Diffusion-annihilation processes in complex networks

@article{citeulike:913843, abstract = {We present a detailed analytical study of the A+A 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.}, author = {Catanzaro, Michele and Boguna, Marian and Satorras, Romualdo P. }, citeulike-article-id = {913843}, doi = {http://dx.doi.org/10.1103/PhysRevE.71.056104}, journal = {Physical Review E (Statistical, Nonlinear, and Soft Matter Physics)}, keywords = {diffusion, networks}, number = {5}, posted-at = {2006-10-26 19:35:25}, priority = {0}, publisher = {APS}, title = {Diffusion-annihilation processes in complex networks}, url = {http://dx.doi.org/10.1103/PhysRevE.71.056104}, volume = {71}, year = {2005} }

TY - JOUR ID - citeulike:913843 L3 - citeulike-article-id:913843 TI - Diffusion-annihilation processes in complex networks JF - Physical Review E (Statistical, Nonlinear, and Soft Matter Physics) VL - 71 IS - 5 PB - APS N2 - We present a detailed analytical study of the A+A 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. KW - diffusion KW - networks AU - Catanzaro, Michele AU - Boguna, Marian AU - Satorras, Romualdo PY - 2005/// UR - http://dx.doi.org/10.1103/PhysRevE.71.056104 ER -