Kinetics of Heterogeneous Single-Species Annihilation
P. L. Krapivsky, E. Ben-Naim and S. Redner
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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