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

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.

References in corpus (7)

• "Diffusing diffusivity": A model for anomalous and "anomalous yet Brownian" diffusion
• Statistical Mechanics of the Fluctuating Lattice Boltzmann Equation
• Driven polymer translocation through a nanopore: a manifestation of anomalous diffusion
• Classification of particle trajectories in living cells: machine learning versus statistical testing hypothesis for fractional anomalous diffusion
• Classification, inference and segmentation of anomalous diffusion with recurrent neural networks
• Test of the diffusing-diffusivity mechanism using near-wall colloidal dynamics
• Frequency-dependent magnetic susceptibility of magnetic nanoparticles in a polymer solution: a simulation study