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.


2022  
Until further notice, the seminar will be held online using Zoom (no registration required).
The link will be send around at WIAS. External guests who want to participate, please contact the organizer provided with the talk for login details. 

Thur. 29.09.2022, 16:00  Bob Eisenberg (Rush University, Chicago) 
Title: From Maxwell to Mitochondria Abstract: Applying Maxwell equations to atoms and ions in a mitochondrion or chloroplast seems a hopeless task: there are so many ions (~10^{18}) and such complexity. But nerve axons, computers and their chips are as complicated. Analysis of nerve conduction is now an old story, so successful it is not known to young scientists. Analysis of the propagating nerve signal, from nerve, to membrane, to conductance, to channel protein, to atoms within the channel is done by computing the flow of ions, using Kirchhoff's law. Charges are not dealt with explicitly: there are just too many to deal with. Kirchhoff's Current Law is also the chief design tool of the circuits that make our computers and phones. Charge is hardly mentioned in circuit design. Kirchhoff's Current Law seems to imply the conservation of ion flux , but Maxwell's equations do NOT conserve ion flux. Maxwell's equations conserve only the total current J_{total} = J + ε_{0} ∂ E / ∂ t. J_{total} equals ion flux plus the `ethereal' displacement current which `flows' everywhere including in a vacuum, where it propagates light. Maxwell and Kirchhoff's discovery of ε_{0} ∂ E / ∂ t as an unavoidable component of total current allows simple circuit laws to compute nerve conduction from atoms to axons. It allows design of systems made of ~10^{12} semiconductor devices, that switch in 10^{10} sec and function reliably over a wide range of conditions: error rate 10^{14} per second. Oxidative phosphorylation provides the chemical energy of animal life. Its components are embedded in the membranes of mitochondria. Cytochrome c Oxidase is a crucial component that can be analyzed using circuit laws, as we (Shixin Xu, Zilong Song, and I, led by Huaxiong Huang) have shown. Diffusion, current flow, water flow, and chemical reactions are included combining the universal conservation of total current with Chun Liu's theory of complex fluids. Our approach applies to active transport systems of mitochondria, chloroplasts, and other cells. It includes the classical theory of nerve conduction. The analysis allows easy inclusion of more molecular and chemical details of oxidative phosphorylation as we learn of them, and they are discovered. In particular, atomic scale chemical reactions are coupled by Kirchhoff's current law with important biological and chemical consequences. Sodium and potassium channels are coupled in an action potential by Kirchhoff's current law. So are the enzyme complexes I, II, III, IV and V in a mitochondrion and chloroplast. 

Mo. 19.09.2022, 13:30  Robert Jack (University of Cambridge) 
Title: Examples of hydrodynamic behaviour in twospecies exclusion processes Abstract: We discuss several different results for simple exclusion processes with two species of particles.
We first show numerical results where inhomogeneous states appear in twodimensional systems where the species are driven in opposite directions, and we explain how these results can be rationalised by considering hydrodynamic PDEs for the density [1].
We then discuss how hydrodynamic equations in such models can be characterised, including a systematic analysis based on the method of matched asymptotics [2].
Finally, I will present some results [3] for large deviations in the hydrodynamic limit, associated with fluctuations of the entropy production in a simple model of active matter [4].


12.07.2022  Steinar Evje (University of Stavanger, Norway) 
Title: A cellfluidmatrix model to understand how aggressive cancer cell behavior possibly is linked to elevated fluid pressure Abstract: Recent research, preclinical (mouse) and clinical (patient) observations, has suggested that high interstitial fluid pressure in a tumor is associated with aggressive cancer cell behavior, i.e., cancer cells tend to detach from the primary tumor and are able to escape to lymphatics vessels outside the tumor (Hompland et al, Cancer Research 2012). This is referred to as metastasis and is the main reason why cancer becomes a deadly disease. How to explain this phenomenon? Our objective has been to formulate a mathematical cellfluidmatrix model that can account for two experimentally observed cancer cell migration mechanisms, as reported by Polacheck et al (PNAS 2011 and 2014). Both mechanisms are sensitive to fluid flow and therefore represent natural candidates when we formulate a model that can explore the possible relation between aggressive cancer cell behavior and interstitial fluid pressure (IFP). In the presentation I will relate the proposed model to the celebrated chemotaxis(Navier)Stokes model, proposed by Tuval et al (PNAS 2005), which has attracted many applied mathematicians and generated a considerable amount of results in mathematical analysis (wellposedness, as well as qualitative characterization). Our approach relies on using a twophase formulation where cells and fluid are described in terms of two separate mass and momentum equations where different interaction forces between cells, fluid, and matrix can be accounted for in the momentum balance law. This type of two phase (Navier)Stokes model (compressible version) represents another active area of research within applied mathematics for those interested in fluid mechanical models. Finally, an example of a reduced version of our cellfluid model is mentioned and a mathematical result obtained for this model (Winkler and Evje, 2020). 

23.06.2022, 14:00  Giovanni Ligorio (HumboldtUniversität zu Berlin) 
Title: Neuromorphic device development: from modification of surfaces to modification of functions Abstract: The versatility offered by organic molecules and polymers holds great functional and economic potential for optoelectronic devices. The chemical modification of electrodes with organic materials is a common approach in our group for tuning the electronic landscape between interlayers in devices, thus facilitating charge carrier injection/extraction and improving device performance. A common tool to modify the electrode interfaces is to use covalently bound molecules carrying a permanent electric dipole group. Beside employing molecules with constant dipole, we also investigated the possibility to use switchable photochromic molecules which undergo structural modification when illuminated with light. This allows a dynamic and reversable control of the electronic properties. The gained control over the device performance enables additional functionalities in devices, such as neuromorphic applications. Neuromorphic engineering takes inspiration from the functionalities and structure of the brain to solve complex tasks and enable learning. Yet, hardware realization that simulates the synaptic activities realized with electrical devices is still not as advanced as the common implementation in computer software. In my talk I will present different approaches to emulate synapses and to fabricate both (i) optical and (ii) electronic synaptic devices. The first (i) were achieved by employing the abovementioned photochromic molecules. This allowed control of the optical properties of gold films by reversibly modulating the surface plasmon resonance. The second (ii) were achieved by fabricating twoterminal devices based on mixed ionicelectronic conducting polymers that serve as active layer for ions and charge carrier conduction. The precise understanding and modeling of device functions will allow to fully exploit the potential of these synthetic synapses. For this purpose, a mathematical description of their behaviour might allow to move from single devices to networks and enable in materia computing. 

31.05.2022  Eric Sonnendrücker (Max Planck Institute for Plasma Physics) 
Title: Geometric Numerical Methods for Models from Plasma Physics Abstract: Many kinetic and fluid plasma models, like the VlasovMaxwellLandau or the Magnetohydrodynamics (MHD) models feature a hamiltonian part that can be described by a Poisson bracket and a Hamiltonian and a dissipative part. The hamiltonian part features in general different kinds of invariants that play a fundamental role in the evolution of the system. On the other hand the dissipative part strictly dissipates an entropy. For an accurate long time numerical simulation of these models, keeping as much as possible from the structure of the original equations is essential, which will automatically enforce the preservation of some important invariants like for example div B = 0. In this talk we will give an overview of structure preserving discretisation of such models based on Discrete Exterior Calculus. In particular we will show how a Particle In Cell discretisation of the Vlasov Equation coupled with a Finite Element Exterior Calculus discretisation for Maxwell's equations involving a discrete de Rham complex and an appropriate Finite Element approximation of each field leads to a Finite Dimensional Hamiltonian system, which then can be discretised in time with geometric integrators like hamiltonian splitting or exact energy preserving discrete gradient methods. 

26.04.2022, 13:30  Alessia Nota (Universitá degli studi dell'Aquila (UnivAq)) 
Title: Stationary nonequilibrium solutions for coagulation equations Abstract: Smoluchowski's coagulation equation, an integrodifferential equation of kinetic type, is a classical model for mass aggregation phenomena extensively used in the analysis of problems of polymerization, particle aggregation in aerosols, drop formation in rain and several other situations. In this talk I will present some recent results on the problem of existence or nonexistence of stationary solutions to coagulation equations, for single and multicomponent systems, under nonequilibrium conditions which are induced by the addition of a source term for small cluster sizes. The most striking feature of these stationary solutions is that, whenever they exist, the solutions to multicomponent systems exhibit an unusual "spontaneous localization" phenomena. More precisely, the stationary solutions to the multicomponent coagulation equation asymptotically localize into a direction determined by the source term. The localization is a universal property of these multicomponent systems. Indeed, it has been recently proved that localization phenomenon occurs with a great degree of generality also for time dependent solutions to mass conserving coagulation equations. (Joint work with M.A. Ferreira, J. Lukkarinen and J.J.L. Velázquez) 

2021  
23.11.2021, 13:30  Silvia Budday (FAU Erlangen) 
Title: Brain mechanics across scales Abstract: tba For a zoom login details, please contact Dirk Peschka. 

2020  
21.04.2020, 14:00  Alfonso Caiazzo (WIAS) 
Title: Modeling of biological flows and tissues Abstract: The talk shows results of ongoing research in RG3 related to modeling of blood flows and biological tissues. After a brief introduction on medical imaging techniques  especially magnetic resonance elastography  the first part of the talk will discuss multiscale models for the simulation of vascularized tissues, using immersed methods. As next, we will introduce the equations and the challenges in computational hemodynamics, recent results and recently started collaborations. For a zoom login details, please contact Dirk Peschka. 

2019  
03.12.2019, 13:30  Michal Pavelka (Charles University, Prag) 
Title: Symmetric Hyperbolic Thermodynamically Compatible (SHTC) equations within GENERIC Abstract: tba 

25.07.2019, 10:00 
Dr. Robert Style (ETH Zürich) 
Title: Arresting phase separation with polymer networks Abstract: Some of the most beautiful colours in nature are seen in birds that have developed materials with extremely monodisperse, colloidal microstructures (these yield vivid structural colours). Previously it has been suggested that these can be grown by a process of arrested phase separation. Here, we take inspiration from such natural materials to grow composites with a uniform microstructure via a process of phase separation in an elastic gel network. These composites consist of uniform liquid droplets embedded in an elastic gel. The size of the droplets can be easily tuned with a number of different parameters, and presents an interesting challenge for modelling. I will also discuss how this process has applications in colloidal synthesis and phaseseparation processes in living cells. 

09.07.2019, 13:30  Carsten Graeser (FU Berlin) 
Title: Truncated nonsmooth Newton multigrid for nonsmooth minimization problems Abstract: Many problems originating from continuum mechanics and material sciencelead to large scale nonsmooth optimization problems after discretization in time and space. Examples are classical binary or multicomponent phase field models for phase transition and separation, frictional contact problems, plasticity, and phase fieldlike approaches for brittle and ductile fracture. Since standard numerical methods like, e.g., multigrid are not directly applicable due to the nonsmoothness, generic nonsmooth optimization methods are frequently used for such problems which often comes at the price of reduced efficiency. In the talk we present the Truncated Nonsmooth Newton Multigrid (TNNMG)method which combines techniques from nonsmooth optimization with multigrid and domain decomposition ideas. Instead of a black box approach this is done in a structure aware fashion leading to iterative methods whose efficiency is comparable to state of the art methods for smooth problems while being robust with respect nonsmoothness. In the talk we will introduce the algorithm, discuss convergence, and present numerical examples for various applications illustrating the efficiency of the presented approach. 

25.06.2019, 13:30  Luca Heltai (SISSA mathLab, Trieste) 
Title: Unconventional frameworks for the simulation of coupled bulkinterface problems Abstract: Partial differential equations with interfaces, holes, cracks, or defects often require the numerical solution of coupled bulkinterface problems. In this talk, I will discuss and analyse some techniques that can be used to tackle this class of problems, using nonmatching discretisations that combine Finite Element Methods, regularization techniques, weighted Sobolev spaces, and reduced order models. 

18.06.2019, 13:30  Amit Acharya (Carnegie Mellon University Pittsburgh) 
Title: Line Defect dynamics and solid mechanics Abstract: Continuum mechanics has been a successful model for studying macroscopic deformations and the forces causing them. The usual framework allows the study of continuous deformations giving way to surfaces of discontinuity, but does not provide an adequate framework for considering the dynamics of the terminating lines of surfaces of discontinuity, were such to occur. It turns out that such terminating lines of surfaces of discontinuity serve as a model of common line defects that arise in a host of materials; dislocations and grain/phase boundary junctions in crystalline and soft matter. I will describe a framework for considering line defect dynamics within continuum mechanics. I will show how the kinematics of line defect dynamics provides a unifying theme for describing the defects mentioned above, resulting in an augmentation of the classical balance laws of continuum mechanics with a microscopic conservation law for topological charge carried by these defect lines. The theory will be illustrated with examples related to dislocation dynamics with inertia, the computation of fields of interfacial defects like the star disclination and grain boundary disconnections. 

04.06.2019, 13:30  Giselle Monteiro (Czech Academy of Sciences , Prague) 
Title: On the convergence of viscous approximation for rateindependent processes with regulated inputs Abstract: The vanishing viscosity method is a popular tool for describing rateindependent evolution. It consists in the analysis of the limiting behavior of a regularized problem obtained by introducing a viscous dissipation mechanism which stabilizes the process. In this talk, we discuss some issues related to viscous approximations to rateindependent processes when different choices of the viscosity operator are considered. We show that the viscous limit exists, and the associated inputoutput operator is continuous in the space of regulated functions. Notably, we observe that the vanishing viscosity limit may exhibit some unexpected behavior when the input has some jump discontinuities. 

14.05.2019  Mirjam Walloth (TU Darmstadt) 
Title: Reliable, efficient and robust a posteriori estimators for the variational inequality in fracture phasefield models Abstract: tba 

07.05.2019, 13:30  Rainer Falkenberg (BAM) 
Title: Aspects on the modelling of material degradation Abstract: Material degradation describes the loss of nominal strength. The physical causes as well as the consequences are often manifold: Mechanical loads exceeding a threshold value or temperature/speciesinduced effects are possible and can lead e.g. to a reduced loadbearing capacity in general or to crack initiation and propagation in a local sense. The formulation and solution of this initial boundary value problem must therefore cover some crucial aspects: e.g. the fulfillment of the second law of thermodynamics by the constitutive as well as the degradation model or the consideration of the PDE system's stability loss when dealing with strict local models. Wellestablished models that will be discussed in the finiteelement framework are the fracturemechanics based cohesive zone model, the damagemechanics based phasefield model and the micromechanicsbased Gursonmodel. Furthermore, an extension will be presented that allows for the simulation of corrosion processes. 

23.04.2019, 13:30  Marijo Milicevic (U Freiburg) 
Title: The alternating direction method of multipliers with variable step sizes for the iterative solution of nonsmooth minimization problems and application to BVdamage evolution Abstract: The alternating direction method of multipliers (ADMM) is a flexible numerical method to solve a large class of convex minimization problems. Its most significant properties are the unconditional convergence with respect to the involved step size and the direct applicability. However, the performance critically depends on the choice of the step size. We propose an automated step size adjustment that relies on the monotonicity of the residual to accelerate the ADMM. Numerical experiments show a remarkable improvement over the standard ADMM with fixed step sizes. The ADMM with variable step sizes is then applied to a model for rateindependent, total variation regularized damage processes. The total variation regularization of the damage variable leads to sharp transitions of damaged to undamaged areas in the material. The results are compared to an H^{1} regularization of the damage and the simulations reveal that, indeed, for the total variation regularization sharp transitions can be observed whereas for the H^{1}regularization the interface is smeared out. 

Thursday 28.02. 10am in Room 406 !!! 
Uwe Thiele (Westfälische WilhelmsUniversität Münster) 
Title: Gradient dynamics models for films of complex fluids and beyond  dewetting, line deposition and biofilms Abstract:
After briefly reviewing a number of experiments on
dewetting and evaporating thin films/drops of simple and complex liquids,
I introduce the concept of a gradient dynamics description of the evolution
of interfacedominated films and drops on solid substrates.
First, the case of films/drops of simple nonvolatile liquid is discussed,
and illustrated with results on droplet patterns and sliding droplets.
As a further example, the diffusion equation is formulated as a gradient dynamics.
The obtained elements are combined into a thermodynamically consistent gradient dynamics formulation for films of mixtures and surfactant suspensions.


29.01.2019, 13:30  Vittorio Romano (University of Catania) 
Title: Charge and phonon transport in graphene Abstract: ( pdf)
The last years have witnessed a great interest for 2Dmaterials due to their promising applications.
The most investigated one is graphene which is considered as a potential new material to exploit in nanoelectronic and optoelectronic devices.


2018  
13.11.2018, 13:30  Alex Christoph Goeßmann (Fritz Haber Institute of the Max Planck Society) 
Title: Representing crystals for kernelbased learning of their properties Abstract: Accurate modeling of manybody systems like crystals requires to capture their quantummechanical nature at the atomic scale. The solution of the associated electronic structure problem is however illusional due to the number of variables, but we obtain certain properties by computationaldemanding methods like densityfunctional theory. In this talk, I will discuss the potential of kernelbased machine learning to circumvent this computational bottleneck and predict crystal properties. A crucial preliminary step is the representation of crystals, which has to satisfy different conditions for the learning to perform optimally. 

16.10.2018, 13:30  Arik Yochelis (BenGurion University of the Negev, Israel) 
Title: From solvent free to dilute electrolytes: A unified continuum approach Abstract: tba 

16.10.2018, 10:15 
Dr. Ch. Kuhn / Dr. A. Schlüter (Technische Universität Kaiserslautern) 
Title: Phase field modelling of fracture  From a mechanics point of view Abstract: tba 

08.05.2018, 13:30  Simon Praetorius (TU Dresden) 
Title: From individual motion to collective cell migration Abstract:
The motion of living cells plays an important role in many important processes, like in wound healing, as part of the immune system, and in tissue development.
Modeling the migration of cells thereby involves the study of the motion of a single cell and on collective behavior of many cells.


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. 