Anomalous Diffusion in Systems with Concentration-Dependent Diffusivity

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.