Stochastic aggregation: rate equations approach

We investigate a class of stochastic-aggregation processes involving two ty pes of clusters: active and passive. The mass distribution is obtained anal ytically for several aggregation rates. When the aggregation rate is consta nt, we find that the mass distribution of passive clusters decays algebraic ally. Furthermore, the entire range of acceptable decay exponents is possib le. For aggregation rates proportional to the cluster masses, we find that gelation is suppressed. In this case, the tail of the mass distribution dec ays exponentially for large masses, and as a power law over an intermediate size range.