Theoretical Aspects of Pattern Formation

Alastair Rucklidge

The workshop Theoretical Aspects of Pattern Formation 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 workshop enjoyed support from the London Mathematical Society and from EPSRC, and one day (Tuesday 20 September) was sponsored by the Institute of Advanced Studies (U Surrey), and was aimed at a broader audience with the goal of surveying the state-of-the-art in the field and outlining promising future directions.

The workshop programme consisted of 19 lectures and 7 posters, covering a broad range of applied, pure, and experimental topics. Among the presenters were experimentalists and theoreticians, applied and pure mathematicians, physicists as well as chemists. Briefly, the talks covered aspects of patterns in convection (including rotating convection, the effects of thermal noise at the onset of convection, and the skewed-varicose instability), flows in thin films, Faraday waves, spiral patterns in plant growth, patterns in excitable media and reaction-diffusion problems, patterns in the formation of bacterial colonies, dynamics of the motion of spirals, patterns leading to intermittent dynamics, spatio-temporal chaos and coarsening, dynamics of defects in 2D patterns, patterns in turbulent flows, the long-time behaviour of solutions 2D and 3D Navier-Stokes equations, robustness of coherent structures such as spiral waves, and a topological perspective on the existence and stability of localised solutions in pattern formation on the plane, where the presence of more than one unbounded direction is known to cause difficulties. Most of the talks presented at the workshop are available on the web.