Nonuniversality and Breakdown of Scaling in Aggregation Process with Removal Term**The project supported by National Natural Science Foundation of China under Grant Nos. 10275048 and 10175008

Abstract

We study the kinetics of an irreversible aggregation model with removal term. We solve the mean-field rate equation to obtain the general solution of the cluster-mass distribution for the case with arbitrary time-dependent removal probability . In particular, we analyze the scaling properties of the cluster distribution in the case with and find that the cluster-mass distribution always obeys a scaling law. We also investigate the kinetic behavior of another simple system, in which the removal probability of a cluster is proportional to its mass, and the results indicate that for this system the scaling description of the cluster-mass distribution breaks down completely.