Theoretical Aspects of Pattern Formation
The workshop was held from 19-23 September 2005 at the University of Surrey as part of the Isaac Newton Institute Programme on Pattern Formation in Large Domains. The programme consisted of 19 lectures and 7 posters, covering a broad range of applied, pure, and experimental topics associated to pattern formation in large domains; with an emphasis on theoretical aspects. Among the presenters were experimentalists and theoreticians, applied and pure mathematicians, physicists as well as chemists. The number of lectures was purposely limited to allow extended opportunities for informal discussions. Almost all of the talks presented at the workshop are available on the web.
There were five distinguished lectures on Tuesday, 20 September, sponsored by the Institute of Advanced Studies, that were aimed at a broader audience with the goal of surveying the state-of-the-art in the field and outlining promising future directions. Summaries of the talks are given below.
Guenter Ahlers (UC, Santa Barbara) gave a wide-ranging survey of historical and recent developments in Rayleigh-Bénard convection, covering a span of 100 years, and discussing experimental and theoretical aspects of convection patterns. The talk also focused on selected topics of current interest, including the effect of thermal noise on bifurcation to convection and spatiotemporal chaos.
Eugene Wayne (Boston) turned to the long-time behaviour of solutions of the two- and three-dimensional Navier-Stokes equations, proving global stability of two-dimensional Oseen vortices, and proving a related result in three dimensions for small initial data, with Burger's vortices taking the place of Oseen vortices.
Dwight Barkley (Warwick) continued the theme of patterns in turbulence, and presented numerical and experimental results of the formation of turbulent stripes in very large aspect ratio planar Couette flows, with a mixture of narrow turbulent regions and wide laminar bands very close to the transition to
Arnd Scheel (Minneapolis) proved results on the robustness of localised coherent structures with two unbounded directions such as spiral waves, sources and sinks, and line defects, overcoming difficulties arising from the essential spectrum. The approach also exhibits obstructions to robustness which can lead to the sudden disappearance of coherent structures.
Alan Newell (Arizona) examined tiling patterns on the surfaces of plants and plant phyllotaxis, outlining new ideas which provide a rational explanation for many observations of patterns on plants, including the prevalence of Fibonacci sequences of spiral families.
The IAS day concluded with an excellent workshop dinner at the Lakeside restaurant. The dinner was attended by most of the participants.
A total of 51 participants, including 5 PhD students, attended the workshop. The nationality of the attendees were: Canada (2), Chile (1), EU (7), Israel (3), UK (23), USA (15). In addition, many staff members from Mathematics at Surrey attended several of the seminars and interacted with the registered participants.
The feedback from participants was extremely positive. Of the 19 questionnaires returned, 14 evaluated the scientific content as Excellent and the remaining 5 as Good. Comments included:
- "One of the best conferences I have attended recently. The level and quality of the participants and of the talks was very high."
- "I thought the scientific level of the presentations was as high as any meeting I have been to recently".
The organisers and participants are very grateful to:
- Engineering and Physical Sciences Research Council
- Institute of Advanced Studies at the University of Surrey
- Isaac Newton Institute
- London Mathematical Society