Can exotic disordered “stealthy” particle configurations tolerate arbitrarily large holes?

Zhang, G.; Stillinger, Frank H.; Torquato, Salvatore

doi:10.1039/c7sm01028a

Cited by 28 publications

(41 citation statements)

References 49 publications

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“…which immediately follows from relation (69). The fact that the function Λ(R) function is bounded implies that periodic point configurations belong to class I hyperuniform systems.…”

Section: Asymptotics For Periodic Point Configurationsmentioning

confidence: 73%

“…Now there is a realization that these systems play a vital role in a number of problems across the physical, materials, mathematical, and biological sciences. Specifically, we now know that these exotic states of matter can exist as both equilibrium and nonequilibrium phases, including maximally random jammed (MRJ) hard-particle packings [36][37][38][39][40][41][42][43][44], jammed athermal soft-sphere models of granular media [45,46], jammed thermal colloidal packings [47,48], jammed bidisperse emulsions [49], dynamical processes in ultracold atoms [50], nonequilibrium phase transitions [51][52][53][54][55][56][57][58], avian photoreceptor patterns [59], receptor organization in the immune system [60], certain quantum ground states (both fermionic and bosonic) [34,61], classical disordered (noncrystalline) ground states [62][63][64][65][66][67][68][69][70], the distribution of the nontrivial zeros of the Riemann zeta function [34,71], and the eigenvalues of various random matrices [14,72].…”

Section: Introductionmentioning

confidence: 99%

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Hyperuniform states of matter

2018

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Hyperuniform states of matter are correlated systems that are characterized by an anomalous suppression of longwavelength (i.e., large-length-scale) density fluctuations compared to those found in garden-variety disordered systems, such as ordinary fluids and amorphous solids. All perfect crystals, perfect quasicrystals and special disordered systems are hyperuniform. Thus, the hyperuniformity concept enables a unified framework to classify and structurally characterize crystals, quasicrystals and the exotic disordered varieties. While disordered hyperuniform systems were largely unknown in the scientific community over a decade ago, now there is a realization that such systems arise in a host of contexts across the physical, materials, chemical, mathematical, engineering, and biological sciences, including disordered ground states, glass formation, jamming, Coulomb systems, spin systems, photonic and electronic band structure, localization of waves and excitations, self-organization, fluid dynamics, number theory, stochastic point processes, integral and stochastic geometry, the immune system, and photoreceptor cells. Such unusual amorphous states can be obtained via equilibrium or nonequilibrium routes, and come in both quantum-mechanical and classical varieties. The connections of hyperuniform states of matter to many different areas of fundamental science appear to be profound and yet our theoretical understanding of these unusual systems is only in its infancy. The purpose of this review article is to introduce the reader to the theoretical foundations of hyperuniform ordered and disordered systems. Special focus will be placed on fundamental and practical aspects of the disordered kinds, including our current state of knowledge of these exotic amorphous systems as well as their formation and novel physical properties.

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“…which immediately follows from relation (69). The fact that the function Λ(R) function is bounded implies that periodic point configurations belong to class I hyperuniform systems.…”

Section: Asymptotics For Periodic Point Configurationsmentioning

confidence: 73%

Section: Introductionmentioning

confidence: 99%

Hyperuniform states of matter

2018

Self Cite

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“…Clearly, if the hole probability has compact support, i.e., E V (r) = 0 at any r > D for a certain length D, then Voronoi tessellations of the associated point patterns always meet the bounded-cell condition for relatively small sample sizes (say 10 d+1 in space dimension d). Examples of such systems include all crystals, disordered stealthy hyperuniform point patterns [88,89], and the saturated random sequential addition (RSA) packings [34,90]. Specifically, RSA is a time-dependent process that irreversibly, randomly, and sequentially adds nonoverlapping spheres into space.…”

Section: A the Bounded-cell Conditionmentioning

confidence: 99%

Methodology to construct large realizations of perfectly hyperuniform disordered packings

Kim

Torquato

2019

Phys. Rev. E

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Disordered hyperuniform packings (or dispersions) are unusual amorphous two-phase materials that are endowed with exotic physical properties. Such hyperuniform systems are characterized by an anomalous suppression of volume-fraction fluctuations at infinitely long-wavelengths, compared to ordinary disordered materials. While there has been growing interest in such singular states of amorphous matter, a major obstacle has been an inability to produce large samples that are perfectly hyperuniform due to practical limitations of conventional numerical and experimental methods. To overcome these limitations, we introduce a general theoretical methodology to construct perfectly hyperuniform packings in d-dimensional Euclidean space R d . Specifically, beginning with an initial general tessellation of space by disjoint cells that meets a "bounded-cell" condition, hard particles are placed inside each cell such that the local-cell particle packing fractions are identical to the global packing fraction. We prove that the constructed packings with a polydispersity in size in R d are perfectly hyperuniform in the infinite-sample-size limit and the hyperuniformity of such packings is independent of particle shapes, positions, and numbers per cell. We use this theoretical formulation to devise an efficient and tunable algorithm to generate extremely large realizations of such packings. We employ two distinct initial tessellations: Voronoi as well as sphere tessellations. Beginning with Voronoi tessellations, we show that our algorithm can remarkably convert extremely large nonhyperuniform packings into hyperuniform ones in R 2 and R 3 . Implementing our theoretical methodology on sphere tessellations, we establish the hyperuniformity of the classical Hashin-Shtrikman multiscale coated-spheres structures, which are known to be two-phase media microstructures that possess optimal effective transport and elastic properties. A consequence of our work is a rigorous demonstration that packings that have identical tessellations can either be nonhyperuniform or hyperuniform by simply tuning local characteristics. It is noteworthy that our computationally designed hyperuniform two-phase systems can easily be fabricated via state-of-theart methods, such as 2D photolithographic and 3D printing technologies. In addition, the tunability of our methodology offers a route for the discovery of novel disordered hyperuniform two-phase materials.

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“…This photonic study provides a vivid example of a class of disordered materials that has advantages over ordered counterparts and has led to a flurry of papers on the study of photonic properties of disordered hyperuniform networks [30][31][32][33][34]. It has been suggested [22] that the novel properties associated with disordered stealthy networks is related to the fact that they cannot possess arbitrarily large "holes" (or cells) [35]. In addition, disordered stealthy hyperuniform two-phase materials were recently found to possess desirable transport properties [25,26].…”

Section: Introductionmentioning

confidence: 99%

Multifunctional hyperuniform cellular networks: optimality, anisotropy and disorder

Torquato

Chen

2018

Multifunct. Mater.

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Disordered hyperuniform heterogeneous materials are new, exotic amorphous states of matter that behave like crystals in the manner in which they suppress volume-fraction fluctuations at large length scales, and yet are statistically isotropic with no Bragg peaks. It has recently been shown that disordered hyperuniform dielectric two-dimensional cellular network solids possess complete photonic band gaps comparable in size to photonic crystals, while at the same time maintaining statistical isotropy, enabling waveguide geometries not possible with photonic crystals. Motivated by these developments, we explore other functionalities of various two-dimensional ordered and disordered hyperuniform cellular networks, including their effective thermal or electrical conductivities and elastic moduli. We establish the multifunctionality of a class of such low-density networks by demonstrating that they maximize or virtually maximize the effective conductivities and elastic moduli. This is accomplished using the machinery of homogenization theory, including optimal bounds and cross-property bounds, and statistical mechanics. We rigorously prove that anisotropic networks consisting of sets of intersecting parallel channels in the lowdensity limit, ordered or disordered, possess optimal effective conductivity tensors. For a variety of different disordered networks, we show that when short-range and long-range order increases, there is an increase in both the effective conductivity and elastic moduli of the network. Moreover, we demonstrate that the effective conductivity and elastic moduli of various disordered networks derived from disordered "stealthy" hyperuniform point patterns possess virtually optimal values. We note that the optimal networks for conductivity are also optimal for the fluid permeability associated with slow viscous flow through the channels as well as the mean survival time associated with diffusion-controlled reactions in the channels. In summary, we have identified ordered and disordered hyperuniform low-weight cellular networks that are multifunctional with respect to transport (e.g., heat dissipation and fluid transport), mechanical and electromagnetic properties, which can be readily fabricated using 3D printing and lithographic technologies.

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Can exotic disordered “stealthy” particle configurations tolerate arbitrarily large holes?

Cited by 28 publications

References 49 publications

Hyperuniform states of matter

Hyperuniform states of matter

Methodology to construct large realizations of perfectly hyperuniform disordered packings

Multifunctional hyperuniform cellular networks: optimality, anisotropy and disorder

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