Characterizing N-dimensional anisotropic Brownian motion by the distribution of diffusivities

TL;DR

This paper introduces a method using the distribution of diffusivities to characterize N-dimensional anisotropic Brownian motion, providing analytical tools to identify anisotropy and diffusion tensor properties from experimental data.

Contribution

It derives analytical expressions for the diffusivity distribution in anisotropic environments and relates these to measurable anisotropy parameters, improving process characterization.

Findings

Distribution of diffusivities reveals anisotropy in diffusion processes.

Analytical expressions enable determination of diffusion tensor properties.

Method applicable to simulated and experimental trajectories in 2D and 3D.

Abstract

Anisotropic diffusion processes emerge in various fields such as transport in biological tissue and diffusion in liquid crystals. In such systems, the motion is described by a diffusion tensor. For a proper characterization of processes with more than one diffusion coefficient an average description by the mean squared displacement is often not sufficient. Hence, in this paper, we use the distribution of diffusivities to study diffusion in a homogeneous anisotropic environment. We derive analytical expressions of the distribution and relate its properties to an anisotropy measure based on the mean diffusivity and the asymptotic decay of the distribution. Both quantities are easy to determine from experimental data and reveal the existence of more than one diffusion coefficient, which allows the distinction between isotropic and anisotropic processes. We further discuss the influence on the analysis of projected trajectories, which are typically accessible in experiments. For the experimentally relevant cases of two- and three-dimensional anisotropic diffusion we derive specific expressions, determine the diffusion tensor, characterize the anisotropy, and demonstrate the applicability for simulated trajectories.