Hyperuniformity classes of quasiperiodic tilings via diffusion spreadability.

Hyperuniform point patterns can be classified by the hyperuniformity scaling exponent α>0, that characterizes the power-law scaling behavior of the structure factor S(k) as a function of wave number k≡|k| in the vicinity of the origin, e.g., S(k)∼|k|^{α} in cases where S(k) varies continuously with k as k→0.

Hyperuniformity of maximally random jammed packings of hyperspheres across spatial dimensions.

The maximally random jammed (MRJ) state is the most random (i.e., disordered) configuration of strictly jammed (mechanically rigid) nonoverlapping objects.

Kinetic Frustration Effects on Dense Two-Dimensional Packings of Convex Particles and Their Structural Characteristics.

The study of hard-particle packings is of fundamental importance in physics, chemistry, cell biology, and discrete geometry. Much of the previous work on hard-particle packings concerns their densest possible arrangements. By contrast, we examine kinetic effects inevitably present in both numerical and experimental packing protocols.