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http://hdl.handle.net/2445/18809
Title: | Diffusion-annihilation processes in complex networks |
Author: | Catanzaro, Michele Boguñá, Marián Pastor-Satorras, R. (Romualdo), 1967- |
Keywords: | Física matemàtica Física mèdica Sistemes no lineals Mathematical physics Medical physics Nonlinear systems |
Issue Date: | 2005 |
Publisher: | The American Physical Society |
Abstract: | We present a detailed analytical study of the $A+A\to\emptyset$ diffusion-annihilation process in complex networks. By means of microscopic arguments, we derive a set of rate equations for the density of $A$ particles in vertices of a given degree, valid for any generic degree distribution, and which we solve for uncorrelated networks. For homogeneous networks (with bounded fluctuations), we recover the standard mean-field solution, i.e. a particle density decreasing as the inverse of time. For heterogeneous (scale-free networks) in the infinite network size limit, we obtain instead a density decreasing as a power-law, with an exponent depending on the degree distribution. We also analyze the role of finite size effects, showing that any finite scale-free network leads to the mean-field behavior, with a prefactor depending on the network size. We check our analytical predictions with extensive numerical simulations on homogeneous networks with Poisson degree distribution and scale-free networks with different degree exponents. |
Note: | Reproducció del document publicat a: http://dx.doi.org/10.1103/PhysRevE.71.056104 |
It is part of: | Physical Review E, 2005, vol. 71, núm. , p. 056104-1-056104-9 |
URI: | http://hdl.handle.net/2445/18809 |
Related resource: | http://dx.doi.org/10.1103/PhysRevE.71.056104 |
ISSN: | 1063-651X |
Appears in Collections: | Articles publicats en revistes (Física de la Matèria Condensada) |
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