TITLE:
Imperfect Trapping in a Random Walk with Both Species Mobile
AUTHORS:
Natalia C. Bustos, Miguel A. Ré
KEYWORDS:
Mobile Trap, Diffusion Mediated Reactions, Continuouos Time Random Walk, Trapping Models
JOURNAL NAME:
Advances in Pure Mathematics,
Vol.8 No.1,
January
31,
2018
ABSTRACT: It is presented here a continuous time random walk model for diffusion mediated reactions with both species mobile. The random walk is carried out over an infinite homogeneouos lattice. They are calculated the probability density for the time of reaction of a pair, the reaction rate and the time evolution of the concentration of the majority species. Analytical results are obtained in the Fourier-Laplace transform representation. Known results for a fixed trap are reobtained with appropriate marginal probabilities. It is thus justified Smoluchowski’s original approximation considering the trap at a fixed position and the majority species diffusing with a coefficient sum of the individual coefficients. The results obtained are illustrated by a one dimensional model with bias.