Condensates in Driven Aggregation Processes
Abstract
We investigate aggregation driven by mass injection. In this stochastic process, mass is added with constant rate r and clusters merge at a constant total rate 1, so that both the total number of clusters and the total mass steadily grow with time. Analytic results are presented for the three classic aggregation rates Ki,j between clusters of size i and j. When Ki,j=const, the cluster size distribution decays exponentially. When Ki,j (i+j) or Ki,j (ij), there are two phases: (i) a condensate phase with a condensate containing a finite fraction of the mass in the system as well as finite clusters, and (ii) a cluster phase with finite clusters only. For Ki,j (i+j), the cluster size distribution, ck, has a power-law tail, ck~k-gamma in either phase. The exponent is a non-monotonic function of the injection rate: gamma=r/(r-1) in the condensate phase, r<2, and γ=r in the cluster phase, r>2.
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