Suppressed Compressibility at Large Scale in Jammed Packings of Size-Disperse Spheres

Berthier, Ludovic; Chaudhuri, Pinaki; Coulais, Corentin; Dauchot, Olivier; Sollich, Peter

doi:10.1103/physrevlett.106.120601

Cited by 97 publications

(150 citation statements)

References 19 publications

(45 reference statements)

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“…We see that Var(φ R ) is independent ofp, and in contrast to the naive expectation vanishes more rapidly, like ∼ 1/R 3 . This is a signature of the hyperuniformity of jammed packings that has been observed exactly at φ J by earlier analyses of the long wavelength limit of the compressibility [14] and the 2-point spectral density function [15]. The solid line in Fig.…”

Section: Hyperuniformitymentioning

confidence: 78%

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Statistics of conserved quantities in mechanically stable packings of frictionless disks above jamming

Teitel

2015

Phys. Rev. E

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We numerically simulate mechanically stable packings of soft-core, frictionless, bidisperse disks in two dimensions, above the jamming packing fraction φJ . For configurations with a fixed isotropic global stress tensor, we compute the averages, variances, and correlations of conserved quantities (stress ΓC, force-tile area AC, Voronoi volume VC, number of particles NC, and number of small particles NsC) on compact subclusters of particles C, as a function of the cluster size and the global system stress. We find several significant differences depending on whether the cluster C is defined by a fixed radius R or a fixed number of particles M . We comment on the implications of our findings for maximum entropy models of jammed packings.

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Section: Hyperuniformitymentioning

confidence: 78%

“…We show that the notion of hyperuniformity [14,15], found for packings exactly at φ J , continues to hold in packings above φ J .…”

Section: Introductionmentioning

confidence: 99%

Statistics of conserved quantities in mechanically stable packings of frictionless disks above jamming

Teitel

2015

Phys. Rev. E

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“…We mention that recent, independent work, appearing in preprint form shortly after our own manuscript was posted, [59] has shown that hyperuniformity and vanishing infinitewavelength local-volume-fraction fluctuations in saturated MRJ packings of polydisperse disks are consistent with certain fluctuation-response relations involving a generalized "compressibility." However, this work does not address the appearance of quasi-long-range pair correlations in MRJ hard-particle packings and does not consider MRJ packings of nonspherical particles as in our companion paper [58].…”

Section: Discussionmentioning

confidence: 91%

Hyperuniformity, quasi-long-range correlations, and void-space constraints in maximally random jammed particle packings. I. Polydisperse spheres

2011

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Hyperuniform many-particle distributions possess a local number variance that grows more slowly than the volume of an observation window, implying that the local density is effectively homogeneous beyond a few characteristic length scales. Previous work on maximally random strictly jammed sphere packings in three dimensions has shown that these systems are hyperuniform and possess unusual quasi-long-range pair correlations decaying as r −4 , resulting in anomalous logarithmic growth in the number variance. However, recent work on maximally random jammed sphere packings with a size distribution has suggested that such quasi-long-range correlations and hyperuniformity are not universal among jammed hard-particle systems. In this paper we show that such systems are indeed hyperuniform with signature quasi-long-range correlations by characterizing the more general local-volume-fraction fluctuations. We argue that the regularity of the void space induced by the constraints of saturation and strict jamming overcomes the local inhomogeneity of the disk centers to induce hyperuniformity in the medium with a linear small-wavenumber nonanalytic behavior in the spectral density, resulting in quasi-long-range spatial correlations scaling with r −(d+1) in d Euclidean space dimensions. A numerical and analytical analysis of the pore-size distribution for a binary MRJ system in addition to a local characterization of the n-particle loops governing the void space surrounding the inclusions is presented in support of our argument. This paper is the first part of a series of two papers considering the relationships among hyperuniformity, jamming, and regularity of the void space in hard-particle packings.

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“…Examples include jamming in amorphous materials [4,5,[7][8][9][10], complete optical band gaps in disordered photonics materials [11][12][13][14][15], and reversibility/irreversibility in periodically driven systems [16][17][18]. Hyperunformity is also important in the arrangement of photoreceptors in the retina [19], and in the large-scale structure of the universe [2].…”

mentioning

confidence: 99%

“…The structural uniformity of a many-body system may be studied in terms of fluctuations in the number [1,2] and volume fraction [3][4][5] of objects inside measuring windows of equal size but different locations. At one extreme, a totally random arrangement exhibits large fluctuations that are Poissonian, such that the volume fraction variance for large L scales as σ φ 2 (L) ∼ 1/L d , where L is the width of the measuring windows and d is dimensionality.…”

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confidence: 99%

Hyperuniformity disorder length spectroscopy for extended particles

Durian¹

2017

Phys. Rev. E

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The concept of a hyperuniformity disorder length h was recently introduced for analyzing volume fraction fluctuations for a set of measuring windows [Chieco et al. (2017)]. This length permits a direct connection to the nature of disorder in the spatial configuration of the particles, and provides a way to diagnose the degree of hyperuniformity in terms of the scaling of h and its value in comparison with established bounds. Here, this approach is generalized for extended particles, which are larger than the image resolution and can lie partially inside and partially outside the measuring windows. The starting point is an expression for the relative volume fraction variance in terms of four distinct volumes: that of the particle, the measuring window, the mean-squared overlap between particle and region, and the region over which particles have non-zero overlap with the measuring window. After establishing limiting behaviors for the relative variance, computational methods are developed for both continuum and pixelated particles. Exact results are presented for particles of special shape, and for measuring windows of special shape, for which the equations are tractable. Comparison is made for other particle shapes, using simulated Poisson patterns. And the effects of polydispersity and image errors are discussed. For small measuring windows, both particle shape and spatial arrangement affect the form of the variance. For large regions, the variance scaling depends only on arrangement but particle shape sets the numerical proportionality. The combined understanding permit the measured variance to be translated to the spectrum of hyperuniformity lengths versus region size, as the quantifier of spatial arrangement. This program is demonstrated for a system of non-overlapping particles at a series of increasing packing fractions as well as for an Einstein pattern of particles with several different extended shapes.The structural uniformity of a many-body system may be studied in terms of fluctuations in the number [1,2] and volume fraction [3-5] of objects inside measuring windows of equal size but different locations. At one extreme, a totally random arrangement exhibits large fluctuations that are Poissonian, such that the volume fraction variance for largewhere L is the width of the measuring windows and d is dimensionality. By contrast, a "hyperuniform" [1] or "superhomogeneous" [2] arrangement exhibits smaller sub-Poissonian fluctuations that decay more rapidly as σ φ 2 (L) ∼ 1/L d+ with 0 < ≤ 1. At the = 1 extreme, two straightforward hyperuniform arrangements are "shuffled lattice" [2] and "Einstein" [6] patterns, where particles are effectively bound by square-well and harmonic potentials, respectively, to fixed crystalline lattice sites and are independently displaced as though by thermal energy. If the root mean square displacement is large compared to the lattice spacing, then the arrangement appears quite random to the eye. In such cases, the underlying crystalline order is well hidden.There has been gro...

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Suppressed Compressibility at Large Scale in Jammed Packings of Size-Disperse Spheres

Cited by 97 publications

References 19 publications

Statistics of conserved quantities in mechanically stable packings of frictionless disks above jamming

Statistics of conserved quantities in mechanically stable packings of frictionless disks above jamming

Hyperuniformity, quasi-long-range correlations, and void-space constraints in maximally random jammed particle packings. I. Polydisperse spheres

Hyperuniformity disorder length spectroscopy for extended particles

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