Programming (rSQP) that is capable of computing efficiently optimal strokes for a variety of micro swimmers, both biological and artificial. We apply this framework to the study of the locomotion of euglenids (one of the best-known groups of flagellates). These organisms exhibit an unconventional motility strategy amongst unicellular eukaryotes, consisting of large-amplitude highly concerted deformations of the entire body (euglenoid movement or metaboly). We identify previously unnoticed features of metaboly, and we find that metaboly accomplishes locomotion at hydrodynamic efficiencies comparable to those of ciliates and flagellates. Our results suggest new quantitative experiments, provide insight into the evolutionary history of euglenids, and suggest that the pellicle may serve as a model for engineered active surfaces with applications in microfluidics.