Determining random packing density and equivalent packing size of superballs via binary mixtures with spheres

1995 ◽

Vol 451 (1943) ◽

pp. 737-746 ◽

Cited By ~ 54

Keyword(s):

Packing Density ◽

Volume Fraction ◽

Random Packing ◽

Experimental Results ◽

Three Dimensions ◽

Approximate Relationship

An investigation has been carried out of the limiting packing density of an array of long straight rigid fibres distributed randomly in space as a function of the length of the fibre. We derive an approximate relationship between the limiting volume fraction V f and the slenderness λ of the fibres defined as length divided by diameter. The formula agrees well with our experimental results and those found in the literature.

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Random sequential coding by Hamming distance

Journal of Applied Probability ◽

10.1017/s0021900200111842 ◽

1986 ◽

Vol 23 (03) ◽

pp. 688-695 ◽

Cited By ~ 1

Author(s):

Yoshiaki Itoh ◽

Herbert Solomon

Keyword(s):

Computer Simulations ◽

Packing Density ◽

Hamming Distance ◽

Random Packing ◽

Empirical Constant ◽

Simple Cubic ◽

Simulation Results ◽

Simple Models

Here we introduce two simple models: simple cubic random packing and random packing by Hamming distance. Consider the packing density γ d of dimension d by cubic random packing. From computer simulations up to dimension 11, γ d +1/γ d seems to approach 1. Also, we give simulation results for random packing by Hamming distance and discuss the behavior of packing density when dimensionality is increased. For the case of Hamming distances of 2 or 3, d–α fits the simulation results of packing density where α is an empirical constant. The variance of packing density is larger when k is even and smaller when k is odd, where k represents Hamming distance.

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Statistical geometrical approach to random packing density of equal spheres

Nature ◽

10.1038/252202a0 ◽

1974 ◽

Vol 252 (5480) ◽

pp. 202-205 ◽

Cited By ~ 100

Author(s):

Keishi Gotoh ◽

John L. Finney

Keyword(s):

Packing Density ◽

Random Packing ◽

Geometrical Approach

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Random sequential coding by Hamming distance

Journal of Applied Probability ◽

10.2307/3214007 ◽

1986 ◽

Vol 23 (3) ◽

pp. 688-695 ◽

Cited By ~ 7

Author(s):

Yoshiaki Itoh ◽

Herbert Solomon

Keyword(s):

Computer Simulations ◽

Packing Density ◽

Hamming Distance ◽

Random Packing ◽

Empirical Constant ◽

Simple Cubic ◽

Simulation Results ◽

Simple Models

Here we introduce two simple models: simple cubic random packing and random packing by Hamming distance. Consider the packing density γ d of dimension d by cubic random packing. From computer simulations up to dimension 11, γ d+1/γ d seems to approach 1. Also, we give simulation results for random packing by Hamming distance and discuss the behavior of packing density when dimensionality is increased. For the case of Hamming distances of 2 or 3, d–α fits the simulation results of packing density where α is an empirical constant. The variance of packing density is larger when k is even and smaller when k is odd, where k represents Hamming distance.

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