UK Nonlinear News Review

UK and Republic of Ireland SIAM Section Annual Meeting
Held 7th January, 2005 in Cork.

James Gleeson and Gabriel Lord

This was the first annual meeting of the section held in the Republic of Ireland and coincided with the opening of Cork as European City of Culture. Despite the rain and wind there was an excellent turnout for the meeting at the University College Cork (UCC).

The first speaker was Neil O' Connell (Warwick) who gave an informative survey talk on random matrices. Starting with some applications of random matrices including telephone encryption he examined the distribution of eigenvalues of random (orthogonal and unitary) matrices. By analogy with electrostatics he explained why the eigenvalues are more regularly spaced than might be expected. An open puzzle is a phase transition in the distribution of eigenvalues of powers of unitary matrices. Finally it was explained how eigenvalues of random unitary matrices are closely related, in a statistical sense, to the zeros of the Riemann zeta function.

Niall O Murchadha (UCC) gave an entertaining talk on the degrees of freedom of the gravitational field as specified by the equations of General Relativity, an appropriate topic in the centenary year of 3 of Einstein's seminal publications. He made extensive use of the analogy with the Maxwell equations of the electromagnetic field to show the necessity of splitting the equations into constraint and evolution parts. His talk placed the research in historical context, and showed how it underlies current efforts in numerical relativity. A question regarding the well-posedness of the evolution equations provided further opportunity for the speaker to demonstrate his enthusiasm for this fascinating subject, and to highlight the difficulty of outstanding research challenges.

After a lunch Ivan Graham (Bath) described efficient boundary element methods (BEMs) for PDEs. Typical applications for the method such as the electrostatic capacitance of a bounded object were presented. This clear and interesting talk contrasted the BEM to a standard finite element or finite difference method and surveyed some recent results. Some of the mathematical challenges were presented such as the irregularity of the solutions due to the irregularity of the boundaries and results presented. It was shown how, with a fast matrix vector multiplication method, that the complexity of the BEM was competitive with that of a FEM. This was both for quasi-uniform and degenerate meshes.

Russell Davies (Aberystwyth) gave an interesting talk on wobble, creep and relaxation where he is modelling materials with memory. He enthusiastically explained that what constitutes a fluid depends on the time scale of the observations : including sagging tombstones and mountains flowing. He talked on the corkscrew instability that arises in extrusion of plastics or similar visco-elastic flows. He then asked why a jelly wobbles. The answer, in terms of mathematics, was given as a Sturm-Liouville problem. An open question, of relevance to the industrial processing of all polymeric materials, is to determine the dominant rate of decay of the transient. The final speaker, Alexei Pokrovskii (UCC), introduced equations with hysteresis nonlinearities. He used computer applets to illustrate the important rate-independent property of hysteresis, which cannot be easily described in terms of standard mathematical formulas. The Krasnoselskii program for investigating hysteresis was outlined, and stress was laid upon the Identification Theorem, which links many types of hysteresis behaviour to the Preisach operator. The lecture concluded with an overview of some recent results on the complicated behaviour of a pendulum subject to hysteresis, including a rigorous proof of the existence of chaos.

Business meeting

This was held after an excellent lunch. The UKIE section president, Martin Stynes, gave a brief overview of the past year and reminded the members present that the posts of President and Vice-President become vacant at the end of March 2005 and nominations for were solicited. The secretary reported on finances and activities funded in the year including the 5 student prizes presented. It was generally agreed that these activities should be continued and if possible extended.

The meeting thanked Trevor Stuart and Andy Wathen for their hard work in trying to arrange a joint meeting with the LMS, IMA, CMS and SIAM in the UK which unfortunately fell through. It was agreed that there is still strong interest in UKIE SIAM in holding SIAM Conferences either the UK or Republic of Ireland. Andy Wathen noted that SIAM will be holding the 2005 SIAM Conference on Optimization in Stockholm and if that goes well further meetings outside the US may occur. He also noted that the European representatives on Board and Council were always willing to raise any points members might have.

In answer to some specific points raised at the meeting.

*) The UKIE section is linked from http://www.siam.org/sectchapt/sections.htm

*) The meeting appeared on http://www.siam.org/meetings/calendar.htm

The next annual meeting will be in January 2006, preferably Jan 6, venue to be decided.