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Reaction-diffusion process driven by a localized source: First-passage properties
Phys. Rev. E 85, 031124 – Published 19 March, 2012
DOI: https://doi.org/10.1103/PhysRevE.85.031124
Abstract
We study a reaction-diffusion process that involves two species of atoms, immobile and diffusing. We start with only immobile atoms uniformly distributed throughout the entire space. Diffusing atoms are injected at the origin by a source that is turned on at time . When a diffusing atom collides with an immobile atom, the two atoms form an immobile stable molecule. The region occupied by molecules is asymptotically spherical with radius growing as in dimensions. We investigate the survival probability that a diffusing atom has not become a part of a molecule during the time interval after its injection. We show that, asymptotically, the survival probability (i) saturates in one dimension, (ii) vanishes algebraically with time in two dimensions (with exponent being a function of the dimensionless flux and determined as a zero of a confluent hypergeometric function), and (iii) exhibits a stretched exponential decay in three dimensions.
Article Text
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