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Volumn 303, Issue 5660, 2004, Pages 990-993

Improving the Density of Jammed Disordered Packings Using Ellipsoids

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; ASPECT RATIO; COMPUTER SIMULATION; DEGREES OF FREEDOM (MECHANICS);

EID: 1142274207     PISSN: 00368075     EISSN: None     Source Type: Journal    
DOI: 10.1126/science.1093010     Document Type: Article
Times cited : (1139)

References (39)
  • 6
    • 0012995926 scopus 로고
    • A. Mehta, Ed. (Springer-Verlag, New York)
    • S. F. Edwards, in Granular Matter, A. Mehta, Ed. (Springer-Verlag, New York, 1994), pp. 121-140.
    • (1994) Granular Matter , pp. 121-140
    • Edwards, S.F.1
  • 11
    • 1142267740 scopus 로고    scopus 로고
    • note
    • The highest density is realized only by stacking variants of the fcc and hcp lattices (34). This is also a trivial lower bound for the maximal density of ellipsoid packings for any aspect ratio; however, it is known that higher densities are possible for sufficiently aspherical ellipsoids (35).
  • 12
    • 1142279884 scopus 로고    scopus 로고
    • note
    • M&M's Candies are a registered trademark of Mars Inc.
  • 13
    • 1142304098 scopus 로고    scopus 로고
    • note
    • We estimate the correction due to the lower density at the surface of the flasks to be about 0.005.
  • 27
    • 1142291992 scopus 로고    scopus 로고
    • note
    • The total number of degrees of freedom would be equal to the number of impenetrability constraints (to within a constant of order 1), each of which is determined by a contact between two touching particles.
  • 28
    • 1142279882 scopus 로고    scopus 로고
    • note
    • It is also often claimed that this is the minimal number of contacts needed to ensure jamming (25). However, this claim is based on a counting argument that is directly applicable only to spheres, whereas handling the impenetrability constraints for ellipsoids requires including higher order corrections because of curvature effects.
  • 31
    • 1142279883 scopus 로고    scopus 로고
    • note
    • More recent simulations and experiments give Z ≤ 6.
  • 32
    • 1142279887 scopus 로고    scopus 로고
    • note
    • Near neighbors (even when very close) leave a spot; touching neighbors leave a spot with a hole in the middle at the contact point.
  • 33
    • 1142304101 scopus 로고    scopus 로고
    • note
    • Note that computer-generated packings can have a small percentage of "rattlers" (particles without any contacts that are not observable in our experiments), which we do not exclude when calculating Z.
  • 34
    • 1142291994 scopus 로고    scopus 로고
    • T. C. Hales, xxx.lanl.gov/math.MG/9811071 (1998)
    • T. C. Hales, xxx.lanl.gov/math.MG/9811071 (1998).
  • 35
    • 0010719941 scopus 로고
    • P. Gritzmann, B. Sturmfels, Eds., vol. 4 of DIMACS Series in Discrete Mathematics and Theoretical Computer Science (American Mathematical Society, Providence, RI)
    • A. Bezdek, W. Kuperberg, in Applied Geometry and Discrete Mathematics, P. Gritzmann, B. Sturmfels, Eds., vol. 4 of DIMACS Series in Discrete Mathematics and Theoretical Computer Science (American Mathematical Society, Providence, RI, 1991), pp. 71-80.
    • (1991) Applied Geometry and Discrete Mathematics , pp. 71-80
    • Bezdek, A.1    Kuperberg, W.2
  • 38
    • 1142267741 scopus 로고    scopus 로고
    • note
    • Wall effects yield lower measured densities. Continued "tapping" of the candies may further density the system, as happens for granular material (36). Furthermore, the somewhat higher density of the computer-generated packings can be explained by taking into account the influence of gravity and friction, which are not included in the simulation. Gravitation-dominated packings always have much lower packing fractions, as low as ψ ≈ 0.4, and have significant orientational ordering (22, 37).
  • 39
    • 1142304100 scopus 로고    scopus 로고
    • note
    • Supported by American Chemical Society PRF grant 36967-AC9 (S.T., A. D., F.H.S.), NASA grant NAG3-1762 (P.H.C.), and NSF grants DMR-0213706 (S.T., P.M.C., A.D., F.H.S.), DMS-0312067 (S.T., A.D., F.H.S.), and DHS-0209595 (R.C.).


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.