Monomer Migration and Annihilation Processes

We propose a two-species monomer migration-annihilation model, inwhich monomer migration reactions occur between any two aggregatesof the same species and monomer annihilation reactions occurbetween two different species. Based on the mean-field rateequations, we investigate the evolution behaviors of theprocesses. For the case with an annihilation rate kernelproportional to the sizes of the reactants, the aggregation sizedistribution of either species approaches the modified scalingform in the symmetrical initial case, while for the asymmetricalinitial case the heavy species with a large initial data scalesaccording to the conventional form and the light one does notscale. Moreover, at most one species can survive finally. For thecase with a constant annihilation rate kernel, both species mayscale according to the conventional scaling law in the symmetricalcase and survive together at the end.