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

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 the Einstein relationship. We found that as the system unjams with increasing vibration intensities Γ, the structural relaxation time τ 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 = 0.20 ± 0.02pd³, 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.