Diffusion-annihilation processes in complex networks
We present a detailed analytical study of the A+A¿/0 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 fo...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2005 |
| País: | España |
| Institución: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/125858 |
| Acceso en línea: | https://hdl.handle.net/2117/125858 https://dx.doi.org/10.1103/PhysRevE.71.056104 |
| Access Level: | acceso abierto |
| Palabra clave: | Annihilation reactions Complex networks Diffusion-annihilation process Uncorrelated networks Reaccions d'anihilació Àrees temàtiques de la UPC::Física |
| Sumario: | We present a detailed analytical study of the A+A¿/0 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. |
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