Reaction Kinetics of Clustered Impurities

Preprint

10 December 1994

preprint
Published by arXiv in arXiv

https://doi.org/10.48550/arXiv.cond-mat/9412048

Abstract

We study the density of clustered immobile reactants in the diffusion-controlled single species annihilation. An initial state in which these impurities occupy a subspace of codimension d' leads to a substantial enhancement of their survival probability. The Smoluchowski rate theory suggests that the codimensionality plays a crucial role in determining the long time behavior. The system undergoes a transition at d'=2. For d'2. Above this critical codimension, d'>=2, the subspace decays indefinitely. At the critical codimension, inverse logarithmic decay occurs, ni(t) ~ log(t)^{-a(d,d')}. Above the critical codimension, the decay is algebraic ni(t) ~ t^{-a(d,d')}. In general, the exponents governing the long time behavior depend on the dimension as well as the codimension.

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All Related Versions

Version 1, 1994-12-09, ArXiv
Version 2, 1994-12-10, ArXiv
Published version: Physical Review E, 53 (2), 1566.

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