Competition between surface relaxation and ballistic deposition models in scale free networks

Abstract

In this paper we study the scaling behavior of the fluctuations in the steady state WS with the system size N for a surface growth process given by the competition between the surface relaxation (SRM) and the Ballistic Deposition (BD) models on degree uncorrelated Scale Free networks (SF), characterized by a degree distribution P(k) ~ k^{−lambda}, where k is the degree of a node. It is known that the fluctuations of the SRM model above the critical dimension (dc = 2) scales logarithmically with N on euclidean lattices. However, Pastore y Piontti et. al. [A. L. Pastore y Piontti et. al., Phys. Rev. E 76, 046117 (2007)] found that the fluctuations of the SRM model in SF networks scale logarithmically with N for lambda< 3 and as a constant for lambda >= 3. In this letter we found that for a pure ballistic deposition model on SF networks WS scales as a power law with an exponent that depends on lambda. On the other hand when both processes are in competition, we find that there is a continuous crossover between a SRM behavior and a power law behavior due to the BD model that depends on the occurrence probability of each process and the system size. Interestingly, we find that a relaxation process contaminated by any small contribution of ballistic deposition will behave, for increasing system sizes, as a pure ballistic one. Our findings could be relevant when surface relaxation mechanisms are used to synchronize processes that evolve on top of complex networks.