All lectures will take place in Lecture Theatre 8W2.1

Abstracts of Lectures

Doug Arnold

Institute for Mathematics and its Applications, University of Minnesota, USA.

Differential complexes such as the de Rham complex have recently come

to play an important role in the design and analysis of numerical

methods for partial differential equations. The design of stable

discretizations of systems of partial differential equations often

hinges on capturing subtle aspects of the structure of the system in

the discretization. In many cases the differential geometric structure

captured by a differential complex has been found to be an essential

element, and a discrete differential complex which is appropriately

related to the original complex is essential. This new geometric

viewpoint provides a unifying understanding of a variety of innovative

numerical methods developed over recent decades, in particular for the

stable approximation of electromagnetic problems. Very recently it has

enabled the development of new algorithms for elasticity problems with

properties previously unattainable. And it seems likely to provide an

important element for the solution of numerical problems beyond current

capabilities, such as the simulation of gravitational wave emission

from colliding black holes.

School of Mathematical Sciences, University of Nottingham, UK

In view of increasing experimental evidence that normal and cancerous

cells alter their behaviour in response to mechanical effects, it is important

to develop mathematical models that can incorporate such features. In this

talk I will explain how multiphase models can provide an appropriate mathematical

framework to do this. I will illustrate this by focusing on tumour encapsulation,

the process by which some tumours become surrounded by a thick collagenous

capsule, and tumour invasion.

School of Mathematics and Statistics, University of Birmingham, UK

In this talk I will give an overview of work that we have done at Birmingham

on modelling a variety of solid oxide fuel cell systems. A solid oxide fuel cell

is a device thatgenerates electricity directly from the combustion of fuel.

I will discuss:

(i) A planar solid oxide fuel cell

(ii) A tubular solid oxide fuel cell

(iii) Surface catalysed combustion waves in tubular fuel cells

The talk will introduce the new filter techniques for nonlinear optimization,

starting from the general constrained programming case. The discussion will

then focus on how these ideas can be extended to the case of nonlinear equations,

and an algorithm will be presented. Some numerical results will then be

given and perspectives drawn.

Department of Mathematical Sciences, University of Bath, UK

eigenvalue in the case that the operators involved are real-analytic.The central

role of real-analyticy in the Stokes-wave problem will be explained, including

its implications for the existence of secondary bifurcations far away from the

primary bifurcation, and periodic-multiplying sub-harmonic bifurcations.