Wave propagation in distributed media

The problem of chemical reaction-diffusion wave propagation through a random, heterogeneous medium is considered using a model based on cubic autocatalysis with decay. The autocatalyst is taken to diffuse and react through a reactant loaded at constant initial concentration in a reaction domain except that there may be gaps of arbitrary width in which the reactant concentration is zero. We first study the propagation of a permanent-form wave across a single gap and determine the critical width of the gap in terms of the kinetic parameters in the system. The numerical results are compared with an analytical estimate. Next, the critical conditions for propagation across two gaps separated by a domain are determined numerically, and this is extended to a series of three gaps. From these results, a series of "rules" is established to allow us to predict whether a wave will pass through an arbitrary random array of gaps of a given size subject to some imposed total void fraction for the material. (c) 2001 American Institute of Physics.