Kinetics of Coagulation with Fragmentation: Scaling Behavior and Fluctuations

Abstract

The standard coagulation process is generalized to include the effects of fragmentation and a scaling description for the cluster size distribution is developed. The Smoluchowski rate equation is used to calculate the critical exponents describing the steady-state size distribution. Predictions of the scaling and the rate equation are tested by numerical simulations. The mean-field rate-equation results are found to be valid in $d>~1$ implying that the upper critical dimension $d_c$ is less than 1.