Conserved-mass aggregation model with mass-dependent diffusion rate on complex networks.

We investigate the condensation phenomena of conserved-mass aggregation (CA) with mass-dependent diffusion rate on scale-free networks (SFNs). In the model, the mass m of a node isotropically diffuses to one of directly linked nodes with rate D(m)=m(-alpha), where alpha>0. With rate omega , unit mass is chipped from the mass and also isotropically diffuses. It was shown that no condensation phase transitions occur on regular lattices. However, on SFNs with degree distribution P(k) approximately k(-gamma), we show from mean-field approximation that the model exhibits various types of condensation phenomena according to alpha and gamma . There exists crossover alphac=(gamma-2)/(gamma-1) over which a system undergoes the same type of the condensation as that of zero-range process with jumping rate p(m)=mdelta regardless of gamma(>2). We find delta=1-alpha for alphac<or=alpha<1 and delta=0 for alpha>or=1. For alpha<alphac, however, the diffusion of masses cannot be ignored and so a system exhibits different behavior according to the network structure, i.e., gamma. For gamma>3, a system exhibits the behavior on regular lattice. For gamma<or=3, the condensation always occurs for any density with non-power-law background mass distribution. We also numerically confirm the mean-field predictions. Therefore, the network structure leads to the various condensation phenomena of the CA model unlike on regular lattices.