Kinetics of Aggregation-Annihilation Processes
E. Ben-Naim and P.L. Krapivsky
We investigate the kinetics of many-species systems with aggregation
of similar species clusters and annihilation of opposite species
clusters. We find that the interplay between aggregation and
annihilation leads to rich kinetic behaviors and unusual conservation
laws. On the mean-field level, an exact solution for the cluster-mass
distribution is obtained. Asymptotically, this solution exhibits a
novel scaling form if the initial species densities are the same while
in the general case of unequal densities the process approaches single
species aggregation. The theoretical predictions are compared with
numerical simulations in 1D, 2D, and 3D. Nontrivial growth exponents
characterize the mass distribution in one dimension.
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