Power-law mass distribution of aggregation systems with injection

Abstract

We introduce a new family of aggregation models with constant interjection. In our models, the asymptotic distribution of particle mass, s, always follows a power law, P(\ensuremath{\ge}s)\ensuremath{\propto}${s}^{\mathrm{\ensuremath{-}}\ensuremath{\alpha}}$, where (1/3\ensuremath{\le}\ensuremath{\alpha}\ensuremath{\le} 1) / 2 . It is clarified that this power law is realized by a balance of two effects, injection and aggregation.