UK Nonlinear News, August 2001


Mathematical Biology in Nottingham (15th May 2001)

Markus Owen (Loughborough) and Helen Byrne (Nottingham)

This half day meeting was held in the Centre for Mathematical Medicine at the University of Nottingham. A fascinating range of topics included ecological waves, immunology and biological fluid dynamics.

Markus Owen (Loughborough) began the afternoon with a talk about How predation can slow, stop or reverse a prey invasion, a study of spatiotemporal interactions between invading species at Mount St. Helens. Oliver Jensen (Nottingham) presented a number of interesting results about Self-excited oscillations in a collapsible channel, motivated by the dynamics of flow in the lung and vasculature. The subject of immunology was represented by Hugo van den Berg (Warwick), who talked about the Efficacy of the T cell repertoire.

After a break for refreshments, Nick Hill (Leeds) brought the meeting to a close with a wide-ranging description of his work on the interaction between fluid flow and motile organisms: Two topics in bioconvection: plumes in deep layers and dispersion of swimmers in shear flows.

Over 30 participants and a relatively informal atmosphere made for a stimulating afternoon of Mathematical Biology.

People interested in participating in future meetings should contact either Markus Owen (email: M.R.Owen@lboro.ac.uk) or Helen Byrne (email: helen.byrne@nottingham.ac.uk).

 


Sixth Siam Conference on Applications of Dynamical Systems

Alona Ben-Tal

May 20-24, 2001, Snowbird, Utah

Our journey from Auckland, New Zealand to Snowbird, Utah started with a symmetry breaking bifurcation. The aircraft we were sitting in crashed into a building in Auckland before take off. As a result the tip of one wing was taken off, the non-symmetric aircraft took off 18 hours later and we missed the first day of the conference. (By "we" I mean Vivien Kirk, James Sneyd and myself.) I therefore apologize for reporting only on 4/5ths of the conference first hand.

More than 500 people participated in the conference this year. A wide range of topics in non-linear dynamics were covered in about 70 minisymposia, nearly 200 contributed talks, 55 posters and 10 invited plenary presentations. The program of the conference can be found in: http://www.siam.org/meetings/ds01/.

Among the highlights this year was the talk by Robert Full on "Dynamics of Galloping Ghosts, Gripping Geckos and Running Robots". Robert Full described in his talk how principles of animal locomotion have inspired the design of autonomous legged robots. (See http://polypedal.berkeley.edu/ and http://ib.berkeley.edu/faculty/fullr.html for more details.) Other interesting talks were given by Steven H. Strogatz (http://www.tam.cornell.edu/Strogatz.html) who talked about "Small-World Networks" (http://www.ams.org/new-in-math/small-world.html) and by James Sneyd (http://www.massey.ac.nz/~jsneyd/) who talked about "The Dynamics of Calcium".

A business meeting of the SIAM Activity Group on Dynamical Systems was held during the conference. A new, all-electronic research journal, "SIAM Journal on Applied Dynamical Systems" was formally introduced. Authors of articles in this journal will be able to use color, animated visualizations and internal links. The journal can be found in: http://www.siam.org/journals/siads/siads.htm. The establishment of a new DSWeb which will replace the current Dynamical Systems Activity Group web site was also announced at the meeting. See http://math.gmu.edu/html/ds/dsnotes/2001.01 for more details.


Dynamics Days Dresden 2001

Thomas Schreiber

The 21st European Dynamics Days were held this June 5-8 in Dresden. It was organised by Holger Kantz, Klaus Richter, and Thomas Schreiber with the support of the Max Planck Institute for the Physics of Complex Systems and took place in the new lecture hall centre of the Technical University of Dresden. It has been the explicit aim of the organisers to revive some of the spirit of the early Dynamics Days of the Eighties, with a wide scope of topics and lively attendence, in particular by young scientists. On the other hand, the maturity of the field was reflected by a different format, with ten plenary talks of introductory and overview character and fifteen mini-symposia for more technical presentations, held in parallel sessions three at a time.

The covered topics ranged from the core of nonlinear dynamical systems to nonequilibrium statistical mechanics, from biophysics to applications in engineering, climate modeling and econophysics. A more detailed program is available at http://www.mpipks-dresden.mpg.de/~ddd2001/. Roughly 300 delegates brought more than 160 posters, in addition to the O(100) plenary and parallel talks.

Certainly. dynamics can be regarded as a branch of mathematics, but the need and abilility to study systems in situations other than static equilibria penetrates almost all fields of science. The achievement of this year's Dynamics Days, if any, was to point out common problems, approaches and methods in seemingly very different scientific disciplines, thereby demonstrating the fundamental importance of dynamical concepts. Maybe the most 'far out' application was presented in a controversial lecture by Christian Beck who showed that a certain chaotic string theory yields accurate numerical coincidences with the as yet unexplained free parameters of the standard model of elementary particle physics.

So far, plans for European Dynamics Days 2002 have not been finalized. Proposals can be discussed with members of the Advisory Committee, there is a link at the above web site.


Nonlinear Dynamics and Chaos: where should we go from here?

Alan Champneys

This meeting was held over a long weekend, 8th-10th June 2001 at Burwalls Conference Centre, University of Bristol overlooking the Brunel's famous Clifton suspension bridge.

First impressions and photos from the conference are available at http://www.enm.bris.ac.uk/anm/colston.html, where a complete list of speakers and organisers may be found.

The aim of the meeting was to allow the next generation of nonlinear scientists to find an agenda for research directions of the future, focussed on three key themes

Neural systems Spatially extended systems and pattern formation Applications to biology, physics and engineering

The format was that fourteen international experts were chosen for their role in the development of the applications of nonlinear mathematics. They each gave a talk of 45 minutes duration with lots of time for discussion; there were no parallel sessions. The remaining participants were selected, largely from among the next generation of researchers who will make a contribution to nonlinear science. The meeting proved extremely popular with approximately 70 people attended; the maximum that Burwalls could accommodate. All participants other than the organisers and the main speakers presented posters on their work.

All the main speakers were both speculative and provocative. Each gave a talk that reflected on what their field has learnt from the explosion of interest in nonlinear dynamics and what needs to be learnt. They also responded to the challenge of each posing ten key open problems. Many unexpected connections emerged between the talks. Discussions were held over the sumptuous dinners (including the conference dinner at Clifton College, where the rules of cricket were explained to the Americans following the revelation that the highest ever individual cricket score was recorded there) and on Burwall's croquet lawn.

So what was learned? The overriding message is that Nonlinear Dynamics needs to get smart. We need to be able to consider systems that are in one sense or another `ill defined'; e.g. exist only for a finite time, are quantum, spatio-temporally complex, are stochastic, massively parallel or incorporate delays. Biology is a grand challenge, where the relation between nonlinear dynamics or `pattern' and function is a key open question. Many of these issues are to appear in the forthcoming book based on the meeting, that will be published by IOP Publishing in 2002, with an accompanying web site. Watch this space for an announcement.

The organising committee would like to thank everyone who attended the conference for making it such a success, and especially the meeting's sponsors the Colston Research Society, EPSRC, London Mathematical Society.


Mathematical Theory of Nonlinear Control

David Arrowsmith

June 18-22, 2001, Department of Mathematical Sciences, University of Bath, UK

The meeting was run as a workshop. There were over 20 participants and most gave a one hour talk - the format gave ample time for a reasonable introduction to key problems and also for exploration of common interests between lectures. The meeting was international with approximately half of the participants from the UK. The range of topics discussed was wide in the sense that both theoretical and practical aspects of Mathematical Control were covered. The style of the meeting was intimate and was the kind needed to bring together so many different approaches to control issues. Many talks were involved with various aspects of the synthesis of stabilizing controllers. These ranged from control of global systems involving nonlinear tracking, synchronization, differential games to stability, convergence of adaptive controls schemes and robustness. The workshop clearly demonstrated the close links between dynamical systems and mathematical control with dynamical systems being the motivating force for the implementation of control in many of the talks. Several contributions covered fundamental problems in the relatively new area of non-smooth phenomena (Fillipov systems). Other talks covered modelling and the associated control design for applied problems, e.g oscillators and traffic flow; computer simulation of cost surfaces and basin boundaries; high-gain adaptive and integral control for tracking of reference signals. Substantial problems involving normal form techniques and partial synchronization for observers were also discussed. The control of partial differential systems was represented with practical problems of optimization and controllability involving distributed parameter systems including plate/beam systems and shallow water type equations.

Organisers: H. Logemann (Bath), E.P. Ryan (Bath), S. Townley (Exeter) (Sponsored by the London Mathematical Society)

List of speakers: D K Arrowsmith, A Astolfi, F Bucci, C I Byrnes, P A Cook, M C French, H Huijberts, A Ilchmann, A J Krener, M Krstic, H Nijmeijer, H Osinga, M C Smith, A van der Schaft, S Townley, R Vinter, F Wirth, A S I Zinober.


Analyis and Continuation of Bifurcations

Willy Govaerts

A workshop "Analyis and Continuation of Bifurcations" was held at the Mathematical Research Institute of the University of Utrecht on 21 - 22 June 2001. The workshop was organized by Yuri A. Kuznetsov (Utrecht, Netherlands) and W. Govaerts (Gent, Belgium). It was a continuation of a series of similar workshops with slightly varying titles organized at Amsterdam and in Gent in previous years. The workshop focused on the bifurcation theory of nonlinear dynamical systems with attention not only to theoretical but also to algorithmic problems, including numerical methods and software demonstrations. The workshop brought together experts in bifurcation analysis and young researchers from the Netherlands and Belgium, Russia (Andreii Shilnikov, Dimitri Turaev and S. Gonchenko), Spain (J. Galan - Vioque, F. Fernandes Sanchez), Canada (Sebius Doedel), the USA (M. Friedman) and the UK (A.R. Champneys,B. Oldeman, P. Collins, B. Krauskopf, H. Osinga). 

As usual in this series of workshops there were many talks on homoclinic orbits but Hamiltonian systems were also prominent. From the applications side there were talks on neural models, delay differential equations, a low - order atmosphere model,the three - body problem and the spring - pendulum problem. Some interesting developments in software were also announced, in particular the C- version of AUTO, AUTO2000 (Sebius Doedel) and the Web - version of Content, WebContent (J. Val) as well as intended work on software for delay differential equations (D. Roose). The total number of participants was about 30, allowing a relaxed and friendly atmosphere. Several subgroups among these people were involved in collaborative projects and used the occasion to further discuss their collaboration. 

Many participants felt that this series of meetings is in a sense unique and should be continued. The United Kingdom Group expressed the intention to organize a similar meeting in 2002 broadly along the same lines. The organizers of the present meeting felt that this was a good idea and so did many other participants.


Lorenz Manifolds and Underground Posters featured in EPSRC Newsline July 2001

Andy Burbanks, Bernd Krauskopf and Hinke Osinga

The World Mathematical Year 2000 series of Posters on the London Underground has been a great success. This project was initiated by the Isaac Newton Institute, with support from the EPSRC and World Scientific Press, which enabled reprinting and distribution of the posters to a large number of schools in the UK and worldwide.

The idea behind the series was to make the general public aware of the importance and beauty of mathematical concepts in everyday life, thus presenting mathematics as a living and growing subject. Nonlinear mathematics was naturally a prominent topic, accounting for half of the poster themes.

The March poster Maths Predicts illustrates the unpredictability of the weather with images of stable and unstable manifolds of the famous Lorenz system. These images were produced by Bernd Krauskopf and Hinke Osinga from the University of Bristol, and were composed into the final poster by the series designer Andy Burbanks.

These manifolds feature prominently on the cover of the July 2001 issue of EPSRC Newsline special on Mathematics, accompanying the article An Underground Movement as part of the larger piece Creative Instincts on the use of Art to bring Maths to the millions. The article also features the June poster Maths Connects, the July poster Maths Evens the Odds and extracts from the May poster Maths Hots up.

The posters that were featured in the EPSRC Newsline article had contributions from Chris Budd (University of Bath), Keith Drummond (Photographer), Steele Hill (NASA) Robert Hunt (DAMTP/INI), Helen Mason (DAMTP), Chris Sangwin (University of Birmingham), Steve Tobias (DAMTP), the initiator of the project Keith Moffatt (INI), and the Stanford-Lockheed TRACE Mission team (NASA Small Explorer program).


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