Simulations support protocol independency of the granular temperature

TL;DR

This study uses computer simulations of polygonal particles under different excitation protocols to test Edwards' statistical theory of granular materials, finding that the granular temperature uniquely determines volume regardless of protocol.

Contribution

The paper demonstrates that the granular temperature is protocol-independent and supports Edwards' theory through simulation results.

Findings

Mean volume is a unique function of granular temperature.

Volume distribution fits a Boltzmann-like distribution.

Results are consistent across different excitation protocols.

Abstract

A possible approach to the statistical description of granular assemblies starts from Edwards' assumption that all blocked states occupying the same volume are equally probable (S.F. Edwards, R. Oakeshott, Physica A 157, 1080 (1989)). We performed computer simulations using two-dimensional polygonal particles excited periodically according to two different protocols: excitation by pulses of "negative gravity" and excitation by "rotating gravity". The first protocol exhibits a non-monotonous dependency of the mean volume fraction on the pulse strength. The overlapping histogram method is used in order to test whether or not the volume distribution is described by a Boltzmann-like distribution, and to calculate the inverse compactivity as well as the logarithm of the partition sum. We find that the mean volume is a unique function of the measured granular temperature, independently of the protocol and of the branch in $\phi(g)$ and all determined quantities are in agreement with Edwards' theory.