Numerical simulations of confined Brownian-yet-non-Gaussian motion

TL;DR

This paper presents efficient numerical simulations of confined Brownian motion, revealing non-Gaussian behaviors and providing detailed statistical analysis of particle dynamics near walls in viscous fluids.

Contribution

It introduces a novel numerical approach to simulate and analyze non-Gaussian Brownian motion under confinement, including a new method for high-order cumulant computation.

Findings

Particles exhibit non-Gaussian displacement distributions near walls.

The method accurately captures space-dependent mobility effects.

High-order cumulants reveal detailed non-Gaussian features.

Abstract

Brownian motion is a central scientific paradigm. Recently, due to increasing efforts and interests towards miniaturization and small-scale physics or biology, the effects of confinement on such a motion have become a key topic of investigation. Essentially, when confined near a wall, a particle moves much slower than in the bulk due to friction at the boundaries. The mobility is therefore locally hindered and space-dependent, which in turn leads to the apparition of so-called multiplicative noises, and associated non-Gaussianities which remain difficult to resolve at all times. Here, we exploit simple, optimized and efficient numerical simulations to address Brownian motion in confinement in a broadrange and quantitative way. To do so, we integrate the overdamped Langevin equation governing the thermal dynamics of a negatively-buoyant single spherical colloid within a viscous fluid confined by two rigid walls, including surface charges. From the produced large set of long random trajectories, we perform a complete statistical analysis and extract all the key quantities, such as the probability distributions in displacements and their main moments. In particular, we propose a novel method to compute high-order cumulants by reducing convergence problems, and employ it to efficiently characterize the inherent non-Gaussianity of the confined process.