Coagulation and fragmentation in cluster-monomer reaction models

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Abstract
We study aggregation kinetics for a model in which both coagulation and fragmentation processes are present. The coagulation kernel is restricted to processes involving monomer-cluster reactions, and only fragmentation processes with monomer break-off are allowed. We consider one model in which both coagulation and fragmentation processes scale with cluster size; in another model, fragmentation is subject to a cutoff at a certain critical size. This resembles physical processes in which a critical nucleus exists. Both sourceless and with-source evolution are considered. The scaling behaviour, steady-state size distributions, and growth exponents are discussed.