Can I read Diffusion in Sparse Networks: Linear to Semi-linear Crossover on EtoBox?

Diffusion in Sparse Networks: Linear to Semi-linear Crossover by de Leeuw, Yaron; Cohen, Doron is a scholarly article available to read on EtoBox.

What is Diffusion in Sparse Networks: Linear to Semi-linear Crossover about?

We consider random networks whose dynamics is described by a rate equation, with transition rates $w_{nm}$ that form a symmetric matrix. The long time evolution of the system is characterized by a diffusion coefficient $D$. In one dimension it is well known that $D$ can display an abrupt percolation-like transition from diffusion ($D>0$) to sub-diffusion (D=0). A question arises whether such a transition happens in higher dimensions. Numerically $D$ can be evaluated using a resistor network calculation, or optionally it can be deduced from the spectral properties of the system. Contrary to a recent expectation that is based on a renormalization-group analysis, we deduce that $D$ is finite; suggest an "effective-range-hopping" procedure to evaluate it; and contrast the results with the linear estimate. The same approach is useful for the analysis of networks that are described by quasi-one-dimensional sparse banded matrices.

Author

de Leeuw, Yaron; Cohen, Doron

Published

2012

Language

EN