UCL Centre for Nonlinear Dynamics and its
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Nonlinear Dynamics and Chaos
Establishment of the Centre
Royal Society Research Fellowships
Collaboration with the Anatomy Department
Grants and Awards
Graduate Programme: PhD By Research
Graduate Programme: MSc Course
The study of nonlinear dynamics is one of the most exciting and fastest growing branches of the mathematical sciences. It is having an increasingly important impact on a variety of applied subjects ranging from the study of turbulence and the behaviour of the weather, through the investigation of electrical and mechanical oscillations in engineering systems, to the analysis of biological and economic phenomena. It has also fired the public's imagination under the popular name of "chaos".
The Centre for Nonlinear Dynamics and its Applications was established at University College London (UCL) in 1991, to act as a focus for interdisciplinary research into the theory of nonlinear dynamics and its applications across science and engineering. It is based within the Department of Civil and Environmental Engineering which has a long history of expertise in the advanced dynamics of engineering structures.
The Centre is under the directorship of Professor J.M.T. Thompson, FRS, whose seminal book on Nonlinear Dynamics and Chaos has played a fundamental role in stimulating the application of nonlinear dynamics throughout engineering and the sciences. Steve Bishop is the Manager of the Centre, and Jaroslav Stark, who joined the Centre from the GEC Hirst Laboratories in 1992, is the coordinator of the graduate programme.
The Centre currently has 31 members. In addition to the 3 permanent staff mentioned above, there are 2 honorary visiting professors, 7 fellows and post-doctoral research assistants, 10 research students (working for a PhD), 6 post-graduate students (working for an MSc), and 3 academic visitors. All are accommodated in an attractive central area of UCL where regular colloquia and a small library of current journals make an exciting and focused research environment. The Centre has good links with many other research groups both in the UK and abroad, and with a number of engineering companies.
An early success of the Centre was the winning of two prestigious Royal Society Research Fellowships. The first was awarded to Allan McRobie to work on topological methods for the dynamics of structures. The second was awarded to Mike Davies to study time series analysis using phase-space reconstruction. A sustained thrust by members of the Centre into the analysis and processing of time series, has been strengthened by the appointment of David Broomhead (DRA, Malvern, formerly the Royal Signals & Radar Establishment) as a Visiting Professor.
In 1993 the Centre hosted a Symposium on Nonlinearity and Chaos in Engineering Dynamics sponsored by the International Union of Theoretical and Applied Mechanics (IUTAM), and the proceedings have been edited into a coherent account of modern developments. The meeting began with an Opening Address by Sir James Lighthill, who was the President of IUTAM during his period as Provost of UCL, followed by a general lecture given by Philip Holmes. Three papers were given by members of the Centre. Stephen Foale and Steve Bishop presented their elegant study of grazing bifurcations in impacting systems, relevant to the rattling of engineering structures. Mike Davies and Jaroslav Stark described their work on noise reduction, relevant to real-time signal processing and the improved reproduction of speech and music. Allan McRobie and Michael Thompson demonstrated how the theory of knots and braids can be used to establish bifurcational precedences in driven oscillators.
A close link has been forged over a number of years by Steve Bishop and Michael Thompson with ES-Consult, a specialised engineering consultancy in Denmark. This consultancy was established in 1990 by Eilif Svensson, who is now Managing Director. One of Eilif's staff is Hans True, who gave a general lecture on the hunting instability of a railway wheel-set at the IUTAM Symposium: Hans is employed half-time by ES-Consult and half-time in the Laboratory of Applied Mathematical Physics at the Technical University of Denmark.
This link has now been strengthened and formalised by the appointmnet of Michael Thompson as Chairman of the Board of Directors of ES-Consult. The consultancy has a strong interest in the aeroelastic instabilities of slender bridge structures, and has worked on tuned mass dampers for the Great Belt bridge, the largest single span suspension bridge in the world. It is now involved with dynamic analysis of the cable-stayed bridge in the new Oresund link between Denamrk and Sweden. ES-Consult is also active in the highly nonlinear dynamics of railway vehicles, including wheel-rail contact forces and the interactions between a moving train and a bridge: related activity is on impact-absorbing crash-barriers for road vehicles.
This train modelling, together with the Centre's work on the capsize of ships (linked with the Ministry of Defence and W.S. Atkins) and a flight dynamics project (linked with British Aerospace), define an emerging theme of vehicle dynamics. Meanwhile Jaroslav Stark's links with the General Electric Company are being maintained by a part-time research student working on irregularaly sampled time series.
The interdisciplinary nature of the Centre was nicely consolidated when Jaroslav Stark won a grant to collaborate on pattern formation in embryonic development with Anne Warner, a Royal Society Research Professor in the Anatomy Department. This work on the electrical and chemical properties of living cells is more focused than earlier studies, and aims to incorporate an embryo's known biological properties into a mathematical model that will generate testable predictions. This work is neatly complemented by studies on the death of cells, by Jaroslav's Mexican research student, Alexandra Chavez-Ross.
The Centre has benefitted from a continuing stream of distinguished visitors from overseas. The IUTAM proceedings, Nonlinearity and Chaos in Engineering Dynamics, edited by Thompson & Bishop, was published by John Wiley in 1994. The appointment of Jaroslav Stark (with Colin Sparrow of the Newton Institute at Cambridge) as editor of the international journal, Dynamics and Stability of Systems, has further strengthened the international standing of the Centre.
A triangular collaboration with Bruce Stewart at Brookhaven and Yoshi Ueda at Kyoto is supported by a travel grant from Monbusho, the Japanese Ministry of Education, Science and Culture. Funding by the European Community supports collaboration on noise in dynamical systems with key European universities, and a fellowship in the Centre under the Human Capital and Mobility scheme. The British Council is supporting collaboration with the University of Strathclyde and a number of Japanese Research Laboratories on the capsize of intact and damaged ships.
The foundations of the Centre were laid by early work in the Civil Engineering Department on nonlinear engineering dynamics which was strongly supported by the Marine Technology Directorate (MTD) of the Science and Engineering Research Council (SERC). Two SERC fellowships, and a grant from the Wolfson Foundation brought total earnings to 1 million before the formal creation of the Centre in 1991. Awards since then have brought the running total to 2 million.
Recent grants have generated fruitful lines of research. Stephen Foale's work on the resonance and rattling of impacting systems was supported by the MTD. New concepts of transient capsize in waves have been formulated under grants from the MTD and the Admiralty: this work has benefitted from fruitful collaboration with Rod Rainey (Chief Engineer, W.S.Atkins), the Centre's visiting Industrial Professor. Steve Bishop's successful studies of flash-over in building fires, the subject of a recent television presentation and an article in New Scientist, were funded jointly by SERC and the Health and Safety Executive.
Three recent grants were awarded by ANM, the Applied Nonlinear Mathematics initiative of what is now the Engineering and Physical Sciences Research Council (EPSRC). One, to Mike Davies, is for work on the stability of chaotically driven systems, using inertial manifolds and ideas from ergodic theory. The second, to Allan McRobie and Michael Thompson, is for work on modal interactions and energy transfer in the nonlinear vibrations of thin shell structures. The third is to Jaroslav Stark for his collaborations with the Anatomy Department.
The Centre has a lively and expanding research group working on a variety of topical problems in the theory and applications of dynamical systems. Research students, working for the PhD of the University of London, typically have first degrees in mathematics, physics or engineering. Financial support has in the past come from various sources, including SERC (one CASE studentship is linked with the Meteorological Office) and the British Council. Current topics of research include: mechanical systems with impacts and stick-slip friction; transient dynamics including the capsize of ships; electronic circuits and the loss of synchronization in phase-locked communication loops; the large scale circulation of the ocean; flash-through phenomena in the dynamics of building fires; the death of cells in biology; chaotic signal processing; the mathematics of quasi-periodic forcing; and the control and use of chaos. Whenever possible, a research topic is chosen to suit the individual strengths, interests and enthusiasms of a new student.
A taught course in Nonlinear Dynamics and Chaos leading to the MSc degree of the University of London was started in 1993. Full time students complete the course in one year, part-time students in two. The course has attracted engineering, physics and mathematics graduates from leading universities including Oxford, Cambridge and London. Mature students have been attracted from the oil-exploration industry, and British Aerospace. After learning the basic theory, students explore a variety of examples drawn from a broad range of subjects using both analytical and computational methods. They discover how to apply the techniques they have learned to real problems in engineering, mathematics and the sciences. A supervised project introducing each student to independent reading and research, culminates in the writing and presentation of a short dissertation. This MSc has now been recognized and supported by the EPSRC, and a number of studentships will be available each year.
UCL Centre for Nonlinear Dynamics and its Applications,
University College London, Gower Street, London, WC1E 6BT, UK.