Condensates in driven aggregation processes.
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 K{i,j} between clusters of size i and j . When K{i,j}=const , the cluster size distribution decays exponentially. When K{i,j} proportional, i+j or K{i,j} proportional, ixj , 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 K{i,j} proportional, i+j , the cluster size distribution, c{k} , has a power-law tail, c{k} approximately k;{-gamma} in either phase. The exponent is a nonmonotonic function of the injection rate gamma=r(r-1) in the condensate phase r<2 and gamma=r in the cluster phase r>2 .
Ben-Naim
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Theoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA.
Krapivsky
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PL