Multiplicity of generation, selection, and classification procedures for jammed hard-particle packings

Hard-particle packings have served as useful starting points to study the s tructure of diverse systems such as liquids, living cells, granular media, glasses, and amorphous solids, Howard Reiss has played a major role in help ing to illuminate our understanding of hard-particle systems, which still o ffer scientists many interesting conundrums. Jammed configurations of hard particles are of great fundamental and practical interest. What one precise ly means by a "jammed" configuration is quite subtle and considerable ambig uity remains in the literature on this question. We will show that there is a multiplicity of generation, selection, and classification procedures for jammed configurations of identical d-dimensional spheres. We categorize co mmon ordered lattices according to our definitions and discuss implications for random disk and sphere packings. We also show how the concept of rigid ity percolation (which has been used to understand the mechanical propertie s of network glasses) can be generalized to further characterize hard-spher e packings.