Cluster survival and polydispersity in aggregation

We study the probability, PS(t), of a cluster to remain intact in one-dimensional cluster-cluster aggregation when the cluster diffusion coefficient scales with size as D(s) ~ sγ. PS(t) exhibits a stretched exponential decay for γ < 0 and the power laws t−3/2 for γ = 0, and t−2/(2 − γ) for 0 < γ < 2. A random walk picture explains the discontinuous and non-monotonic behavior of the exponent. The decay of PS(t) determines the polydispersity exponent, τ, which describes the size distribution for small clusters. Surprisingly, τ(γ) is a constant τ = 0 for 0 < γ < 2.