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.


2018  
08.05.2018  Simon Praetorius (TU Dresden) 
Title: tba 

27.03.2018, 13:30  Dr. Esteban Meca (Agronomy Department, University of Cordoba, Spain) 
Title: Localized Instabilities in PhaseChanging Systems: The Effect of Elasticity Abstract: tba 

07.03.2018, 14:00 
Matthias Liero (WIAS) 
ErhardSchmidt lecture room 
Title: Modeling and simulation of charge transport in organic semiconductors via kinetic and driftdiffusion models Abstract:
The use of organic materials in electronic applications such as displays, photovoltaics, lighting, or transistors, has seen an substantial increase in the last decade.
This is mainly due to the lower production cost, sustainability, and flexibility.
Moreover, the toolbox of organic chemistry opens an enormous potential for new device concepts.

21.02.2018 
joint seminar with Langenbach Seminar
Dr. M. Morandotti (TU München) 
Title: Dimension reduction in the context of structured deformations Abstract: The theory of structured deformations shows good potential to deal with mechanical problems where multiple scales and fractures are present. Math ematically, it amounts to relaxing a given energy functional and to show also the relaxed one has an integral representation. In this seminar, I will focus on a problem for thin objects: the derivation of a 2D relaxed energy via dimension reduction from a 3D energy, incorporat ing structured deformations in the relaxation procedure. I will discuss the twostep relaxation (first dimension reduction, then structured deformations and vice versa) and I will compare it with another result in which the two relaxation procedures are carried out simultaneously. An explicit example for purely interfacial initial energies will complete the presentation. These results have been obtained in collaboration with G. Carita, J. Matias, and D.R. Owen. 

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 NavierStokesFourier (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. 

2017  
14.12.2017, 14:00 
Bartlomiej Matejczyk (University of Warwick ) 
ErhardSchmidt 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.

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 nonhomogeneous 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 (KarlFranzensUniversität Graz) 
starts at 1:45 PM 
Title: Homogenization of the generalized PoissonNernstPlanck system with nonlinear interface conditions Abstract: We consider the generalized system of nonlinear PoissonNernstPlanck 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 quasiFermi 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 electrochemical reactions on the interface in a periodic twophase medium. We aim at a proper variational modeling, wellposedness, 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 energydissipation 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.


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 macroscale. Starting from the most known MultiFunctional materials, a common modeling approach, based on the definition of constitutive relationships, is discussed.

17.05.2017
starts at 3:15 PM 
joint seminar with Langenbach Seminar
Riccarda Rossi (University of Brescia) 
Title: In Between Energetic and Balanced Viscosity solutions of rateindependent systems: the ViscoEnergetic concept, with some applications to solid mechanics Abstract: This talk focuses on weak solvability concepts for rateindependent systems.
ViscoEnergetic solutions have been recently obtained by passing to the time
continuous limit in a timeincremental scheme, akin to that for Energetic
solutions, but perturbed by a "viscous" correction term, as in the case of
Balanced Viscosity solutions. However, for ViscoEnergetic 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.
ViscoEnergetic evolution can be thus thought as "inbetween" Energetic and Balanced Viscosity evolution.


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.

09.05.2017  Mathias Schäffner (TU Dresden) 
Title: Stochastic homogenization of discrete energies with degenerate growth Abstract:
We present a discretetocontinuum 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 Gammaconverges almost surely to a deterministic, homogeneous and nondegenerate integral functional.


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 multiscale 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 nanorobots, 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 bestknown groups of flagellates). These organisms exhibit an unconventional motility strategy amongst unicellular eukaryotes, consisting of largeamplitude 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. 