# Toward the jamming threshold of sphere packings: Tunneled crystals

@article{Torquato2007TowardTJ, title={Toward the jamming threshold of sphere packings: Tunneled crystals}, author={Salvatore Torquato and Frank H. Stillinger}, journal={Journal of Applied Physics}, year={2007}, volume={102}, pages={093511} }

We have discovered a family of three-dimensional crystal sphere packings that are strictly jammed (i.e., mechanically stable) and yet possess an anomalously low density. This family constitutes an uncountably infinite number of crystal packings that are subpackings of the densest crystal packings and are characterized by a high concentration of self-avoiding “tunnels” (chains of vacancies) that permeate the structures. The fundamental geometric characteristics of these tunneled crystals command…

## 52 Citations

Jammed hard-sphere hcp crystals permeated with trivacancy tunnels

- Materials Science
- 2019

Supported by simple table-top experiments involving stackings of ball bearings and theoretical analysis, we have discovered crystal packings of identical hard spheres that are permeated by a high…

Disordered strictly jammed binary sphere packings attain an anomalously large range of densities.

- Physics, MedicinePhysical review. E, Statistical, nonlinear, and soft matter physics
- 2013

It is reported that disordered strictly jammed binary packings can be produced with an anomalously large range of average packing fractions 0.634≤φ≤0.829 for small to large sphere radius ratios α restricted to α≥0.100, and an unusual feature of the packing fraction of jammed backbones (packings with rattlers excluded).

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

- Physics
- 2010

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…

Nonuniversality of density and disorder in jammed sphere packings

- Physics
- 2011

We show for the first time that collectively jammed disordered packings of three-dimensional monodisperse frictionless hard spheres can be produced and tuned using a novel numerical protocol with…

Existence of isostatic, maximally random jammed monodisperse hard-disk packings

- Engineering, MedicineProceedings of the National Academy of Sciences
- 2014

Establishing that the MRJ state for monodisperse hard disks is isostatic and qualitatively distinct from commonly observed polycrystalline packings contradicts conventional wisdom and sheds light on the nature of disorder.

Structure and Rigidity in Maximally Random Jammed Packings of Hard Particles

- Materials Science
- 2016

Packings of hard particles have served as a powerful, yet simple model for a wide variety of physical systems. One particularly interesting subset of these packings are so-called maximally random…

Structural transitions in granular packs: statistical mechanics and statistical geometry investigations

- Physics
- 2008

We investigate equal spheres packings generated from several experiments and from a large number of different numerical simulations. The structural organization of these disordered packings is…

Jamming criticality of near-crystals

- Physics, Materials ScienceEPL (Europhysics Letters)
- 2021

Amorphous and crystalline solids have long been considered as two distinct kinds of rigidity at the opposite ends of the order-disorder continuum. Crystals are usually treated in equilibrium with…

Optimal packings of superdisks and the role of symmetry.

- Physics, MedicinePhysical review letters
- 2008

The candidate maximal packing arrangements are achieved by certain families of Bravais lattice packings, and the maximal density is nonanalytic at the "circular-disk" point (p=1) and increases dramatically as p moves away from unity.

Characterization of void space in polydisperse sphere packings: Applications to hard-sphere packings and to protein structure analysis

- Materials Science, MedicineThe European physical journal. E, Soft matter
- 2013

The efficacy of the method for analyzing protein structure is shown, by computing various quantities such as the distribution of sizes of buried cavities and pockets, the scaling of solvent accessible area to the corresponding occupied volume, the composition of residues lining cavities, etc.

## References

SHOWING 1-10 OF 47 REFERENCES

Lattice-based random jammed configurations for hard particles.

- Mathematics, MedicinePhysical review. E, Statistical, nonlinear, and soft matter physics
- 2003

It is stressed that at least some aspects of these enumeration problems might benefit from the formal transcription to a lattice-gas/Ising-model representation with vacancy interactions chosen to enforce the packing category of interest.

Jamming in hard sphere and disk packings

- Physics
- 2004

Hard-particle packings have provided a rich source of outstanding theoretical problems and served as useful starting points to model the structure of granular media, liquids, living cells, glasses,…

Pair correlation function characteristics of nearly jammed disordered and ordered hard-sphere packings.

- Mathematics, PhysicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2005

The computational data unambiguously separate the narrowing delta -function contribution to g(2) due to emerging interparticle contacts from the background contribution due to near contacts and find that ordering has a significant impact on the shape of P(f) for small forces.

Unusually dense crystal packings of ellipsoids.

- Physics, MedicinePhysical review letters
- 2004

This Letter reports on the densest-known packings of congruent ellipsoids, consisting of crystal arrangements of spheroids with a wide range of aspect ratios, and with density phi always surpassing that of the denser Bravais lattice packing phi approximately equal to 0.7405.

Multiplicity of Generation, Selection, and Classification Procedures for Jammed Hard-Particle Packings †

- Computer Science, Physics
- 2001

It is shown that there is a multiplicity of generation, selection, and classification procedures for jammed configurations of identical d-dimensional spheres, and the concept of rigidity percolation can be generalized to network glasses.

Diversity of order and densities in jammed hard-particle packings.

- Mathematics, MedicinePhysical review. E, Statistical, nonlinear, and soft matter physics
- 2002

This investigation shows that, even in the large-system limit, jammed systems of hard spheres can be generated with a wide range of packing fractions from phi approximately 0.52 to the fcc limit, indicating that the density alone does not uniquely characterize a packing.

Geometric properties of random disk packings

- Mathematics
- 1990

Random packings ofN⩽2000 rigid disks in the plane, subject to periodic boundary conditions on a square primitive cell, have been generated by a concurrent construction which treats all disks on an…

Jamming at zero temperature and zero applied stress: the epitome of disorder.

- Mathematics, MedicinePhysical review. E, Statistical, nonlinear, and soft matter physics
- 2003

The results provide a well-defined meaning for "random close packing" in terms of the fraction of all phase space with inherent structures that jam, and suggest that point J is a point of maximal disorder and may control behavior in its vicinity-perhaps even at the glass transition.

Breakdown of elasticity theory for jammed hard-particle packings: conical nonlinear constitutive theory

- Mathematics
- 2003

Abstract Hard-particle packings have provided a rich source of outstanding theoretical problems and served as useful starting points to model the structure of granular media, liquids, living cells,…

A linear programming algorithm to test for jamming in hard-sphere packings

- Materials Science, Physics
- 2002

Jamming in hard-particle packings has been the subject of considerable interest in recent years. In a paper by Torquato and Stillinger [J. Phys. Chem. B 105 (2001)], a classification scheme of jammed…