Competition between aggregation and migration processes of a multi-species system

We propose a solvable multi-species aggregation-migration model, in which irreversible aggregations occur between any two aggregates of the same species and reversible migrations occur between any two different species. The kinetic behaviour of an aggregation-migration system is then studied by means of the mean-field rate equation. The results show that the kinetics of the system depends crucially on the details of reaction events such as initial concentration distributions and ratios of aggregation rates to migration rate. In general, the aggregate mass distribution of each species always obeys a conventional or a generalized scaling law, and for most cases at least one species is scaled according to a conventional form with universal constants. Moreover, there is at least one species that can survive finally.