Random diffusivity scenarios behind anomalous non-Gaussian diffusion

TL;DR

This paper investigates how heterogeneity and correlations in diffusivity lead to anomalous, non-Gaussian diffusion patterns, providing a general framework to interpret population spread in complex environments.

Contribution

It introduces a comprehensive framework linking individual heterogeneity and correlations to observed anomalous diffusion behaviors.

Findings

Different diffusivity scenarios produce distinct non-Gaussian spreading patterns.

The framework applies to well-known processes like Laplace and nonlinear diffusion.

Limitations are discussed regarding the inference of microscopic features from macroscopic observations.

Abstract

The standard diffusive spreading, characterized by a Gaussian distribution with mean square displacement that grows linearly with time, can break down, for instance, under the presence of correlations and heterogeneity. In this work, we consider the spread of a population of fractional (long-time correlated) Brownian walkers, with time-dependent and heterogeneous diffusivity. We aim to obtain the possible scenarios related to these individual-level features from the observation of the temporal evolution of the population spatial distribution. We develop and discuss the possibility and limitations of this connection for the broad class of self-similar diffusion processes. Our results are presented in terms of a general framework, which is then used to address well-known processes, such as Laplace diffusion, nonlinear diffusion, and their extensions.