Oscillons, spiral waves, and stripes in a model of vibrated sand

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Abstract
A semicontinuum model of a thin layer of vibrated sand is proposed that qualitatively reproduces experimental observations of localized subharmonic excitations (“oscillons”) in addition to globally striped patterns. Numerical simulations recover a phase diagram similar to experimental observations and physical mechanisms for the transitions across phase boundaries are proposed. A scaling law is given for the size of the stripes and oscillons. Simulations in a different region of phase space reveal spiral waves.