Statistical analysis of granular gases, pattern formation, and crumpling through real space imaging.

摘要

The statistical properties of driven dissipative systems is investigated experimentally with the use of high speed, and high resolution imaging. A variety of experiments that range from idealized granular gases to systems with anisotropic interactions and pattern formation is explored. These experiments can be divided into three classes: granular gases, granular fluids with anisotropic interactions, and pattern formation.; The statistical properties of spherical particles that are excited into a dilute gas state are investigated. The particles are constrained to roll on an inclined plane, which reduces the effects of gravity, allowing real space particle tracking with high precision. Energy is given to the particles through a single vibrating boundary. If the driving is at a high frequency and amplitude, the particles resemble molecules of equilibrium liquids or gases. I will demonstrate that a number of fundamental statistical measures of equilibrium fluids, such as distribution of velocities and path lengths are not consistent with those of inelastic gases. However, the particle motion remains diffusive and the velocity autocorrelation functions decays exponentially. Recent theoretical approaches to granular hydrodynamics also are discussed. In the case where the driving frequency and amplitude are sufficiently low, the particles undergo a spontaneous transition from a quiescent to patterned state. The patterns formed are similar to those found in three-dimensional granular fluids. By introducing a temporally dependent measure of the spatial correlation of the velocities, an accurate determination of the wavelength and onset of patterns is determined. The phase averaged temperature is measured to show that patterns arise when the temperature of the layer is at minimum. These results could be used to develop a linear stability analysis of granular fluids.; A quasi-two-dimensional granular system of particles with embedded dipole moments is investigated, and it is found that the system exhibits a coexisting gas-like and liquid-like phase driven by the dipolar interactions. As the kinetic energy of the particles is lowered, clusters spontaneously nucleate and grow in a universal fashion. If the kinetic energy of the particles is rapidly lowered, a metastable state emerges. The metastable liquid-like phase directly reflects the inherent anisotropy of the dipolar potential between the particles.; I investigate a system of granular rods driven in a one-dimensional annulus. The rods are found to undergo a ratchet-like motion. The experiments are compared to the results of a simple phenomenological model and molecular dynamics simulations. I also demonstrate that the mechanism for rod motion describes the observations of early work in granular vortices.; The geometry of large crumpled sheets is studied through laser topography and surface characterization. Sheets of different thickness are crumpled into balls of fixed radius and then uncrumpled to reveal the network of plastically deformed ridges. The distributions of curvatures and lengths of the ridges are measured. The ridge distributions are found to agree with a recently proposed model.