Article

Improving the density of jammed disordered packings using ellipsoids

Department of Mathematics, Cornell University, Итак, New York, United States
Science (Impact Factor: 31.48). 02/2004; 303(5660):990-3. DOI: 10.1126/science.1093010
Source: PubMed

ABSTRACT 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 . 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.

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