Catalytic coagulation

We introduce an autocatalytic aggregation model in which the rate at which two clusters merge is controlled by the third "catalytic" cluster, whose mass must equal the mass of one of the reaction partners. The catalyst is unaffected by the joining event and can participate in or catalyze subsequent reactions. This model is meant to mimic the self-replicating reactions that occur in models for the origin of life. We solve the kinetics of catalytic coagulation for the case of mass-independent reaction rates and show that the total cluster density decays as t^{-1/3}, while the density of clusters of fixed mass decays as t^{-2/3}. These behaviors contrast with the corresponding t^{-1} and t^{-2} scalings for classic aggregation. We extend our model to mass-dependent reaction rates, to situations where only "magic" mass clusters can catalyze reactions, and to include steady monomer input.