Unusually dense crystal packings of ellipsoids.

@article{Donev2004UnusuallyDC,
  title={Unusually dense crystal packings of ellipsoids.},
  author={Aleksandar Donev and Frank H. Stillinger and Paul M. Chaikin and Salvatore Torquato},
  journal={Physical review letters},
  year={2004},
  volume={92 25 Pt 1},
  pages={
          255506
        }
}
In this Letter, we report on the densest-known packings of congruent ellipsoids. The family of new packings consists of crystal arrangements of spheroids with a wide range of aspect ratios, and with density phi always surpassing that of the densest Bravais lattice packing phi approximately equal to 0.7405. A remarkable maximum density of phi approximately equal to 0.7707 is achieved for maximal aspect ratios larger than sqrt[3], when each ellipsoid has 14 touching neighbors. Our results are… 

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References

SHOWING 1-10 OF 49 REFERENCES
Disks vs. spheres: Contrasting properties of random packings
Collections of random packings of rigid disks and spheres have been generated by computer using a previously described concurrent algorithm. Particles begin as infinitesimal moving points, grow in
Sphere packings, I
  • T. Hales
  • Physics, Mathematics
    Discret. Comput. Geom.
  • 1997
TLDR
A program to prove the Kepler conjecture on sphere packings is described and it is shown that every Delaunay star that satisfies a certain regularity condition satisfies the conjecture.
Jamming in hard sphere and disk packings
TLDR
Rigorous and efficient linear-programming algorithms are introduced to assess whether a hard-sphere packing is locally, collectively, or strictly jammed, as defined by Torquato and Stillinger.
Geometric properties of random disk packings
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
Is random close packing of spheres well defined?
TLDR
It is argued that the current picture of RCP cannot be made mathematically precise and support this conclusion via a molecular dynamics study of hard spheres using the Lubachevsky-Stillinger compression algorithm.
Diversity of order and densities in jammed hard-particle packings.
TLDR
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.
Multiplicity of Generation, Selection, and Classification Procedures for Jammed Hard-Particle Packings †
TLDR
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.
Improving the Density of Jammed Disordered Packings Using Ellipsoids
TLDR
It is shown experimentally and with a new simulation algorithm that ellipsoids can randomly pack more densely and suggested that the higher density is directly related to the higher number of degrees of freedom per particle and thus the larger number of particle contacts required to mechanically stabilize the packing.
An overview of the Kepler conjecture
This is the first in a series of papers giving a proof of the Kepler conjecture, which asserts that the density of a packing of congruent spheres in three dimensions is never greater than
Neighbor List Collision-Driven Molecular Dynamics Simulation for Nonspherical Particles. I. Algorithmic Details II. Applications to Ellipses and Ellipsoids
TLDR
A novel partial-update near-neighbor list (NNL) algorithm that is superior to previous algorithms at high densities, without compromising the correctness of the algorithm.
...
1
2
3
4
5
...