## Autumn 2011

Date Speaker Title/Abstract
7 Oct Sophia Demoulini
University of Cambridge
Weak and yet weaker solutions of time-dependent nonlinear elasticity and viscoelasticity
For three dimensional elasticity we discuss a global existence theorem of measure-valued solutions with polyconvex stored energy function, and weak-strong uniqueness (recovery of strong solutions). This in particular makes use of the polyconvex structure, namely the null Lagrangians. We will also see the use of relative entropy as a tool in the analysis of weak and measure-valued solutions. For viscoelasticity we discuss conditions for both global measure-valued and classical weak solutions, and conditions under which the recovery of the classical weak solution is guaranteed from a measure-valued solutions.
14 Oct Landscape seminar
21 Oct Florian Theil
University of Warwick
Periodic ground state in two and three dimensions
We consider the asymptotic behavior of minimizers of pair interaction interaction energies $$E(y) = \sum_{1 \leq i < j \leq N} V(|y_i - y_j|)$$ as $N$ tends to infinity, where $y_i \in R^d$, $d =2$ or $d=3$. Intuitively one expects that for 'reasonable' potentials the limit will be a highly symmetric structure: a lattice. We construct open sets of potentials in $C^2$ for which it can be shown rigorously that the the minimizers converge to a triangular lattice in two dimensions and a face-centered cubic lattice in three dimensions. The proof relies on several new results in discrete geometry. Those results are established with the support of a computer program.
28 Oct Landscape seminar
4 Nov
CNRS – Paris 6
Travelling fronts for time heterogeneous Fisher-KPP equations
11 Nov Landscape seminar
18 Nov Aram Karakhanyan
University of Edinburgh
Regularity of free boundary for a stationary heat transfer problem
In this talk I will discuss the Stefan problem with given constant convection. The objective is to study the optimal regularity of the solution and the free boundary for both one phase and two phase problem.
25 Nov Landscape seminar
2 Dec Ali Taheri
University of Sussex
Energy minimisers on elastic annuli, generalised twists, SO(n) and the Spinor groups
9 Dec Landscape seminar
16 Dec Simon Blatt
University of Warwick
Analysis of O'Hara's knot energies
Abstract
12 Jan Hannes Uecker
University of Oldenburg
Approximating the dynamics of active cells in a diffusive medium by ODEs – Homogenization with Localization
joint work with J. Müller, TU München
Bacteria may change their behavior depending on the population density. Here we study a dynamical model in which cells of radius $R$ within a diffusive medium communicate with each other via diffusion of a signalling substance produced by the cells. The model consists of an initial boundary value problem for a parabolic PDE describing the exterior concentration $u$ of the signalling substance, coupled with $N$ ODEs for the masses $a_i$ of the substance within each cell. We show that for small $R$ the model can be approximated by a hierarchy of models, namely first a system of $N$ coupled delay ODEs, and in a second step by $N$ coupled ODEs. We give some illustrations of the dynamics of the approximate model.
Note: Despite this being a Thurday, this seminar takes place at 4.15 in 4W 1.7.