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.
We propose two solvable cluster growth models, in which an irreversible aggregation spontaneously occurs between any two clusters of the same species; meanwhile, monomer birth or death of species A occurs with the help of species B. The system with the size-dependent monomer birth/death rate kernel K（i, j） = Jijv is then investigated by means of the mean-field rate equation. The results show that the kinetic scaling behaviour of species A depends crucially on the value of the index v. For the model with catalysis-driven monomer birth, the cluster-mass distribution of species A obeys the conventional scaling law in the v ≤ 0 case, while it satisfies a generalized scaling form in the v ≥ 0 case; moreover, the total mass of species A is a nonzero value in the v 〈 0 case while it grows continuously with time in the v ≥ 0 case. For the model with catalysis-driven monomer death, the cluster-mass distribution also approaches the conventional scaling form in the v 〈 0 case, while the conventional scaling description of the system breaks down in the v ≥ 0 case. Additionally, the total mass of species A retains a nonzero quantity in the v 〈 0 case, but it decreases to zero with time in the v ≥ 0 case.
