Non-Gaussian displacement distributions in models of heterogeneous active particle dynamics

TL;DR

This paper investigates how heterogeneity in diffusivities and speeds causes non-Gaussian displacement distributions in active particle models, revealing distinct shapes and differences from passive diffusion, and validating with biological data.

Contribution

It introduces models showing non-Gaussian displacement distributions due to heterogeneity, contrasting active and passive noise effects, and compares results with experimental data.

Findings

Non-Gaussian distributions emerge in active models with heterogeneity.

Active-noise models align well with biological displacement data.

Displacement shapes differ markedly from passive diffusion models.

Abstract

We study the effect of randomly distributed diffusivities and speeds in two models for active particle dynamics with active and passive fluctuations. We demonstrate how non-Gaussian displacement distributions emerge in these models in the long time limit, including Cauchy-type and exponential (Laplace) shapes. Notably the resulting shapes of the displacement distributions with distributed diffusivities for the active models considered here are in striking contrast to passive diffusion models. For the active motion models our discussion points out the differences between active- and passive-noise. Specifically, we demonstrate that the case with active-noise is in nice agreement with measured data for the displacement distribution of social amoeba.