Diffusion on spatial network

[摘要] In this work, we study the problem of diffusing a product (idea, opinion, disease etc.) among agents on spatial network. The network is constructed by random addition of nodes on the planar. The probability for a previous node to be connected to the new one is inversely proportional to their spatial distance to the power of . The diffusion rate between two connected nodes is inversely proportional to their spatial distance to the power of β as well. Inspired from the Fick's first law, we introduce the diffusion coefficient to measure the diffusion ability of the spatial network. Using both theoretical analysis and Monte Carlo simulation, we get the fact that the diffusion coefficient always decreases with the increasing of parameter and β, and the diffusion sub-coefficient follows the power-law of the spatial distance with exponent equals to β+2. Since both short-range diffusion and long-range diffusion exist, we use anomalous diffusion method in diffusion process. We get the fact that the slope index δ in anomalous diffusion is always smaller that 1. The diffusion process in our model is sub-diffusion.

[发布机构] School of Electrical and Electronic Engineering, Wuhan Polytechnic University, Wuhan; 430032, China^1;School of Mathematics and Computer Science, Wuhan Polytechnic University, Wuhan; 430032, China^2;LUNAM Universite, ISMANS, Ave. Bartholdi, 44, Le Mans; 72000, France^3;Complexity Science Center, Institute of Particle Physics, Hua-Zhong (Central China) Normal University, Wuhan; 430079, China^4;LUNAM Universite, Universite du Maine, UMR CNRS 6087, Le Mans; 72085, France^5

[效力级别] 数学

[关键词] Anomalous diffusion;Diffusion process;Diffusion rate;Fick's first law;Long-range diffusion;Power-law;Spatial distance;Spatial network