EVENT DETAILS AND ABSTRACT

Title: Generic stability results for steady periodic patterns and their application to convection problems
Speaker: Professor A. Skeldon
Speaker Info: City University, London, UK
Brief Description:
Special Note:
Abstract:

Generic stability results for steady spatially periodic patterns and their application to convection problems

Transition from a spatially uniform state to a periodic pattern occurs in many applications, such as the Rayleigh-Benard problem and reaction-diffusion systems. Periodic patterns such as hexagons, rolls and squares have long been known to exist, and weakly nonlinear analysis has allowed the relative stability of hexagons and rolls or squares and rolls to be found.

Based on symmetry arguments, we have derived generic amplitude equations, which apply to the same physical scenarios, but allow for a wider variety of solutions. This extends previous work in both allowing for the existence of more exotic spatially periodic patterns and in considering stability with respect to an infinite number of perturbations.

We demonstrate, for a p.d.e. describing long wavelength convection, that our work can be applied with little additional effort.