Phase bubbles and spatiotemporal
chaos in granular patterns
Abstract:
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
) 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 andf/6
patterns.
Phys. Rev. E 65,
011301 (2002).
Manuscript available in PDF and PS formats.