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Conservative model for synchronization problems in complex networks

C. E. La Rocca1, L. A. Braunstein1,2, and P. A. Macri1

  • 1Instituto de 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
  • 2Center for Polymer Studies, Boston University, Boston, Massachusetts 02215, USA

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Phys. Rev. E 80, 026111 – Published 12 August, 2009

DOI: https://doi.org/10.1103/PhysRevE.80.026111

Abstract

In this paper we study the scaling behavior of the interface fluctuations (roughness) for a discrete model with conservative noise on complex networks. Conservative noise is a noise which has no external flux of deposition on the surface and the whole process is due to the diffusion. It was found that in Euclidean lattices the roughness of the steady state Ws does not depend on the system size. Here, we find that for scale-free networks of N nodes, characterized by a degree distribution P(k)∼k−λ, Ws is independent of N for any λ. This behavior is very different than the one found by Pastore y Piontti et al. [Phys. Rev. E 76, 046117 (2007)] for a discrete model with nonconservative noise, which implies an external flux, where Ws∼ln N for λ<3, and was explained by nonlinear terms in the analytical evolution equation for the interface [La Rocca et al., Phys. Rev. E 77, 046120 (2008)]. In this work we show that in these processes with conservative noise the nonlinear terms are not relevant to describe the scaling behavior of Ws.

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Phys. Rev. E 80, 026111– Published 12 August, 2009
  • Received 3 June 2009

© 2009 American Physical Society

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