Critical Exponents for Granular Phase Transitions

TL;DR

This study numerically investigates the solid-fluid phase transition in granular materials, identifying it as a second-order transition with distinct universal critical exponents for kinetic energy and granular temperature.

Contribution

It introduces two order parameters to precisely determine the fluidization point and analyzes their critical scaling behavior.

Findings

The phase transition is second-order.

Kinetic energy and granular temperature have different universal critical exponents.

The fluidization point scales with external vibration acceleration.

Abstract

The solid--fluid phase transition of a granular material shaken horizontally is investigated numerically. We find that it is a second-order phase transition and propose two order parameters, namely the averaged kinetic energy and the averaged granular temperature, to determine the fluidization point precisely. It scales with the acceleration of the external vibration. Using this fluidization point as critical point, we discuss the scaling of the kinetic energy and show that the kinetic energy and the granular temperature show two different universal critical point exponents for a wide range of excitation amplitudes.