From ageing to immortality: cluster growth in stirred colloidal solutions
Abstract
This model describes cluster aggregation in a stirred colloidal solution Interacting clusters compete for growth in this 'winner-takes-all' model; for finite assemblies, the largest cluster always wins, i.e. there is a uniform sediment. In mean-field, the model exhibits glassy dynamics, with two well-separated time scales, corresponding to individual and collective behaviour; the survival probability of a cluster eventually falls off according to a universal law ( t)-1/2. In finite dimensions, the glassiness is enhanced: the dynamics manifests both ageing and metastability, where pattern formation is manifested in each metastable state by a fraction of immortal clusters.
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