Wed, 07 Mar 2007
12:00
Comlab

Team Meeting

Guest speaker Antonio Orlando
(Swansea)
Abstract

The modelling of the elastoplastic behaviour of single

crystals with infinite latent hardening leads to a nonconvex energy

density, whose minimization produces fine structures. The computation

of the quasiconvex envelope of the energy density involves the solution

of a global nonconvex optimization problem. Previous work based on a

brute-force global optimization algorithm faced huge numerical

difficulties due to the presence of clusters of local minima around the

global one. We present a different approach which exploits the structure

of the problem both to achieve a fundamental understanding on the

optimal microstructure and, in parallel, to design an efficient

numerical relaxation scheme.

This work has been carried out jointly with Carsten Carstensen

(Humboldt-Universitaet zu Berlin) and Sergio Conti (Universitaet

Duisburg-Essen)

Mon, 05 Mar 2007
14:15
DH 3rd floor SR

Pinning of a polymer in a random medium and interacting particle system.

Dr Vincent Beffara
(ENS Lyon)
Abstract
  We present a link between polymer pinning by a columnar defect in a random medium and a particular model of interacting particles on the line, related to polynuclear growth. While the question of whether an arbitrarily small intensity for the defect always results in pinning is still open, in a 'randomized' version of the model, which is closely related to the zero-temperature Glauber dynamics of the Ising model, we are able to obtain explicit results and a complete understanding of the process. This is joint work with Vladas Sidoravicius and Maria Eulalia Vares.  
Fri, 02 Mar 2007
16:30
L2

How model theory looks at Lie groups and Lie Algebra

Prof. Angus MacIntyre
(Queen Mary University, London)
Abstract
  Model theory typically looks at classical mathematical structures in novel ways. The guiding principle is to understand what relations are definable, and there are usually related questions of effectivity. In the case of Lie theory, there are two current lines of research, both of which I will describe, but with more emphasis on the first. The most advanced work concerns exponentials and logarithms, in both real and complex situations. To understand the definable relations, and to show various natural problems are decidable, one uses a mixture of analytic geometry with number-theoretic conjectures related to Schanuel's Conjecture. More recent work, not yet closely connected to the preceding, concerns the limit behaviour (model-theoretically), of finite -dimensional modules over semisimple Lie algebras, and here again, for decidability, one seems obliged to consider number-theoretic decision problems, around Siegel's Theorem.
Thu, 01 Mar 2007

14:00 - 15:00
Comlab

Linear and nonlinear semidefinite programs in structural optimization

Prof Michal Kocvara
(University of Birmingham)
Abstract

Several formulations of structural optimization problems based on linear and nonlinear semidefinite programming will be presented. SDP allows us to formulate and solve problems with difficult constraints that could hardly be solved before. We will show that sometimes it is advantageous to prefer a nonlinear formulation to a linear one. All the presented formulations result in large-scale sparse (nonlinear) SDPs. In the second part of the talk we will show how these problems can be solved by our augmented Lagrangian code PENNON. Numerical examples will illustrate the talk.

Joint work with Michael Stingl.