Publisher's Note: Random close packing revisited: Ways to pack frictionless disks [Phys. Rev. E<b>71</b>, 061306 (2005)]

Xu, Ning; Bławzdziewicz, Jerzy; O’Hern, Corey S.

doi:10.1103/physreve.72.019901

Cited by 62 publications

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“…It is crucial to perform an error analysis on the contact number z J , which is described in Appendix A. Packing Fraction We show results for the average packing fraction φ J versus thermal quench rate r over five orders of magnitude obtained from Protocol 1 in of rate, which agrees with studies that employ athermal compression/decompression packing-generation algorithms [2,17]. For r < r * , φ J increases approximately as [log 10 (r − r * )] 0.5 with decreasing rate.…”

Section: Structural and Mechanical Propertiessupporting

confidence: 65%

“…For example, if all MS packings in a given system are known, one can measure accurately the frequency with which each MS packing occurs, and determine how the packing frequencies and materials properties depend on the preparation history [2,3]. Further, MS packing frequencies are important for identifying the appropriate statistical mechanical ensemble for weakly perturbed granular materials [4].…”

Section: Introductionmentioning

confidence: 99%

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Tuning jammed frictionless disk packings from isostatic to hyperstatic

2011

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We perform extensive computational studies of two-dimensional static bidisperse disk packings using two distinct packing-generation protocols. The first involves thermally quenching equilibrated liquid configurations to zero temperature over a range of thermal quench rates r and initial packing fractions followed by compression and decompression in small steps to reach packing fractions φJ at jamming onset. For the second, we seed the system with initial configurations that promote microand macrophase-separated packings followed by compression and decompression to φJ . Using these protocols, we generate more than 10 4 static packings over a wide range of packing fraction, contact number, and compositional and positional order. We find that amorphous, isostatic packings exist over a finite range of packing fractions from φmin ≤ φJ ≤ φmax in the large-system limit, with φmax ≈ 0.853. In agreement with previous calculations, we obtain φmin ≈ 0.84 for r > r * , where r * is the rate above which φJ is insensitive to rate. We further compare the structural and mechanical properties of isostatic versus hyperstatic packings. The structural characterizations include the contact number, bond orientational order, and mixing ratios of the large and small particles. We find that the isostatic packings are positionally and compositionally disordered, whereas bondorientational and compositional order increase with contact number for hyperstatic packings. In addition, we calculate the static shear modulus and normal mode frequencies of the static packings to understand the extent to which the mechanical properties of amorphous, isostatic packings are different from partially ordered packings. We find that the mechanical properties of the packings change continuously as the contact number increases from isostatic to hyperstatic.PACS numbers: 83.80.

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Section: Structural and Mechanical Propertiessupporting

confidence: 65%

Section: Introductionmentioning

confidence: 99%

Tuning jammed frictionless disk packings from isostatic to hyperstatic

2011

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“…Of particular recent interest are (nonequilibrium) disordered jammed packings of hard spheres and their statistical and mechanical properties, such as the maximally random jammed (MRJ) state [1,2], pair correlations [3], isostaticity [3], and density fluctuations [4]. Such packings have been intensely studied computationally in two and three dimensions [1,2,3,4,5,6,7,8,9,10,11] and in this paper we extend these studies to four, five and six dimensions.…”

Section: Introductionmentioning

confidence: 99%

Packing hyperspheres in high-dimensional Euclidean spaces

et al. 2006

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We present the first study of disordered jammed hard-sphere packings in four-, five-and sixdimensional Euclidean spaces. Using a collision-driven packing generation algorithm, we obtain the first estimates for the packing fractions of the maximally random jammed (MRJ) states for space dimensions d = 4, 5 and 6 to be φ M RJ ≃ 0.46, 0.31 and 0.20, respectively. To a good approximation, the MRJ density obeys the scaling formand c 2 = 2.56, which appears to be consistent with high-dimensional asymptotic limit, albeit with different coefficients. Calculations of the pair correlation function g 2 (r) and structure factor S(k) for these states show that short-range ordering appreciably decreases with increasing dimension, consistent with a recently proposed "decorrelation principle," which, among othe things, states that unconstrained correlations diminish as the dimension increases and vanish entirely in the limit d → ∞. As in three dimensions (where φ M RJ ≃ 0.64), the packings show no signs of crystallization, are isostatic, and have a power-law divergence in g 2 (r) at contact with power-law exponent ≃ 0.4. Across dimensions, the cumulative number of neighbors equals the kissing number of the conjectured densest packing close to where g 2 (r) has its first minimum. Additionally, we obtain estimates for the freezing and melting packing fractions for the equilibrium hard-sphere fluid-solid transition, φ F ≃ 0.32 and φ M ≃ 0.39, respectively, for d = 4, and φ F ≃ 0.19 and φ M ≃ 0.24, respectively, for d = 5. Although our results indicate the stable phase at high density is a crystalline solid, nucleation appears to be strongly suppressed with increasing dimension. * Electronic address: torquato@electron.princeton.edu 2

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“…We show that this optimized sampling method allows to thermalize polydisperse hard spheres up to unprecedentedly-large densities. In particular, we achieve thermal equilibrium in a region of densities where the jamming transition ϕ J can also be located by accepted methods [9,15,27]. This directly shows, without extrapolating any dynamical data, that point J of jamming does not correspond to the end-point of the fluid equilibrium states.…”

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confidence: 99%

“…These fast compressions yield ϕ (1) J ≈ 0.6487. In an independent protocol, we use energy minimization procedures converting the hard sphere potential into soft harmonic repulsive springs [15,27], which defines 'point J' [15]. We iteratively compress or expand the system starting from a dilute random system distribution until particles are precisely at contact [27].…”

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Equilibrium Sampling of Hard Spheres up to the Jamming Density and Beyond

et al. 2016

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We implement and optimize a particle-swap Monte-Carlo algorithm that allows us to thermalize a polydisperse system of hard spheres up to unprecedentedly-large volume fractions, where previous algorithms and experiments fail to equilibrate. We show that no glass singularity intervenes before the jamming density, which we independently determine through two distinct non-equilibrium protocols. We demonstrate that equilibrium fluid and non-equilibrium jammed states can have the same density, showing that the jamming transition cannot be the end-point of the fluid branch.PACS numbers: 05.20.Jj,We clarify the behavior of non-crystalline states of hard spheres at very large densities where both a glass transition (in colloidal systems) and a jamming transition (in non-Brownian systems) are observed [1][2][3]. Glass and jamming transitions are usually studied through distinct protocols, and understanding the relation between these two broad classes of phase transformations and the resulting amorphous arrested states is an important research goal [1][2][3][4][5]. These questions impact a wide range of fields, from the rheological properties of soft materials to optimization problems in computer science [1,6].Let us first consider Brownian hard spheres. When size polydispersity is introduced, crystallization can be prevented and the thermodynamic properties of the fluid studied at increasing density until a glass transition takes place, where particle diffusivity becomes very small [7]. Upon further compression, the pressure of the glass increases until a jamming transition occurs, where particles come at close contact and the pressure diverges [8]. Because the laboratory glass transition arises from using a finite observation timescale, two scenarios were proposed to describe the hypothetical situation where thermalization is no longer an issue [9]. A first possibility is that slower compressions reveal an ideal glass transition density, ϕ 0 , above which the equilibrium state is a glass, not a fluid [2]. Jamming would then be observed upon further non-equilibrium compression of these glass states [10]. Alternatively, it may be that slower compressions continuously shift the kinetic glass transition to higher densities. In this view, it is plausible that jamming becomes the end-point of the equilibrium fluid branch [11,12].Distinguishing between these two scenarios by direct numerical measurements is challenging. For a wellstudied binary mixture of hard spheres, for instance, thermalization can be achieved up to ϕ max ≈ 0.60 [9,13]. The location of the glass transition must be extrapolated using empirical fits based on activated relaxation. Values in the range ϕ 0 = 0.615 − 0.635 were obtained [9], depending on the fitting function. Fitting the relaxation times to a power law yields ϕ mct ≈ 0.59 < ϕ max , so that the associated mode-coupling transition [14] corresponds to an avoided singularity. For the same system, jamming transitions were located in the range ϕ J = 0.648 − 0.662 depending on the chosen protocol [15][1...

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Publisher's Note: Random close packing revisited: Ways to pack frictionless disks [Phys. Rev. E71, 061306 (2005)]

Cited by 62 publications

References 0 publications

Tuning jammed frictionless disk packings from isostatic to hyperstatic

Tuning jammed frictionless disk packings from isostatic to hyperstatic

Packing hyperspheres in high-dimensional Euclidean spaces

Equilibrium Sampling of Hard Spheres up to the Jamming Density and Beyond

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