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Kinetics of Heterogeneous Single-Species Annihilation

P. L. Krapivsky·E. Ben-Naim·S. Redner
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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.

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P. L. Krapivsky, E. Ben-Naim, S. Redner. 1994-06-27. Kinetics of Heterogeneous Single-Species Annihilation. https://doi.org/10.1103/physreve.50.2474

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