Jammed hard-particle packings: From Kepler to Bernal and beyond

By Salvatore Torquato, Frank H. Stillinger. 2010

595 citations recorded by the source corpus.

This review describes the diversity of jammed configurations attainable by frictionless convex nonoverlapping (hard) particles in Euclidean spaces and for that purpose it stresses individual-packing geometric analysis. A fundamental feature of that diversity is the necessity to classify individual jammed configurations according to whether they are locally, collectively, or strictly jammed. Each of these categories contains a multitude of jammed configurations spanning a wide and (in the large system limit) continuous range of intensive properties, including packing fraction $\phi$, mean contact number $Z$, and several scalar order metrics. Application of these analytical tools to spheres in three dimensions (an analog to the venerable Ising model) covers a myriad of jammed states, including maximally dense packings (as Kepler conjectured), low-density strictly-jammed tunneled crystals, and a substantial family of amorphous packings. With respect to the last of these, the current approach displaces the historically prominent but ambiguous idea of ``random close packing" (RCP) with the precise concept of ``maximally random jamming" (MRJ). This review also covers recent advances in understanding jammed packings of polydisperse sphere mixtures, as well as convex nonspherical particles, e.g., ellipsoids, ``superballs", and polyhedra. Because of their relevance to error-correcting codes and information theory, sphere packings in high-dimensional Euclidean spaces have been included as well. We also make some remarks about packings in (curved) non-Euclidean spaces. In closing this review, several basic open questions for future research to consider have been identified.

Subfields: Condensed Matter Physics, Materials Chemistry, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/c5da9bfe282f7016ff6d2e71c114ccad1eeb43b2

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Citations in the corpus

Topological boundary modes in isostatic lattices (2013, methodology): “The zero-mode count on each surface is compared with equations (3), (8) and (9).”
Edwards Statistical Mechanics for Jammed Granular Matter (2016, background): “Nevertheless, many different packing protocols and algorithms seem to robustly achieve disordered packings with maximal densities around φ ≈ 0.64, which coincides with the densities of MRJ packings for many different order parameters (Torquato and Stillinger, 2010).”
Universality of the SAT-UNSAT (jamming) threshold in non-convex continuous constraint satisfaction problems (2017, background): “Crystals are usually denser than disordered arrangements, and therefore the SAT-UNSAT transition usually happens within the crystal phase, although the situation is somewhat uncertain in large dimensions [ 26 ] .”
The role of local structure in dynamical arrest (2014, methodology): “[524] S. Torquato and F. Stillinger.”
Concrete material science: Past, present, and future innovations (2018, background): “Bernal packing is therefore often called dense random packing or, yet more frequently, random close packing (rcp), which may itself be replaced by the more rigorous maximally random jamming idea [86].”
Hyperuniform states of matter (2018, methodology): “To this end, a variety of scalar order metrics ψ have been employed and applied that depend on the configurational coordinates of a packing [199, 247] with the normalization 0 ≤ ψ ≤ 1, where ψ = 0 corresponds to the most disordered state (i.”
Universality of jamming of nonspherical particles (2018, unknown): “Journal of Physics: Condensed Matter 22(3):033101.”