Scaling in steady-state aggregation with injection

A mean-field approach for steady-state aggregation with injection is presented. It is shown that for a wide variety of aggregation processes the resulting steady-size distribution obeys a power law (Formula presented) with (Formula presented) and (Formula presented) the degree of homogeneity of the coagulation kernel. The general conditions for this to happen are obtained. Some applications are studied. In particular, it predicts a potential behavior for coagulation in atmospheric aerosols with exponent (Formula presented) in agreement with observations. The theoretical results also agree with some animal group-size distributions and with numerical simulations in fractal aggregates. © 2001 The American Physical Society.