SIAM UK and Republic of Ireland Section
Annual Meeting
University of Bath, January 10th 2003
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 in numerical analysis
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.

Helen Byrne
School of Mathematical Sciences, University of Nottingham, UK

Multiphase models of solid tumour growth
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.

John Billingham
School of Mathematics and Statistics, University of Birmingham, UK

Mathematical Modelling of   Solid Oxide Fuel Cells
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

Philippe Toint
Department of Mathematics,  University of Namur, Belgium

The filter idea and its application to nonlinear equations and nonlinear least-squares
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.

John Toland
Department of Mathematical Sciences, University of Bath, UK

Global Real-analytic bifurcation theory and its use in Stokes-wave theory
This lecture will survey the global implications of bifurcation from a simple
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.