Conserved-mass aggregation model with mass-dependent fragmentation on complex networks.

We study the conserved-mass aggregation model with mass-dependent fragmentation on random networks (RNs) and scale-free networks (SFNs) with degree distribution Pk approximately k(-gamma). In the model, masses isotropically diffuse with unit rate. With rate omega, a mass m(lambda) is fragmented from a node with mass m , and moves to one of the linked nodes with the equal probability. For lambda=0 , the model is known to undergo the condensation phase transitions at a certain criticality rho(c) . From the mean-field balance equation for an aggregate, we analytically show that the present model exhibits different behavior depending on network structures. The condensation always occurs for lambda<0 . For 0<lambda<1 , finite-sized systems on RNs and SFNs with gamma>3 undergoes the condensation transitions (sharp crossovers) at rho(c) which diverges with network size N as N(lambda). Hence, in the limit N-->infinity , masses uniformly distribute without the condensation (fluid phase). On the other hand, for gamma< or =3 , a crossover lambda(c)=1(gamma-1) exists. The condensation always occurs for lambda<lambda(c) , while the fluid phase is always stable at any nonzero density for lambda> or =lambda(c) . The phase separation results from the competition between the heterogeneity of network structure and the enhanced chipping by lambda . We numerically confirm all the predictions.