An empirical method to characterize displacement distribution functions for anomalous and transient diffusion

TL;DR

This paper introduces an empirical fitting function to effectively characterize non-Gaussian displacement distributions in heterogeneous diffusion, providing physical insights beyond kurtosis and applicable to various anomalous diffusion scenarios.

Contribution

The paper presents a new empirical method for fitting displacement distribution functions that yields more physical information than kurtosis in heterogeneous and anomalous diffusion.

Findings

Fitting parameters indicate where distribution tails begin.

Parameters converge to Gaussian values in less anomalous systems.

Method validated with simulations of colloidal particles and obstacle models.

Abstract

We propose a practical empirical fitting function to characterize the non-Gaussian displacement distribution functions (DispD) often observed for heterogeneous diffusion problems. We first test this fitting function with the problem of a colloidal particle diffusing between two walls using Langevin Dynamics (LD) simulations of a raspberry particle coupled to a lattice Boltzmann (LB) fluid. We also test the function with a simple model of anomalous diffusion on a square lattice with obstacles. In both cases, the fitting parameters provide more physical information than just the Kurtosis (which is often the method used to quantify the degree of anomaly of the dynamics), including a length scale that marks where the tails of the DispD begin. In all cases, the fitting parameters smoothly converge to Gaussian values as the systems become less anomalous.