Aggregation process on complex networks.

Abstract

We study the dynamics of the aggregation of particles and the evolution of the mass distribution, on a complex network which is built following the Watts-Strogatz model. The particles perform random walks following the links on the network, and aggregate when they meet other particles. On disordered networks the density of particles decays as t(-1), while on regular networks it decays as t(-1/2). For intermediate levels of network disorder the dynamics follows that of regular networks at intermediate density, and for low density the disorder of the network becomes relevant and the density decays as t(-1). The crossover time between these two regimes scales with network disorder as t approximately p(-2). We study also an annealed model for the aggregation process, in which the quenched disorder of the network is replaced by stochastic long range jumps in the particle dynamics. The annealed model is found to obey a different scaling with network disorder, with a crossover time t approximately p(-1).