Irreversible aggregation is an archetypal example of a system driven far from equilibrium by sources and sinks of a conserved quantity (mass). The source is a steady input of monomers and the evaporation of colliding particles with a small probability is the sink. Using exact and heuristic analyses, we find a universal regime and two distinct non-universal regimes distinguished by the relative importance of mergers between small and large particles. At the boundary between the regimes we find an analogue of the logarithmic correction conjectured by Kraichnan for two-dimensional turbulence.
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