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

Le Qiao, Nicholas Ilow, Maxime Ignacio and Gary W. Slater

Physica A: Statistical Mechanics and its Applications, 2022, vol. 604, issue C

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.

Keywords: Anomalous diffusion; Non-Gaussian; Wall-hindered; Obstacles; Displacement distribution; Lattice Boltzmann (search for similar items in EconPapers)
Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:604:y:2022:i:c:s0378437122004526

DOI: 10.1016/j.physa.2022.127676

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