Aggregation process on complex networks

LUIS G. MORELLI AND HILDA A. CERDEIRA

PHYSICAL REVIEW E - STATISTICAL PHYSICS, PLASMAS, FLUIDS AND RELATED INTERDISCIPLINARY TOPICS

Año: 2004 vol. 69 p. 511071 - 511078

1063-651X

We  study  the  dynamics  of  the aggregation of particles and theevolution  of the mass distribution, on a complex network which isbuilt  following  the  Watts-Strogatz model. The particles performrandom  walks  following  the  links on the network, and aggregatewhen they meet other particles. On disordered networks the densityof  particles  decays  as  $t^{-1}$,  while on regular networks itdecays  as $t^{-1/2}$. For intermediate levels of network disorderthe  dynamics  follows  that  of  regular networks at intermediatedensity,  and  for low density the disorder of the network becomesrelevant  and  the  density decays as $t^{-1}$. The crossover timebetween  these two regimes scales with network disorder as $t \simp^{-2}$.  We  study  also  an  annealed  model for the aggregationprocess, in which the quenched disorder of the network is replacedby  stochastic  long  range  jumps  in  the particle dynamics. Theannealed  model  is found to obey a different scaling with networkdisorder,    with    a    crossover    time   $t   \sim   p^{-1}$.