The Centre For Non-Linear Studies

University of Leeds, Leeds, LS2 9JT, UK

1. History and Character
2. Aims
3. Activities
4. Principal Current Research Areas

1. History and Character

The CNLS was formally set up by the Council of The University of Leeds on November 17th 1984. Its creation was motivated by the recognition that scientific research in a number of fields across a wide range of disciplines was dependent on, or could be illuminated by, the ideas and concepts associated with the applied mathematics of low-order nonlinear dynamics and by the wish to exploit the rapidly developing advances in that area. The Centre was built upon, and formalised, a number of existing collaborations within the university and sought to share appropriate expertise between such groups and to develop and foster further collaboration, particularly across traditional academic disciplines.

The CNLS is not a formal employer, nor does it have its own research facilities. Its success depends entirely on the enthusiasm and activity of its members, whose responsibilities to their own academic departments has remained undiminished. The Centre is not funded directly in any formal sense: the financial resources available are limited to small sums principally intended to pay for visiting lecturers. More substantial grants for the support of research programmes are held by individual members on the CNLS within their parent departments.

Through its regular meetings and workshops, the Centre has begun to act as a national focus for the `nonlinear community', not least through the role played by Professor John Brindley as chairman of the SERC Applied Nonlinear Mathematics panel.

The Centre has various formal and informal links with other similar `centre' at other institutions within the UK and abroad.

2. Aims

The aims of the Centre as originally defined:

To a great extent these continue accurately to reflect the major focus of activity within the Centre as it approaches the end of its first decade.

3. Activities

The Centre plays host to many visitors, either formally or informally, usually in collaboration with a particular research project. Such visitors generally present one or more seminars during their stay. In some cases, these seminars constitute a longer lecture series or form the focus for short workshops. The Centre also runs regular half-day meetings (three per year) on topics of interest to its members at which invited speakers from outside the university join the local specialists or visitors. The Centre contributes to the seminar programme of the Department of Applied Mathematical Studies and considerable benefit has also developed from our close links with the recently-established Centre for Studies in Biomechanics and Medical Engineering (CBME).

The Centre also mounts regular postgraduate courses, such as An Introduction to Dynamical Systems, Nonlinear Wave Phenomena in Reaction-Diffusion Systems and Fundamental Concepts of Classical Chaos, that also are integrated into departmental postgraduate programmes.

Several members of the executive Committee are involved as editors of primary research journals in the general field of nonlinear science (Physica D; Physics Letters A; Chaos; Bifurcation and Chaos; Chaos Solitons and Fractals) or as series editors in nonlinear science for various publishing houses.

The Centre benefits from advice and active participation of its Visiting Professors and Fellows: J.F. Clarke FRS, D.G. Crighton FRS, P. Gray FRS and J.M.T. Thompson FRS.

4. Principal Current Research Areas

The expertise within the Centre membership enables us to bring relevant experience to areas covering almost the whole range of nonlinear problems in science and selected aspects of engineering. Some of the most active current areas of research in the CNLS are described below.

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.

Nonlinear Problems in Combustion. A particularly important class of chemical system exhibiting feedback and nonlinearity is the field of combustion. Professor Clarke, Drs. Griffiths and McIntosh help link the activities of the mathematical chemists (Brindley, Scott, etc.) to the Centres for Combustion and Energy and for Computational Fluid Dynamics in this active area. Recent projects have been funded by industry and by Research Councils and three postdoctoral fellows and three research students are currently involved.

Biological Fluid Dynamics Professor Pedley and Dr. Hill head a large group including five postdoctoral fellows and seven research students in various aspects of biomechanics. Areas of current interest include collapsible tube oscillations, the motion generated in suspension of swimming micro-organisms, including the response of algae to light, gravity and viscous forces, bioconvective pattern formation, the imaging of coronary arteries, peristaltic pumping, fish swimming and fluid dynamic problems arising in the lung. Additionally, a small but active group of four research students under Professor Brindley is concerned with plankton modelling and other aspects of oceanic ecology.

Theoretical Neuroscience. Dr. 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. This work is partially funded as part of a CEC ESPRIT Basic Research Action in association with Professor John Tucker at University College, Swansea. Professor Brindley is also involved with studies of the general behaviour of `excitable media'.

Integrable Systems. Dr. A.P. Fordy, his students and postdoctoral research fellows work on soliton theory and completely integrable Hamiltonian systems. The main emphasis has been on bi- and multi-Hamiltonian systems and their stationary flows, including the Lie algebraic and loop group aspects of these. Another aspect of this research is the Painlevé properties of differential equations. The soliton group continues its connections with centres in Moscow, Paris, Rome, St. Petersburg and Warsaw.

Further details of these areas of interest can be obtained from the relevant committee member through the Centre for Nonlinear Studies or via their parent department.


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