Kinetic anomalies in addition-aggregation processes

We investigate irreversible aggregation in which monomer-monomer, monomer-cluster and cluster-cluster reactions occur with constant but distinct rates K-MM,, K-MC and K-CC, respectively. The dynamics crucially depends on the ratio gamma = K-CC / K-MC and secondarily on is an element of = K-MM / K-MC. For is an element of = 0 and gamma < 2, there is conventional scaling in the long-time limit, with a single mass scale that grows linearly in time. For y greater than or equal to 2, there is unusual behaviour in which the concentration of clusters of mass k, c(k) decays as a stretched exponential in time within a boundary layer k < k* proportional to t(1-2/gamma) (k* proportional to In t for gamma = 2), while c(k) proportional to t(-2) in the bulk region k > k*. When is an element of > 0, analogous behaviours emerge for gamma < 2 and y greater than or equal to 2.