## Bristol Centre for Applied Nonlinear Mathematics

The EPSRC funded Bristol Centre for Applied Nonlinear Mathematics (BCANM) officially came to life on 1st October 2002 when Jan Sieber, formerly at WIAS-Berlin, started his appointment as the first Research Assistant on the grant. He will be working on Dynamical systems with delays, one of five research themes. The second Research Assistant of the Centre will be Piotr Kowalczyk, who will start in January 2003 to work on the second theme Dynamics of piecewise smooth systems. Elsewhere on in this issue you will find an announcement for the first BCANM workshop Delay Equations and Their Applications and an advertising for two more postdoctoral positions to start in October 2004. See also the BCANM seminar series for our programme of talks.

Source: Bernd Krauskopf

## Visitors to Mathematics at Warwick

Host: Robert MacKay, contact welcome.

• Anna Litvak-Hinenzon (Weizmann): transferred from an EC network postdoc to a Marie Curie Individual Fellowship, Aug 02 - Aug 04
• Arno Berger (Vienna): EC network postdoc, Sep 02 - Feb 03
• Vladimir Ten (Moscow): LMS Young Russian, 25 Oct - 10 Nov, and will be giving a lecture tour on aspects of Hamiltonian mechanics: Warwick (x2), Surrey, Cambridge and Loughborough
• Jerome Dorignac (Dresden): EC network postdoc, Nov - Dec 02, followed by Jan 03 - Feb 04 at Heriot-Watt
• Xinchu Fu (Shanghai): Chinese Research Fellowship, 20 Jan - 19 July 03
• Joan Ramon (Barcelona): UPC fellowship, Feb 03 - Jan 04

Source: Robert MacKay.

## Vassili Gelfreich appointed to a lectureship in the Mathematics Institute Warwick

Vassili Gelfreich took up a lectureship in the Mathematics Institute on 30 June. His research interests are primarily in Hamiltonian dynamics, singular perturbations, bifurcation theory and Stokes phenomenon in Dynamical systems. His achievements include proving the original Lazutkin asymptotic formula for the exponentially small splitting of separatrices and explaining the origin of Lazutkin's constant (equivalently, the Peierls-Nabarro barrier for Frenkel-Kontorova models; note that it is NOT equal to Peierl's guess!). He can be contacted on gelf@maths.warwick.ac.uk .

Source: Robert MacKay FRS.

## John Terry appointed to a lectureship in Mathematics at Loughborough

Dr John R. Terry has been appointed as a five year temporary lecturer within the Mathematical Biology Group of the Department of Mathematical Sciences at Loughborough University.

John received his PhD from the University of Surrey in May 2000, having been supervised by Peter Ashwin (now at Exeter). During his PhD studies, he spent a year in the School of Physics at the Georgia Institute of Technology under the guidance of Professor Rajarshi Roy (now Maryland). John spent 18 months as a postdoc at the University of Warwick and 9 months as a postdoc at the University of Queensland.

His research interests lie in the areas of theory and applications of coupled dynamical systems and time series analysis techniques, where recently he has been concentrating on development of nonlinear analysis tools for studying human EEG data and on the modelling of large and small scale neural systems using ideas from nonlinear oscillator theory.

Source:Steve Coombes.

## Graeme Wake appointed as Adjunct Professor of Industrial Mathematics at Massey University

Graeme Wake has been appointed as an Adjunct Professor of Industrial Mathematics within the Institute of Information and Mathematical Sciences, Massey University at Albany. Professor Wake will take up the 3-year part-time appointment in March 2003.

Professor Wake held the Chair in Applied Mathematics at Massey University from 1986 to 1995. Currently Professor of Applied Mathematics at the University of Canterbury, Graeme is one of New Zealand's eminent applied mathematicians, with significant experience and expertise in industrial applications. He won the Marsden Medal in 1999, is a Fellow of the NZ Mathematical Society, is currently Director of the AgResearch Mathematical Biology Unit, and will retain a part-time connection with Canterbury during 2003 while supervising PhD students who have not yet completed.

Professor Wake will be attached to the recently-formed Centre for Mathematics in Industry (CMI) which is based in the Institute of Information and Mathematical Sciences. Preparation for two major industrial mathematics meetings, the Mathematics in Industry Study Groups, MISG2004 and MISG2005, will be focused within the CMI.

It is expected that Professor Wake's appointment will provide a significant impetus for the applied and industrial mathematics activity within Massey University through the Centre for Mathematics in Industry.

Robert McKibbin Head, Institute of Information and Mathematical Sciences Massey University at Albany

1st October 2002

## A new test for chaos

Recently, Ian Melbourne (Surrey) and Georg Gottwald (MASIE postdoc at Surrey, recently appointed to a Lectureship at the University of Sydney) have developed a new test for determining whether a given deterministic dynamical system is chaotic or nonchaotic. This test is an alternative to and distinct from the usual approach of computing the largest Lyapunov exponent. The method is a 0-1 test for chaos (the output is a 0 signifying nonchaotic or a 1 signifying chaotic) and is independent of the dimension of the dynamical system. Moreover, the underlying equations need not be known. The test works equally well for continuous and discrete time.

The diagnostic is the real-valued function

p(t) = \int_0^t F(x(s))\cos(\omega_0 s) ds

where F is an observable on the underlying dynamics x(t) and $\omega_0\neq0$ is fixed arbitrarily. Let M(t) be the mean-square-displacement for p(t) and set

K=\lim_{t \rightarrow \infty} \log M(t)/\log t.

Then, for almost all choices of F and $\omega_0$, K=0 or K=1 typically, and moreover K=0 signifies nonchaotic dynamics whereas K=1 signifies chaotic dynamics.

The test is easy to implement, but is based on some new technical ergodic-theoretical results of Ashwin (Exeter), Field (Houston), Nicol (Surrey) and Melbourne. The test has been successfully applied to the forced van der Pol oscillator, and other applications are in progress. A downloadable preprint is available at

Source Tom Bridges ( t.bridges@eim.surrey.ac.uk).

## SIAM Prizes in Dynamical Systems

The SIAM Dynamical Systems Activity Group is pleased to announce two prizes: The Moser Lecture and the J.D. Crawford Prize. These prizes will be awarded at the Activity Group meeting in Snowbird, May 27, 2003.

The prize specifications may be viewed at the SIAM website:

http://www.siam.org/prizes

The Moser Lecture will be awarded "to a person who has made distinguished contributions to nonlinear science" and the Crawford Prize will be awarded "to one individual for recent outstanding work on a topic in nonlinear science, as evidenced by a publication in English in a peer-reviewed journal within the four calendar years preceding the SIAG/DS meeting at which the prize is awarded."

Nominees may be suggested for each award. The nominator should include a short narrative (up to a page or two) in support of the nominee and the nominee's vita. Electronic submission of the supporting material would be appreciated. To guarantee consideration nomination material must be received by November, 1, 2002 for the Moser Lecture Prize and December 1, 2002 for the J.D. Crawford Prize. This material should be sent to either The Moser Lecture Prize or to The J.D. Crawford Prize

attn: Allison Bogardo
Society for Industrial and Applied Mathematics
3600 University City Science Center

or by e-mail to: bogardo@siam.org.

The Prize Selection Committees are:
 Krystyna Kuperberg Auburn University Peter Lax Courant Institute, NYU Yakov Sinai Princeton University C. Eugene Wayne Boston University (Chair) Jim Yorke University of Maryland

 M. Gregory Forest Univ. of North Carolina (Chair) Mark Levi Pennsylvania State University Bjorn Sandstede Ohio State University Mary Silber Northwestern University Harry Swinney University of Texas, Austin

David W. McLaughlin
Chair SIAM Activity Group on Dynamical Systems

## New book series from Chapman & Hall/CRC Press

### Editors-in-Chief: T.J. Bridges (Surrey) & G. Chen (Texas A&M)

 Frederic Dias Ecole Normale Superieure de Cachan Brenny van Groesen University of Twente Sze-Bi Hsu National Tsing Hua University, Hsinchu, Taiwan Kunihiko Kaneko University of Tokyo, Komaba Guido Schneider Universitat Karlsruhe Sivaguru S. Sritharan Joint & National Systems Naval Division Michael I. Weinstein Bell Laboratories-Lucent Technologies

#### Aims and Scope

In its broadest interpretation, the subject of Applied Mathematics is situated somewhere between pure mathematics and the subjects where quantitative models are relevant: the natural, life and physical sciences, engineering, economics, finance and sociology, etc. In practice, applied mathematics is continually looking to pure mathematics for new paradigms and methods, and is continually looking to applications for new problems which require mathematical representation. An area which is currently having a major impact on the evolution of applied mathematics is nonlinear science. Nonlinear science in applied mathematics simply puts an emphasis on nonlinearity in the design and analysis of models for phenomena. It is inherently interdisciplinary and now has attained the status as a fully established scientific discipline of its own, with new research opportunities and challenges remaining extraordinarily numerous.

The C&H/CRC series on Applied Mathematics and Nonlinear Science aims to capture developments in applied mathematics and exciting new directions in nonlinear science. A breakdown of the five main topics of interest in the series are listed below.

• Chaos and Dynamical Systems: bifurcation theory, nonlinear electronics, control and synchronisation, strange attractors, hyperbolic sets, equivariant dynamics, Hamiltonian dynamics, quantum chaos, spatio-temporal chaos.
• Adaption and Self-organisation: cellular automata, population ecology, sociophysics, cellular and molecular biology, genetics, coherent structures and turbulence, genomes, neural networks, lattice Boltzmann methods.
• Pattern Formation: nonlinear waves, modulation equations, solitons, optical patterns, reaction-diffusion, solitary waves and fronts, oceanic patterns, biological patterns, symplectic patterns, complex and chaotic patterns.
• Nonlinear PDEs: integrable systems, Hamiltonian and Lagrangian systems, PDEs on manifolds, classical and quantum mechanics, control of PDEs, nonlinear optics, computer vision, variational methods.
• Computation and Nonlinearity: level set methods, geometric numerics, molecular dynamics simulations, symplectic integrators, numerics of chaos, computational electromagnetics, numerics of conservation laws, numerics on manifolds, multiscale methods.

#### Call for Authors

Chapman & Hall/CRC has been a leading publisher of books on mathematics, science and engineering for many years (formerly as independent units, Chapman & Hall and CRC Press, and now jointly). This new series takes its place among other critically-acclaimed series from Chapman & Hall/CRC, including the Research Notes in Mathematics Series, the Modern Mechanics and Mathematics Series, Monographs and Surveys in Pure and Applied Mathematics, and the Engineering Handbook series. See http://www.crcpress.com.

The publisher is now actively seeking contributions to this new series. Please contact the Editors-in-Chief or any member of the Editorial Board for proposal and manuscript guidelines.

The official website for the book series is under development at
http://www.maths.surrey.ac.uk/books/am-nl/

Source: Tom Bridges ( t.bridges@eim.surrey.ac.uk).

## Chaos, complexity and the use of evidence

Ideas from chaos and complexity may have important applications to evidence based practice. Evidence based practice - medicine, health, policy, etc., positioned as the standard for quality practice, is coming under increasing challenge, with the increasing recognition of its limitations, notably from within the UK.

London Professor of Medicine, Philip Alexander Poole-Wilson, President Elect of the World Heart Federation recently delivered an Opening Address at the Canadian Cardiovascular Congress entitled "Limitations of Evidence Based Medicine in Health Care." Tricia Greenhalgh, a London Professor of primary health care, in discussing the limitations of evidence, proposes a practice that includes evidence and intuition. David Kernick and others in the UK have proposed using complexity ideas in health care responding to the limitations of evidence. A major limitation, described for health by Professor Greenhalgh as, "Clinicians in particular have claimed that the patient's unique and complex predicament is poorly served by applying a recommendation derived, however objectively, from an average result in a select population sample," would apply across other areas of practice.

Science has changed to include chaos and complexity and thus the scientific base for evidence based practice should also change. If the world works, either somewhat or mostly by chaos and complexity, then the evidence has been acquired in this setting and should be used in this context. Practice of medicine and health, and probably most disciplines is an art and science. The science should now include chaos and complexity, and the art include things like intuition etc, which could still fall within the purview of chaos and complexity, which can be art, science and philosophy. The subtitle of John Briggs' book "Fractals, the Patterns of Chaos: discovering a new aesthetic of art, science and nature" and the titles of this writer's books, "Chaos From Cos to Cosmos: a new art, science and philosophy of medicine...and everything else" and "A new chaos (and complexity) based medicine: the response to evidence" suggest that chaos and complexity can become the base for a new scientific, evidence based practice, overcoming the limitations being increasingly described. A new chaos and complexity based practice would be evidence based in context, the context reflecting chaos and complexity.

In the interest of interdisciplinary discussion and debate, it was thought useful to bring this thinking emerging in medicine and health to the attention of the wider nonlinear community. This novel application of chaos and complexity may have far-reaching consequences in the perception and use of evidence, not only in medicine, but much further afield.

Source: Dr VS Rambihar MD, Toronto (vashna@rogers.com).

## Chaos, complexity and Redesigning Health Care for the 21st Century

Dr V. Rambihar in Toronto has sent two brief submissions to the Romanow Commission and the Kirby Senate Committee on Canadian Health Care proposing the inclusion of chaos and complexity science in Redesigning Canadian Health Care for the 21st Century. In one proposal he suggested that chaos and complexity can be a model for diversity and ethnicity and health, and in both he suggested that chaos and complexity be used as a tool for change, referring to his recent health promotion projects doing this.

Source: Dr VS Rambihar MD, Toronto (vashna@rogers.com).

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Last Updated: 1 November 2002.
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