Breakdown of Scaling in Aggregation-Fragmentation- Annihilation Process of n-Species Systems

The kinetic behaviors of aggregation-fragmentation-annihilation processes of three n-species systems arestudied in this paper. Aggregation reaction occurs only between the same species but irreversible annihilation reactionoccurs between two different species, and meanwhile the fragmentation reaction coexists. Based on the mean-field theory,we investigate the rate equations of the processes and obtain the asymptotic descriptions of the cluster-mass distributionsfor the symmetrical cases. We find that the fragmentation reaction may lead to the complete breakdown of the standardscaling description for the cluster-mass distribution of each species contrast to the scaling behavior of aggregation-annihilation processes without fragmentation.In our joint annihilation model, we also observe that the kinetic behaviorsof distinct species are quite complicated for the case with different initial concentrations. The cluster-mass distributionof heavy species with the largest initial concentration possesses peculiar scaling properties, while that of light species hasnot scaling behavior.