-
1
-
-
0042393482
-
-
N. E. Cates, M. R. Evans, Eds, (Institute of Physics, London)
-
P. M. Chaikin, in Soft and Fragile Matter, Nonequilibrium Dynamics, Metastability and Flow, N. E. Cates, M. R. Evans, Eds, (Institute of Physics, London, 2000), pp. 315-348.
-
(2000)
Soft and Fragile Matter, Nonequilibrium Dynamics, Metastability and Flow
, pp. 315-348
-
-
Chaikin, P.M.1
-
3
-
-
0003643241
-
-
Springer-Verlag New York, ed. 3
-
J. H. Conway, N. J. A. Sloane, Sphere Packings, Lattices, and Groups (Springer-Verlag New York, ed. 3, 1999).
-
(1999)
Sphere Packings, Lattices, and Groups
-
-
Conway, J.H.1
Sloane, N.J.A.2
-
6
-
-
0012995926
-
-
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
-
-
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
-
-
note
-
M&M's Candies are a registered trademark of Mars Inc.
-
-
-
-
13
-
-
1142304098
-
-
note
-
We estimate the correction due to the lower density at the surface of the flasks to be about 0.005.
-
-
-
-
14
-
-
0002087305
-
-
M. P. Allen, G. T. Evans, D. Frenkel, B. M. Mulder, Adv. Chem. Phys. 86, 1 (1993).
-
(1993)
Adv. Chem. Phys.
, vol.86
, pp. 1
-
-
Allen, M.P.1
Evans, G.T.2
Frenkel, D.3
Mulder, B.M.4
-
27
-
-
1142291992
-
-
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
-
-
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
-
-
note
-
More recent simulations and experiments give Z ≤ 6.
-
-
-
-
32
-
-
1142279887
-
-
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
-
-
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
-
-
T. C. Hales, xxx.lanl.gov/math.MG/9811071 (1998)
-
T. C. Hales, xxx.lanl.gov/math.MG/9811071 (1998).
-
-
-
-
35
-
-
0010719941
-
-
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
-
36
-
-
0000290276
-
-
J. B. Knight, C. G. Fandrich, C. N. Lau, H. M. Jaeger, S. R. Nagel, Phys. Rev. E 51, 3957 (1995).
-
(1995)
Phys. Rev. E
, vol.51
, pp. 3957
-
-
Knight, J.B.1
Fandrich, C.G.2
Lau, C.N.3
Jaeger, H.M.4
Nagel, S.R.5
-
38
-
-
1142267741
-
-
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
-
-
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.).
-
-
-
|