Some Observations on the Random Packing of Hard Ellipsoids

Chaikin, P. M.; Donev, Aleksandar; Man, Weining; Stillinger, Frank H.; Torquato, Salvatore

doi:10.1021/ie060032g

Cited by 99 publications

(114 citation statements)

References 25 publications

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“…The influence of order in ellipsoid packings deposited under the influence of gravity is detailed in the following Section II B. An isocounting conjecture, which states that for large disordered jammed packings the average contact number per particle is twice the number of degrees of freedom per particle, does in general not apply to nonspherical particles [59,60]. 2 also indicates decreasing packing fraction for particles with large aspect ratio.…”

Section: Three-dimensional Systemsmentioning

confidence: 99%

Granular materials composed of shape-anisotropic grains

2013

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Granulate physics has made considerable progress during the past decades in the understanding of static and dynamic properties of large ensembles of interacting macroscopic particles, including the modeling of phenomena like jamming, segregation and pattern formation, the development of related industrial applications or traffic flow control. The specific properties of systems composed of shape-anisotropic (elongated or flattened) particles have attracted increasing interest in recent years. Orientational order and self-organization are among the characteristic phenomena that add to the special features of granular matter of spherical or irregular particles. An overview of this research field is given.Final version published in Soft Matter,

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Section: Three-dimensional Systemsmentioning

confidence: 99%

Granular materials composed of shape-anisotropic grains

2013

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“…Combining these two limits gives the isostatic value C = 10. In [10,35] it is noted that the isostatic contact value is not reached when spherocylinders are only slightly deviating from spheres. The number of degrees of freedom changes discontinuously and via the isostatic conjecture the number of contacts should Fig.…”

Section: Aspect Ratio Dependence For Random Rod Packingsmentioning

confidence: 99%

On contact numbers in random rod packings

2009

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Random packings of non-spherical granular particles are simulated by combining mechanical contraction and molecular dynamics, to determine contact numbers as a function of density. Particle shapes are varied from spheres to thin rods. The observed contact numbers (and packing densities) agree well with experiments on granular packings. Contact numbers are also compared to caging numbers calculated for sphero-cylinders with arbitrary aspect-ratio. The caging number for rods arrested by uncorrelated point contacts asymptotes towards γ = 9 at high aspect ratio, strikingly close to the experimental contact number C ≈ 9.8 for thin rods. These and other findings confirm that thin-rod packings are dominated by local arrest in the form of truly random neighbor cages. The ideal packing law derived for random rod-rod contacts, supplemented with a calculation for the average contact number, explains both absolute value and aspect-ratio dependence of the packing density of randomly oriented thin rods.

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“…This may be checked just by testing the J-point procedure with a packing of non-spherical (e.g. ellipsoidal) particles, which are generically hypostatic [47]: if the J-point for ellipsoids turns out to be critical, then it will be clear that isostaticity is not a necessary condition for criticality.…”

Section: Jamming Transitionmentioning

confidence: 99%

Landscape analysis of constraint satisfaction problems

2007

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We discuss an analysis of Constraint Satisfaction problems, such as Sphere Packing, K-SAT and Graph Coloring, in terms of an effective energy landscape. Several intriguing geometrical properties of the solution space become in this light familiar in terms of the well-studied ones of rugged (glassy) energy landscapes. A 'benchmark' algorithm naturally suggested by this construction finds solutions in polynomial time up to a point beyond the 'clustering' and in some cases even the 'thermodynamic' transitions. This point has a simple geometric meaning and can be in principle determined with standard Statistical Mechanical methods, thus pushing the analytic bound up to which problems are guaranteed to be easy. We illustrate this for the graph three and four-coloring problem. For Packing problems the present discussion allows to better characterize the 'J-point', proposed as a systematic definition of Random Close Packing [1], and to place it in the context of other theories of glasses.

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Some Observations on the Random Packing of Hard Ellipsoids

Cited by 99 publications

References 25 publications

Granular materials composed of shape-anisotropic grains

Granular materials composed of shape-anisotropic grains

On contact numbers in random rod packings

Landscape analysis of constraint satisfaction problems

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