Diffusion on spatial network

4th International Workshop on Statistical Physics and Mathematics for Complex Systems

物理学;数学

Hui, Zi^1 ; Tang, Xiaoyue^2 ; Li, Wei^4 ; Greneche, Jean-Marc^3,5 ; Wang, Qiuping A.^3,5

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

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

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/604/1/012008/pdf
DOI  :  10.1088/1742-6596/604/1/012008

来源: IOP

【 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.