Dynamic synchrotron X-ray imaging study of effective temperature in a vibrated granular medium

TL;DR

This study uses dynamic synchrotron X-ray imaging to measure the effective temperature in a vibrated granular medium, revealing how structural relaxation time relates to vibration intensity and pressure, consistent with hard sphere models.

Contribution

It introduces a novel application of synchrotron X-ray imaging to quantify effective temperature in vibrated granular systems, linking relaxation dynamics to thermodynamic parameters.

Findings

Structural relaxation time increases with vibration intensity.

Effective temperature follows an Arrhenius law with pressure.

Relaxation energy scale matches hard sphere simulation results.

Abstract

We present a dynamic synchrotron X-ray imaging study of the effective temperature $T_{eff}$ in a vibrated granular medium. By tracking the directed motion and the fluctuation dynamics of the tracers inside, we obtained $T_{eff}$ of the system using Einstein relation. We found that as the system unjams with increasing vibration intensities $\Gamma$, the structural relaxation time $\tau$ increases substantially which can be fitted by an Arrhenius law using $T_{eff}$. And the characteristic energy scale of structural relaxation yielded by the Arrhenius fitting is $E = 0.21 \pm 0.02$ $pd^3$, where $p$ is the pressure and $d$ is the background particle diameter, which is consistent with those from hard sphere simulations in which the structural relaxation happens via the opening up of free volume against pressure.