Florentin PaladiCLUSTER-BASED APPROACH TO THE

Abstract

The non-stationary cluster size distribution in a network of agents which evolves without preferential behavior has been studied at early and late stages of clusters formation, when they are expected to grow and decay mainly by gaining and losing single agents. We developed a further model for the dynamics of an open system formed by time-dependent number of agents. Groups of agents (clusters) change their sizes by all possible transitions: addition/removal of agent(s) (monomers, dimers etc.) to/from the system, coagulation of two clusters of sizes r and k-r, where 1<r<k-1 (k>3), attachment of monomers, dimers, trimers etc. to clusters of size k or disappearance of a cluster of size k by coagulation with another cluster, and detachment of monomers, dimers, trimers etc. Both non-zero initial cluster size distribution and when only free agents (monomers) are present in the system at the initial moment have been studied, and we describe accordingly the effect of arbitrary pre-existing clusters on the time evolution of the interacting agents. PACS: 02.60.Cb; 05.40.−a; 89.65.G