Anomalous diffusion from Brownian motion with random confinement

TL;DR

This paper introduces a model of anomalous diffusion caused by particles in Brownian motion confined by randomly placed boundaries, leading to subdiffusive behavior and non-Gaussian displacement distributions, relevant for single-particle tracking analysis.

Contribution

The paper provides exact and asymptotic calculations of mean squared displacement for a new confinement-based anomalous diffusion model with power-law distributed compartments.

Findings

Mean squared displacement increases subdiffusively, either as a power or logarithm of time.

Displacement probability density function is non-Gaussian.

Model relates to diffusion on percolation processes.

Abstract

We present a model of anomalous diffusion consisting of an ensemble of particles undergoing homogeneous Brownian motion except for confinement by randomly placed reflecting boundaries. For power-law distributed compartment sizes, we calculate exact and asymptotic values of the ensemble averaged mean squared displacement and find that it increases subdiffusively, as either a power or the logarithm of time. Numerical simulations show that the probability density function of the displacement is non-Gaussian. We discuss the relevance of the model for the analysis of single-particle tracking experiments and its relation to other sources of subdiffusion. In particular we discuss an intimate connection with diffusion on percolation processes.