Stationary state volume fluctuations in a granular medium

TL;DR

This study investigates volume fluctuations in a granular medium, demonstrating a stationary state with Gaussian-distributed volume fractions and enabling the measurement of a temperature-like variable called compactivity.

Contribution

It provides experimental evidence for a stationary state in granular materials and introduces a method to measure compactivity, a key concept in granular statistical mechanics.

Findings

Volume fractions are history independent and Gaussian distributed.

Standard deviation of volume fraction shows a minimum at a specific state.

Measurement of compactivity X from fluctuations supports statistical theory.

Abstract

A statistical description of static granular material requires ergodic sampling of the phase space spanned by the different configurations of the particles. We periodically fluidize a column of glass beads and find that the sequence of volume fractions phi of post-fluidized states is history independent and Gaussian distributed about a stationary state. The standard deviation of phi exhibits, as a function of phi, a minimum corresponding to a maximum in the number of statistically independent regions. Measurements of the fluctuations enable us to determine the compactivity X, a temperature-like state variable introduced in the statistical theory of Edwards and Oakeshott [Physica A {\bf 157}, 1080 (1989)].