Random channel kinetics for reaction-diffusion systems (Q972253)

The motivation of this work was a study of the kinetics of the decay and preservation of marine organic carbon. The authors observe tht their approach to this problem can be used to describe other disordered kinetic catalytic processes with random pathways. The specific setting is this: there is a catalyst and an active species. The catalyst is produced by a variable number of independent sources randomly distributed in space. It diffuses from the sources and degrades according to a first-order kinetic law. The generation, degradation and diffusion of the catalyst balance to produce a stationary concentration field. The active species decays according to a second-order kinetic law with a decay rate proportional to the product of the concentrations of the catalyst and the active species. The main results of the paper are the following: The resulting concentration field can be represented as a sum of Yukawa-type potentials. Also, the average value of the survival function for the active species is expressible as a grand canonical average of a nonlinear functional of the catalyst field, and can in principle be evaluated exactly. Furthermore, one can compute a good approximation using a simple nearest neighborhood approach.