Velocity statistics in excited granular media

TL;DR

This experimental study investigates velocity distributions in excited granular media, revealing non-Gaussian behavior, dependence on boundary velocity, and energy sharing among particles, with results aligning with recent theoretical predictions.

Contribution

The paper provides experimental validation of a non-Gaussian velocity distribution in driven granular media and explores how particle density and mass affect kinetic energy sharing.

Findings

Velocity distribution follows P(v) ~ exp(-|v/v_c|^1.5)

Granular temperature peaks at intermediate densities

More massive particles have higher kinetic energy

Abstract

We present an experimental study of velocity statistics for a partial layer of inelastic colliding beads driven by a vertically oscillating boundary. Over a wide range of parameters (accelerations 3-8 times the gravitational acceleration), the probability distribution P(v) deviates measurably from a Gaussian for the two horizontal velocity components. It can be described by P(v) ~ exp(-|v/v_c|^1.5), in agreement with a recent theory. The characteristic velocity v_c is proportional to the peak velocity of the boundary. The granular temperature, defined as the mean square particle velocity, varies with particle density and exhibits a maximum at intermediate densities. On the other hand, for free cooling in the absence of excitation, we find an exponential velocity distribution. Finally, we examine the sharing of energy between particles of different mass. The more massive particles are found to have greater kinetic energy.