Volume 101, Number 1, January 2013
|Number of page(s)||5|
|Section||Condensed Matter: Structural, Mechanical and Thermal Properties|
|Published online||14 January 2013|
Competition between surface relaxation and ballistic deposition models in scale-free networks
1 Investigaciones Físicas de Mar del Plata (IFIMAR)-Departamento de Física, Facultad de Ciencias Exactas y Naturales, Universidad Nacional de Mar del Plata-CONICET - Funes 3350, (7600) Mar del Plata, Argentina
2 Center for Polymer Studies, Boston University - Boston, MA 02215, USA
Received: 15 October 2012
Accepted: 7 December 2012
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.
PACS: 68.35.Ct – Interface structure and roughness / 05.45.Xt – Synchronization; coupled oscillators / 89.75.Da – Systems obeying scaling laws
© EPLA, 2013
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.