Dynamical arrest of topological defects in 2D hyperuniform disk packings

We investigate collective motions of points in 2D systems, orchestrated by Lloyd algorithm. The algorithm iteratively updates a system by minimising the total quantizer energy of the Voronoi landscape of the system. As a result of a tradeoff between energy minimisation and geometric frustration, we find that optimised systems exhibit a defective landscape along the process, where strands of 5- and 7-coordinated dislocations are embedded in the hexatic phase. In particular, dipole defects, each of which is the simplest possible pair of a pentagon and a heptagon, come into the picture of dynamical arrest, as the system freezes down to a disordered hyperuniform state. Moreover, we explore the packing fractions of 2D disk packings associated to the obtained hyperuniform systems by considering the maximum inscribed disks in their Voronoi cells.

Rotational diffusion and rotational correlations in frictional amorphous disk packings under shear

Particles in a packing will rotate when the packing is deformed. We find that rotations display diffusive dynamics set by particle friction and packing fraction. Rotations are spatially anticorrelated and directly indicative of the system pressure.

Contact network changes in ordered and disordered disk packings

There are two ways to transition between different contact networks, point and jump changes, as shown in a packing fraction-strain landscape.

Bounds for several-disk packings of hyperbolic surfaces

For any given [Formula: see text], this paper gives upper bounds on the radius of a packing of a complete hyperbolic surface of finite area by [Formula: see text] equal-radius disks in terms of the surface’s topology. We show that these bounds are sharp in some cases and not sharp in others.

Rotation in a gravitational billiard

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.