skip to content

Kink stochastics

Thursday 1st July 2010 - 10:10 to 11:00
INI Seminar Room 1
Localised coherent structures are a striking feature of noisy, nonlinear, spatially-extended systems. In one space dimension with local bistability, coherent structures are kinks. At late times, a steady-state density is dynamically maintained: kinks are nucleated in pairs, diffuse and annihilate on collision. Long-term averages can be calculated using the transfer-integral method, developed in the 1970s, giving exact results that can be compared with large-scale numerical solutions of SPDE. More recently, the equivalence between the stationary density (in space) of an SPDE and that of a suitably-chosen diffusion process (in time) has been used, by a different community of researchers, to perform sampling of bridge diffusions. In this talk, diffusion-limited reaction is the name given to a reduced model of the SPDE dynamics, in which kinks are treated as point particles. Some quantities, such as the mean number of particles per unit length, can be calculated exactly.
The video for this talk should appear here if JavaScript is enabled.
If it doesn't, something may have gone wrong with our embedded player.
We'll get it fixed as soon as possible.
University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons