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ItemLattice dynamics and melting of a nonequilibrium pattern(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.
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ItemPhase bubbles and spatiotemporal chaos in granular patterns(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.
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ItemContinuum-type stability balloon in oscillated granular layers(Georgia Institute of Technology, 1998-08-17) De Bruyn, John R. ; Bizon, C. ; Shattuck, M. D. ; Goldman, Daniel I. ; Swift, J. B. ; Swinney, Harry L.The stability of convection rolls in a fluid heated from below is limited by secondary instabilities, including the skew-varicose and crossroll instabilities. We observe a stability boundary defined by these same instabilities in stripe patterns in a vertically oscillated granular layer. Molecular dynamics simulations show that the mechanism of the skew-varicose instability in granular patterns is similar to that in convection. These results suggest that pattern formation in granular media can be described by continuum models analogous to those used in fluid systems.
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ItemAbsence of inelastic collapse in a realistic three ball model(Georgia Institute of Technology, 1998-04) Goldman, Daniel I. ; Shattuck, M. D. ; Bizon, C. ; McCormick, W. D. ; Swift, J. B. ; Swinney, Harry L.Inelastic collapse, the process in which a number of partially inelastic balls dissipate their energy through an infinite number of collisions in a finite amount of time, is studied for three balls on an infinite line and on a ring (i.e., a line segment with periodic boundary conditions). Inelastic collapse has been shown to exist for systems in which collisions occur with a coefficient of restitution r independent of the relative velocities of the colliding particles. In the present study, a more realistic model is assumed for r: r=1 for relative velocity equal to zero, and r decreases monotonically for increasing relative velocity. With this model, inelastic collapse does not occur for three balls on a line or a ring.