Vibrating granular particles are typical experimental systems for exploring the properties of granular materials and can serve as platforms for the study of the non-equilibrium statistical physics. In contrast to the intensively studied collective motions of vibrating granular particles, the single particle motion on a vibrating stage has rarely been explored. Here, we measure the motions of two types of single particle on a vertically vibrating stage. The first one is platelets confined in a quasi 2D box (chapter 2-4). The second one is a spherical shell, i.e. a mini-ping-pong ball, on an open vibration plate (chapter 5).
In chapter 2, we report the unusual dynamics of a vibrating disk confined in quasi-2D. Both translational and rotational displacements obeyed Lorentz distributions. In contract to the sub-diffusive translational motion, the rotational motion is super- diffusive at short times to diffusive at long times. In addition, we found more than 70% of kinetic energy was allocated into the rotational motion, in violation of the equipartition theorem. In chapter 3, we show that the five-point star has similar dynamics to the disk except that the diffusion rate decreases with the frequency.
In chapter 4, we show that four other platelets (five-petaled flower, mickey-like, shuriken and square) have similar behaviors to that of the disk. The rotational diffusions are slower for rougher surfaces of the particles.
In chapter 5, we measured the dynamics of isotropic and anisotropic spherical shell on an open vibration plate. The isotropic spheres move fast with circular-like trajectories. The translational speed has a bimodal distribution. By contrast, the anisotropic shell with one end slightly heavier than the other moves relatively slower in xy plane and exhibits Lorentz distribution of translational displacements.
These results are of basic importance for a better understanding of the collective motions of vibrating granular particles.