Kinetic Behavior of Aggregation-Fragmentation Process with Annihilation

The kinetic behavior of an aggregation-fragmentation-annihilation system with two distinct species is stead-ied. We propose that the aggregation reaction occurs only between two clusters of the same species, and the irreversibleannihilation reaction occurs only between two clusters of different species, meanwhile there exists the fragmentationreaction of a cluster into two smaller clusters for either species. Based on the mncan-field theory, we investigate therate equations of the process with constant reaction rates and obtain the asymptotic descriptions of the cluster-massdistribution. In the case of the same initial concentrations of two species, the scaling descriptions for the cluster-massdistributions of the two species are found to break down completely. It is also observed that the kinetic behaviors ofdistinct species are quite complicated for the case of different initial concentrations of the two species. Tile clusters oflarger initial concentration species (heavy species) possess peculiar scaling properties, while the cluster-mass distributionoflight species has not scaling behavior. The exponents describing the scaling behavior for heavy species strongly dependon its fragmentation rate and initial monomer concentrations of two kinds of reactants.