Abstract
Granular particles exhibit rich collective behaviors on a vibration stage, but the motion of an isolated particle is not well understood even for a simple uniform particles such a disk or sphere. In this thesis, we systematically measure the translational and rotational motions of single disks and spheres on the vibration stage by taking videos and image processing.
Chapter 2 presents experiments of single disks confined in a quasi-2D container on a vibration stage. The disk’s motions under fixed vibration amplitude, fixed vibration frequency or acceleration are systematically measured. Under high vibration amplitudes, the disk’s translational displacements are subdiffusive and negatively correlated in short times while its rotational displacements are superdiffusive and positively correlated. The disk’s energy distribution violates the equipartition theorem. Under lower vibration amplitude, its motions randomly switch between active and inactive modes in both translation and rotation. Three types of motion (rolling, lying flat, and fluttering) give rise to the two modes. The disk’s translational and rotational mean squared displacements, autocorrelations, and power spectra collapse in active modes but not in inactive mode.
Chapter 3 presents experiments of single spheres on a vibration stage. The rotations of two types of spheres (hollow ping-pong ball and solid 3d-printed sphere) are characterized by four methods: translational motions of the markers on the sphere’s surface, axis-angle description, Euler angles, and quaternions. Spheres tend to rotate around axes parallel to the xy plane. On flat vibration substrate, the sphere exhibits spiral trajectories which are weakly correlated with rotation under fast rotation regime but not under slow rotation regime. The sphere’s vertical motion dominates the kinetic energy and its distribution exhibits discrete levels.