Rotation in a gravitational billiard

Abstract

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.

Rotational transport via spontaneous symmetry breaking in vibrated disk packings

“…For these, rotation invariably appears whenever the system is tilted with respect to gravity, thus explicitely breaking reflection symmetry. Rotation is seen in both the persistent-contact [34] (low drive) and bouncing [33] (moderate drive) regimes, which are also observed for this simplified toy model.…”

“…We have made some analytical progress as well, for highly simplified situations. We studied [33,34] threedisk toy models [35] or billiards, consisting of one freely moving disk supported against gravity by two vibrating ones. For these, rotation invariably appears whenever the system is tilted with respect to gravity, thus explicitely breaking reflection symmetry.…”

Sustained rotation in a vibrated disk with asymmetric supports

“…Although persistent rotation is observed in both dynamical regimes, it results from different dynamical processes in each regime. The case of rotation in the medium driving, bouncing regime, has been already addressed numerically in previous work [17]. The present investigation focuses on the rotational phenomenon for low-intensity driving, that is, in the regime of permanent contacts.…”

“…This system is sketched in Figure 1. When the support disks are vibrated, numerical simulations and experiments [17] show that the upper disk rotates steadily. In our model system, the rotating object is non-chiral, i.e.…”

Sustained rotation in a vibrated disk with asymmetric supports

“…This system is sketched in figure 1. When the support disks are vibrated, numerical simulations and experiments [17] show that the upper disk rotates steadily. In our model system, the rotating object is nonchiral, i.e.…”