Random diffusivity scenarios behind anomalous non-Gaussian diffusion

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. (c) 2021 Elsevier Ltd. All rights reserved.

Automated summary

This study focuses on the diffusion characteristics of fractional Brownian walkers, aiming to understand individual-level features through the temporal evolution of population spatial distribution. A general framework is developed to address the possibilities and limitations of connecting these features to various diffusion processes. The results are presented in terms of well-known processes, such as Laplace diffusion and nonlinear diffusion.