Two modes of motions for a single disk on the vibration stage

The motion of a single granular particle is important for understanding their collective motions on vibration stage, but it remains poorly studied for simple shaped particles, such as a disk. Here, we systematically measure the motions of a single disk with different vibration amplitudesAat a fixed vibration frequencyfor a fixed accelerationa. The distributions, time-correlations, and power spectra of displacements per step, mean squared displacements and couplings for translational and rotational motions are measured. These analyses reveal that the motions randomly switch between active and inactive modes. Bothaandfare important to particle's motions and the fraction of active mode. The translational and rotational kinetic energy deviates from Boltzmann distribution and violates the equipartition theorem in each mode. We find three types of motion: rolling, lying flat, and fluttering, which give rise to active and inactive modes. The translational and rotational mean squared displacements, autocorrelations, and power spectra at differentacollapse in active modes, because the disk rolls along its rim with a fixed inclination angle though our system is under vibration and confinement. The nonzero cross-correlations between particle's translational and rotational motions indicate that only translational motions are insufficient for understanding dense particle systems.