Abstract

BUSTOS, Natalia C  and  RE, Miguel A. Statistical properties of the diffusion mediated reaction process for a mobile imperfect trap. An. AFA [online]. 2015, vol.26, n.1, pp.40-45. ISSN 0327-358X.

Diffusion mediated reaction schema has been particularly useful for modelling processes in Physics, Chemistry, Biology and recently in Ecology. Usually it is assumed the diffusion of walkers, the majority species designed here by A, in the presence of a trap designed here by T, the minority species, assumed in a fixed position in the lattice. When a walker reaches the trap position the reaction may take place with an in general finite probability. In these models it is assumed that the diffusion coefficient of the walkers is the sum of the diffusion coefficient of both species. Nevertheless there are processes that are better described by both species diffusing. We present in this communication a Continuous Time Random Walk (CTRW) model on an one dimensional lattice in which both species diffuse with different diffusion coeffcients. It is assumed an uniform initial distribution of the majority species in the presence of a trap, representing the minority species. Even when the lattice spacing is the same for both species, the diffusion coefficients are different since we assume different transitions rates. The reaction is not inmediate when both species meet at a lattice site and there are realizations in which reactives move appart without reacting. Analytical results are presented in the Laplace domain for the reaction probability, reaction rate and majority species concentration.

Keywords : Moble trap; Reaction-diffusion; Random Walk; Nearest neighbor.

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