Phase Bubbles and Spatiotemporal Chaos in Granular Patterns

Details Phase Bubbles and Spatiotemporal Chaos in Granular Patterns Phase Bubbles and Spatiotemporal Chaos in Granular Patterns

2001-08-31

arxiv.org/abs/cond-mat/0108550v1

Phys. Rev. E 65, 011301 (2002)

Physics

Condensed Matter

Soft Condensed Matter

6 pages, 12 figures, submitted to Phys. Rev. E on July 1st, 2001. for better quality figures, visit http://chaos.ph.utexas.edu

Scientific paper

10.1103/PhysRevE.65.011301

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 {\em 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 $\pi$) to that of the surrounding pattern; a localized phase shift is often called an ${\em arching}$ 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 this 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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