Non-Gaussian Velocity Distribution Function in a Vibrating Granular Bed

TL;DR

This study investigates the velocity distribution in a vibrating granular bed, revealing an exponential-like distribution caused by Coulomb friction, and introduces a Langevin model to describe the system's dynamics.

Contribution

It demonstrates the role of Coulomb friction in shaping the velocity distribution and proposes a Langevin equation incorporating Coulomb friction for modeling granular particle motion.

Findings

Velocity distribution is exponential-like during vibration.

Distribution deviates from exponential in free-cooling states.

Coulomb's friction is responsible for the exponential-like distribution.

Abstract

The simulation of granular particles in a quasi two-dimensional container under the vertical vibration as an experimental accessible model for granular gases is performed. The velocity distribution function obeys an exponential-like function during the vibration and deviates from the exponential function in free-cooling states. It is confirmed that this exponential-like distribution function is produced by Coulomb's friction force. A Langevin equation with Coulomb's friction is proposed to describe the motion of such the system.