Evolution Behaviour of Migration-Driven Growth with Catalyzed Decline

Abstract

A migration-driven aggregation model with catalyzed decline process of two species is proposed, in which migration-driven aggregation occurs between any two aggregates of the same species with the size-dependent rate kernel . Meanwhile, a monomer decline of A-species aggregates occurs under the catalysis by B-species aggregates with the catalyzed decline rate kernel . The kinetic behavior of A species is investigated by means of the mean-field theory, which is found to depending crucially on the catalysis rate kernel parameter μ: in case, the migration-driven aggregation reaction dominates the process, and the aggregate size distribution of A species approaches the conventional scaling form, and A species will survive in the end; while incase, the catalyzed decline reaction dominates the process, the aggregate size distribution of A aggregate does not scale, and A species will die out in the end.