UK Nonlinear News, May 1996

Nonlinear Research at Heriot-Watt

General

There is a large research group at Heriot-Watt in applied nonlinear systems. This comprises J.M. Ball, K.J. Brown, J. Carr, D.B. Duncan, J.C. Eilbeck, R.N. Hills, R.J. Knops, A.A. Lacey, M. Levitin, O. Penrose, D.G. Roxburgh, B.P. Rynne and K. Zhang.

Its basic research themes are the modelling of physical systems, the analysis of the resulting ordinary and partial differential equations, and the use of scientific computation to analyse the resulting models. The main areas of activity are Elasticity and the Calculus of Variations, Infinite-Dimensional Dynamical Systems, Reaction-Diffusion Equations, Statistical Physics and Phase Transitions, Nonlinear Waves and Solitons. Over many years this group has pioneered the use of analysis in modelling and has demonstrated that these methods give scientific information not available by other means. Examples of this include material microstructure, and the use of Statistical Physics in continuum modelling, such as phase-field models with applications to diffusion induced grain boundary motion.

International Centre for Mathematical Sciences

The department has strong links with the International Centre for Mathematical Sciences (ICMS), a joint venture of Edinburgh and Heriot-Watt Universities, founded in 1990 to provide a centre of excellence in the Mathematical Sciences.

Research Grants

The department has received a number of EC HCM grants for EC fellows in nonlinear areas, and coordinates an HCM network in `Reaction-Diffusion Equations' containing a total of 6 sites with a budget of 400,000 ecus.

Members of the department are involved in a EC network `Phase Transitions and Surface Tension' and INTAS networks in `Exactly solvable 3D models of statistical mechanics' and `Nonlinear modes in quasi-one-dimensional polymers and high-temperature superconductors'.

Applied Nonlinear Research

The work of the nonlinear systems group is especially relevant to the areas of modelling, simulation and prediction of complex systems. One example is the work with Unilever on the dynamics of populations of mixed micelles modelled by coagulation fragmentation equations.

In materials modelling, a key challenge for future years is to understand how to derive and reconcile models for the same system at different length-scales (e.g. atomic, continuum), for which the group's work on statistical physics and material microstructure is particularly pertinent.

We also place great value on our links with industry and other organisations. In recent years this has included collaboration with the British Geological Survey in modelling seismic wave interactions with complicated rock formations and with British Gas in modelling flow in their main transmission network.

We were recently awarded a Teaching Company Scheme grant for modelling and simulation of the welltest process used in oil reservoir exploration. We have also gained a variety of industrial projects for the research component of our MSc in the Mathematics of Nonlinear Models (a joint course run with Edinburgh University).

An interesting collaboration has been developed with Professor M Russell at the Rutherford Laboratory, who has been appointed to a visiting professorship at Heriot-Watt, in the area of solitons and breathers in solid state physics. This work has many potential applications in the areas of High Temperature Superconductivity and in spluttering technologies in material science.

Some staff research interests in Nonlinear Science


Chris Eilbeck / Heriot-Watt University / chris@ma.hw.ac.uk

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