RT Journal Article
SR Electronic
T1 Improving the Density of Jammed Disordered Packings Using Ellipsoids
JF Science
JO Science
FD American Association for the Advancement of Science
SP 990
OP 993
DO 10.1126/science.1093010
VO 303
IS 5660
A1 Donev, Aleksandar
A1 Cisse, Ibrahim
A1 Sachs, David
A1 Variano, Evan A.
A1 Stillinger, Frank H.
A1 Connelly, Robert
A1 Torquato, Salvatore
A1 Chaikin, P. M.
YR 2004
UL http://science.sciencemag.org/content/303/5660/990.abstract
AB Packing problems, such as how densely objects can fill a volume, are among the most ancient and persistent problems in mathematics and science. For equal spheres, it has only recently been proved that the face-centered cubic lattice has the highest possible packing fraction \batchmode \documentclass[fleqn,10pt,legalpaper]{article} \usepackage{amssymb} \usepackage{amsfonts} \usepackage{amsmath} \pagestyle{empty} \begin{document} \({\varphi}={\pi}{/}\sqrt{18}{\approx}0.74\) \end{document}. It is also well known that certain random (amorphous) jammed packings have φ ≈ 0.64. Here, we show experimentally and with a new simulation algorithm that ellipsoids can randomly pack more densely—up to φ= 0.68 to 0.71for spheroids with an aspect ratio close to that of M&M's Candies—and even approach φ ≈ 0.74 for ellipsoids with other aspect ratios. We suggest 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. We measured the number of contacts per particle Z ≈ 10 for our spheroids, as compared to Z ≈ 6 for spheres. Our results have implications for a broad range of scientific disciplines, including the properties of granular media and ceramics, glass formation, and discrete geometry.