Abstract
Diffusion-limited cluster-cluster aggregation subject to the condition that single particles are fed into the system at a rate h, while clusters larger than a fixed size are removed is investigated. Fluctuation effects in this system are treated on a phenomenological level by a scaling generalization of the Smoluchowski equation. We find that the cluster size distribution obeys scaling and all the relevant exponents are expressible through a single homogeneity index. This index is determined by arguing that the zero feed-rate process is in one universality class with the diffusive annihilation problem. The scaling theory is checked on the example of one-dimensional diffusive annihilation in the presence of particle sources. We calculate exactly the steady-state particle density n ¯ and the relaxation time of homogeneous density fluctuation τ. They are found to scale in the h → 0 limit as n ¯ ∼ h 1/3 and τ ∼ h −2/3 in agreement with the scaling theory.
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