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Coherent motion is found to emerge out of fluctuations in a vibrated asymmetric particle. Depending on the parameters, amplitude, and frequency of the box, the motion of the particle is classified into several phases. The transition between fluctuating motion and unidirectional motion occurs with constant acceleration in the low-frequency regime and constant amplitude in the high-frequency regime. We show through dimensional analysis that this behavior does not depend on the detailed geometry of the particle.
Yamada et al. (Tue,) studied this question.