Kinetics of aggregation annihilation processes

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 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 one dimension, 2D, and 3D. Nontrivial growth exponents characterize the mass distribution in one dimension.