Reaction Diffusion Processes

Reaction-Diffusion Processes

The kink-antikink annihilation process A + A -> 0 (which describes domain-wall annihilation in the coarsening dynamics of one-dimensional Glauber-Ising model) is a simple example of a reaction-difusion process. The domain walls diffuse independently and annihilate (react) on contact. In collaboration with R. A. Blythe, I have recently solved a long-standing problem of this type, namely determining the asymptotic (long time) behavior of the minority species density in the two-species annihilation reaction A + B -> 0 in one and two spatial dimensions. The interest in these cases is that the usual rate-equation approaches fail because spatial fluctuations in the majority species density cannot be neglected.

In more recent work with Blythe, S. N. Majumdar and L. Anton, I have developed a new mathematical formalism capable of going beyond the leading asymptotic behaviour for the related trapping reaction A + B -> B, which has the same asymptotic behavoiur as two-species annihilation. Going beyond leading order is important, because the corrections to the leading forms are significant on all reasonable timescales. The new method is based on eliminating the trapping (B) species from the problem to leave a model of independent A-particles moving with an effective dynamics.