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

Abstract

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, 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. 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.

40 pages, 15 figures

References in corpus (11)

• Jammed Hard-Particle Packings: From Kepler to Bernal and Beyond
• Modeling Heterogeneous Materials via Two-Point Correlation Functions: I. Basic Principles
• Hyperuniform long-range correlations are a signature of disordered jammed hard-particle packings
• Point processes in arbitrary dimension from fermionic gases, random matrix theory, and number theory
• Suppressed compressibility at large scale in jammed packings of size disperse spheres
• Statistical properties of determinantal point processes in high-dimensional Euclidean spaces
• Anomalous local coordination, density fluctuations, and void statistics in disordered hyperuniform many-particle ground states
• Reformulation of the Covering and Quantizer Problems as Ground States of Interacting Particles
• Non-Universality of Density and Disorder in Jammed Sphere Packings
• Hyperuniformity, quasi-long-range correlations, and void-space constraints in maximally random jammed particle packings. II. Anisotropy in particle shape
• Tilings of space and superhomogeneous point processes

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