Non-Gaussian diffusion of mixed origins

TL;DR

This paper investigates how combining different heterogeneities affects diffusion processes, providing exact solutions for propagators and first-passage times in complex biological systems with non-Gaussian behavior.

Contribution

It introduces a combined subordination technique to derive exact propagators for mixed-origin heterogenous diffusion processes, advancing understanding of complex biological diffusion.

Findings

Derived exact propagators for mixed heterogeneity diffusion

Analytically calculated first-passage time statistics

Identified new classes of strongly heterogeneous processes

Abstract

The properties of diffusion processes are drastically affected by heterogeneities of the medium that can induce non-Gaussian behavior of the propagator in contrast with the idealized realm of Brownian motion. In this paper we analyze the diffusion propagator when distinct origins of heterogeneity (e.g. time-fractional diffusion, diffusing diffusivity, distributed diffusivity across a population) are combined. These combinations allow one to describe new classes of strongly heterogeneous processes relevant to biology. Based on a combined subordination technique, we obtain the exact propagator for different instructive examples. This approach is then used to calculate analytically the first-passage time statistics (on half-real line and in any bounded domain) for a particle undergoing non-Gaussian diffusion of mixed origins.