(Georgia Institute of Technology, 2003-03-14)
Goldman, Daniel I.; Shattuck, M. D.; Moon, Sung Joon; Swift, J. B.; Swinney, Harry L.
We present a new description of nonequilibrium square patterns as a harmonically coupled crystal lattice. In a vertically oscillating granular layer, different transverse normal modes of the granular square-lattice pattern are observed for different driving frequencies (fd) and accelerations. The amplitude of a mode can be further excited by either frequency modulation of (fd) or reduction of friction between the grains and the plate. When the mode amplitude becomes large, the lattice melts (disorders), in accord with the Lindemann criterion for melting in two dimensions.
(Georgia Institute of Technology, 2001-12-04)
Moon, Sung Joon; Shattuck, M. D.; Bizon, C.; Goldman, Daniel I.; Swift, J. B.; Swinney, Harry L.
We use inelastic hard sphere molecular dynamics simulations and laboratory experiments to study patterns in vertically oscillated granular layers. The simulations and experiments reveal that phase bubbles spontaneously nucleate in the patterns when the container acceleration amplitude exceeds a critical value, about 7g, where the pattern is approximately hexagonal, oscillating at one-fourth the driving frequency (f/4). A phase bubble is a localized region that oscillates with a phase opposite (differing by π) to that of the surrounding pattern; a localized phase shift is often called an arching in studies of two-dimensional systems. The simulations show that the formation of phase bubbles is triggered by undulation at the bottom of the layer on a large length scale compared to the wavelength of the pattern. Once formed, a phase bubble shrinks as if it had a surface tension, and disappears in tens to hundreds of cycles. We find that there is an oscillatory momentum transfer across a kink, and the shrinking is caused by a net collisional momentum inward across the boundary enclosing the bubble. At increasing acceleration amplitudes, the patterns evolve into randomly moving labyrinthian kinks (spatiotemporal chaos). We observe in the simulations that f/3 and f/6 subharmonic patterns emerge as primary instabilities, but that they are unstable to the undulation of the layer. Our experiments confirm the existence of transient f/3 and f/6 patterns.