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Experiments on vertically oscillated granular layers in an evacuated container reveal a sequence of well-defined pattern bifurcations as the container acceleration is increased. Period doublings of the layer center of mass motion and a standing wave instability interact to produce hexagons and more complicated patterns composed of distinct spatial domains of different relative phase separated by kinks (phase discontinuities). A simple model displays quantitative agreement with the observed transition sequence.
Melo et al. (1995) studied this question.