Monte Carlo simulations of aggregation phenomena

(Received 16 July 1992, revised 23 December 1992, accepted 22 January 1993)

Abstract
We discuss the evolution of many-body systems under merging interactions between their components; the realizations that are considered here can be related to various physical systems from the evolution of systems of galaxies to the growth of structures in colloids. We run Monte Carlo simulations of aggregation processes of clusters with mass  M, for various merging probabilities , and study the evolution of the resulting mass distribution (MD). We find out evidence for the known phase transition around the critical value . We extend the analysis of the aggregation to the case of spatial fluctuations of the cluster distribution by means of a multifractal analysis. The distribution of clusters turns out to be fractal in the mass space and multifractal in the real space. The phase transition produces an enhancement of the spatial dishomogeneity for large masses, that is quantified in terms of different values of the generalized fractal dimension D_r(q). A correspondence between the effects of the phase transition in the mass space and in the coordinates is also found.