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Gravitational billiards composed of a viscoelastic frictional disk bouncing on a vibrating wedge have been studied previously, but only from the point of view of their translational behavior. In this work, the average rotational velocity of the disk is studied under various circumstances. First, an experimental realization is briefly presented, which shows sustained rotation when the wedge is tilted. Next, this phenomenon is scrutinized in close detail using a precise numerical implementation of frictional forces. We show that the bouncing disk acquires a spontaneous rotational velocity whenever the wedge angle is not bisected by the direction of gravity. Our molecular dynamics (MD) results are well reproduced by event-driven (ED) simulations. When the wedge aperture angle [Formula: see text], the average tangential velocity [Formula: see text] of the disk scales with the typical wedge vibration velocity [Formula: see text], and is in general a nonmonotonic function of the overall tilt angle [Formula: see text] of the wedge. The present work focuses on wedges with [Formula: see text], which are relevant for the problem of spontaneous rotation in vibrated disk packings. This study makes part of the PhD Thesis of G. G. Peraza-Mues.

International audienceIf we pour spherical beads in a container and then gently shake it to increase the compaction of the system, the packing fraction will converge logarithmically to 0.64, the density of a random close packing. If the system is specially sheared, or tapped through an annealing procedure, lattices may self-organize. In this work we study granular crystallization induced by magnetic cohesion. We observe an interesting granular polymorphism probably due to an effective van der Waals-like interaction

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A single frictional elastic disk, supported against gravity by two others, rotates steadily when the supports are vibrated and the system is tilted with respect to gravity. Rotation is here studied using molecular dynamics simulations, and a detailed analysis of the dynamics of the system is made. The origin of the observed rotational ratcheting is discussed by considering simplified situations analytically. This shows that the sense of rotation is not fixed by the tilt but depends on the details of the excitation as well.