Kinetics of Heterogeneous Single-Species Annihilation
Abstract
We investigate the kinetics of diffusion-controlled heterogeneous single-species annihilation, where the diffusivity of each particle may be different. The concentration of the species with the smallest diffusion coefficient has the same time dependence as in homogeneous single-species annihilation, A+A-->0. However, the concentrations of more mobile species decay as power laws in time, but with non-universal exponents that depend on the ratios of the corresponding diffusivities to that of the least mobile species. We determine these exponents both in a mean-field approximation, which should be valid for spatial dimension d>2, and in a phenomenological Smoluchowski theory which is applicable in d<2. Our theoretical predictions compare well with both Monte Carlo simulations and with time series expansions.
Keywords
Cite
@article{arxiv.cond-mat/9406109,
title = {Kinetics of Heterogeneous Single-Species Annihilation},
author = {P. L. Krapivsky and E. Ben-Naim and S. Redner},
journal= {arXiv preprint arXiv:cond-mat/9406109},
year = {2009}
}
Comments
TeX, 18 pages