Analytical kinetics of clustering processes with cooperative action of aggregation and fragmentation

Abstract

Some models of clustering processes are formulated and analytically solved employing generating functions methods. Those models include events which result from combined action of the coagulation and fragmentation processes. Fragmentation processes of two kinds, so-called similar and arbitrary, ones, are brought forward, and the explicit forms of their solutions are produced. This implies some possibility of existence of different aggregation mechanisms for clusters creation differing in their inner structure. All the models are based on "the three-level bunch" scheme of interaction between the system states. Those states are described in terms of the probability to find the system in the state with an exactly given number of clusters. The models are linear in the probability functions due to the assumption that the rates of elementary acts are permanent. Some peculiarities of application of the generating function method to solution of the linear differential-difference equations are revealed. The illustration of the problem in terms of a traffic jam picture is not a specific one.