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 N(m)similar tom(-alpha) with alpha=(3 + beta)/2 and beta 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 alpha approximate to2, in agreement with observations. The theoretical results also agree with some animal group-size distributions and with numerical simulations in fractal aggregates.