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 (SF) networks, characterized by a degree distribution P (k) ∼ k −λ , where k is the degree of a node. It is known that the fluctuations of the SRM model above the critical dimension (dc = 2) scale logarithmically with N on Euclidean lattices. However, Pastore y Piontti et al. (Phys. Rev. E, 76 (2007) 046117) found that the fluctuations of the SRM model in SF networks scale logarithmically with N for λ < 3 and as a constant for λ 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 λ. 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.

Study of Scaling Exponents of the Surface Evolved in 2 + 1 Dimension through Competitive Growth between Random Deposition and that with Surface Relaxation

“…[6] In 2013, Rocca et al reported a continuous crossover and proposed a scaling involving occurrence probability and system size for a CGM. [7] Xun et al also reported deviation in the scaling exponent values in higher dimensions for the EW universality class in 2015. [8] Also in 2015, Kolakowska and Novotny reported a deviation of scaling exponents along with a new proposed scaling for competitive growth.…”

“…reported a continuous crossover and proposed a scaling involving occurrence probability and system size for a CGM. [ 7 ] Xun et al. also reported deviation in the scaling exponent values in higher dimensions for the EW universality class in 2015.…”

Effect of particle size on optical and electrical properties of thin films – a simulation approach

“…Basic models include random deposition (RD), ballistic deposition (BD), random deposition with surface relaxation (RDSR), and solid-on-solid (SoS) [4]. Competitive Growth Models (CGM) are developed for a more precise description of thin film growth that incorporates more than one discrete growth mechanism in a single growth process [5][6][7].…”