A Freezing/Melting Transition in a Vibrated and Sheared Granular Material*

We describe experiments on an annular layer of granular material that is sheared from above and vibrated from below. Key control parameters are the shear rate, $\Omega$ and the dimensionless acceleration, $\Gamma = A\omega^2/g$, where $A$ and $\omega$ are respectively the amplitude and frequency of shaking. We measure the pressure, $P$, at the base of the layer, and volume, $V$, hence the mean packing fraction of the layer. The outer sidewall is transparent, and we image/characterize the particles in the outer layer. We find a hysteretic transition from a state with 3D order to a disordered state as the shear rate, $\Omega$, is increased. The boundary between these two phases corresponds to equal energy inputs from shearing and shaking. We also characterize distributions for $P$ and $V$. These are strongly fluctuating quantities, with broad distributions. The Kurtosis of the distributions for $P$ and $V$ are strongly cusped at the transition. This striking behavior suggests that a temperature-like variable may control the transition between the two states. We propose that the non-equilibrium fluctuation-dissipation theorem may provide such a temperature and explore this possibility by measuring the response function, $R$ (for volume) to step changes in $\Omega$. We also determine the volume correlation function, $C$ and use this to determine an effective $kT$ from the slope of the $R$ vs. $C$ curve.