Anomalous Diffusion in Systems with Concentration-Dependent Diffusivity
Statistical Mechanics
2019-12-13 v1
Abstract
We show analytically that there is anomalous diffusion when the diffusion constant depends on the concentration as a power law with a positive exponent or a negative exponent with absolute value less than one and the initial condition is a delta function in the concentration. On the other hand, when the initial concentration profile is a step, the profile spreads as the square root of time. We verify our results numerically using particles moving stochastically.
Cite
@article{arxiv.1912.05856,
title = {Anomalous Diffusion in Systems with Concentration-Dependent Diffusivity},
author = {Alex Hansen and Eirik G. Flekkøy},
journal= {arXiv preprint arXiv:1912.05856},
year = {2019}
}
Comments
10 pages, 10 figures