CNLS Research

The cross-disciplinary and inter-departmental nature of the CNLS is reflected in the wide range of research areas described below. As well as fundamental mathematical developments in dynamical systems and soliton theory, there are numerous applications to the physical and biological sciences and to engineering. On this page, we give a brief description of the main areas, pointing to other pages for more details.

Research Groups

A Brief Description of the Research Groups

Dynamical Systems . Most people are working with dynamical systems, but the people mentioned here work on fundamental mathematical developments or apply dynamical systems to a wide range of physical systems. Specifically, J. Brindley, D.W. Hughes, D.G. Knapp, C. Knudsen, and B.D. Sleeman, and their post-doctoral research assistants and research students work in both finite and infinite dimensional dynamical systems, including toral flows, noninvertible iterated maps, fractal geometry, numerical analysis, and hydrodynamical systems and applications to, for instance, physiology, chemistry, population dynamics, and engineering.

The research group has links and active collaborations with many dynamical systems groups around the world, e.g., USA, Germany, Italy, and Denmark.

Integrable Systems . The group consists of A.P. Fordy, A.V. Mikhailov, F.W. Nijhoff, V.B. Kuznetsov and their post-doctoral research assistants and research students. The group has a wide range of interests in soliton theory and integrable systems, including completely integrable Hamiltonian systems, classical and quantum many body problems, Painlevé analysis, symmetries and conservation laws, Darboux transformations, geometry and nonlinear optics.

This group has very strong links and active collaborations with many groups around the world, particularly in Russia and FSU countries, France, Holland, Italy and the USA.

Reaction-Diffusion Systems . This group has a wide range of interests in the theory and application of nonlinear reaction-diffusion systems. The group consists of J.H.Merkin, B.D.Sleeman, their post-doctoral fellows and students.

Nonlinear Combustion Research . The University of Leeds contains one of the largest combustion research groups in the UK. Many different departments including Fuel and Energy, Mechanical Engineering, Chemistry and Chemical Engineering are brought together through the Centre for Combustion and Energy Studies, which runs its own MSc course and encourages collaborative research. Further links with Applied Mathematics and Physical Chemistry, through the CNLS, concerns research in a wide range of issues related to nonlinear combustion phenomena. These include: the mathematical and numerical investigation of nonlinear combustion mechanisms (Dr A.Tomlin, M.Pilling), the study of the properties and structure of flames and their coupling with acoustic disturbances (A.Macintosh, J.Brindley, G.Dixon-Lewis) and Ignition and explosion phenomena and chaos in combustion (S.K.Scott, J.Griffiths, G.Andrews).

Mathematical Chemistry . Professors Brindley and Scott, in association with Professors Gray, Merkin and Pilling, lead a substantial team of postdoctoral and postgraduate workers in this area covering instabilities (ignition and extinction), oscillations, chaos and travelling waves in chemical systems showing feedback. The group is widely recognised internationally for its outstanding experimental and theoretical contributions in this field, and this position has been reinforced by the publication of three books in the period of this report. Collaboration is particularly strong with Professor Ken Showalter (West Virginia University) and with workers in Budapest and Princeton in the area of lumping and model reduction in combustion (see below) and environmental projects.

Mathematical Biological . A sizable and active group, including J. Brindley, B.D. Sleeman, their post-doctoral research fellows and students is concerned with population dynamics, plankton modelling and other aspects of oceanic ecology,

Professor Holden leads a group involved in `reconstructing hearts and minds' through computational biology, making extensive use of computer visualisation. The general areas of interest here include synchronisation and attention in visual recognition and heart dynamics with particular reference to spatiotemporal dynamics of muscle excitation. Professor Brindley is also involved with studies of the general behaviour of `excitable media'.

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Last Updated: 21st. March, 1996.