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 ratesKMM,KMC andKCC, respectively. The dynamics crucially depends on the ratio γ = KCC/KMC and secondarily on = KMM/KMC. For = 0 and γ < 2, there is conventional scaling in the long-time limit, with a single mass scale that grows linearly in time. For γ 2, there is unusual behaviour in which the concentration of clusters of mass k, ck decays as a stretched exponential in time within a boundary layer k < k∗ ∝ t1−2/γ (k∗ ∝ ln t for γ = 2), while ck ∝ t−2 in the bulk region k > k∗. When > 0, analogous behaviours emerge for γ < 2 and γ 2. PACS numbers: 02.50.−r, 05.40.−a, 68.43.Jk