Kinetic behaviour of two-species-group aggregation process with complete annihilation

We propose a two-species-group aggregation-annihilation model in which an irreversible aggregation reaction occurs between any two clusters of the same species, and an irreversible joint annihilation reaction occurs between two distinct species groups. Based on the mean-field theory, we have investigated the rate equations of the process with constant reaction rates to obtain the asymptotic descriptions of the cluster-mass distributions. The results indicate that for the symmetrical initial cases the kinetic behaviour of the system depends crucially on the ratio of the equivalent aggregation rate to the annihilation rate. The cluster-mass distribution of each species always obeys a conventional or modified scaling law in each individual case. Moreover, all the species cannot finally survive except for the cases in which at least one equivalent aggregation rate is less than twice the annihilation rate.