# Hyperuniformity and its generalizations.

@article{Torquato2016HyperuniformityAI, title={Hyperuniformity and its generalizations.}, author={Salvatore Torquato}, journal={Physical review. E}, year={2016}, volume={94 2-1}, pages={ 022122 } }

Disordered many-particle hyperuniform systems are exotic amorphous states of matter that lie between crystal and liquid: They are like perfect crystals in the way they suppress large-scale density fluctuations and yet are like liquids or glasses in that they are statistically isotropic with no Bragg peaks. These exotic states of matter play a vital role in a number of problems across the physical, mathematical as well as biological sciences and, because they are endowed with novel physical… Expand

#### Figures and Topics from this paper

#### 80 Citations

Disordered hyperuniform heterogeneous materials.

- Physics, Medicine
- Journal of physics. Condensed matter : an Institute of Physics journal
- 2016

New rigorous criteria that disordered hyperuniform two-phase heterogeneous materials must obey are derived and implications for the design of such novel amorphous materials are explored. Expand

Random scalar fields and hyperuniformity

- Physics
- 2017

Disordered many-particle hyperuniform systems are exotic amorphous states of matter that lie between crystals and liquids. Hyperuniform systems have attracted recent attention because they are… Expand

Transport, geometrical, and topological properties of stealthy disordered hyperuniform two-phase systems.

- Physics, Medicine
- The Journal of chemical physics
- 2016

As the extent of short-range order increases, stealthy disordered two-phase media can attain nearly maximal effective diffusion coefficients over a broad range of volume fractions while also maintaining isotropy, and therefore may have practical applications in situations where ease of transport is desirable. Expand

Hyperuniform States of Matte

- Physics
- 2018

Hyperuniform states of matter are correlated systems that are characterized by an anomalous suppression of long-wavelength (i.e., large-length-scale) density fluctuations compared to those found in… Expand

Multifunctional Hyperuniform Cellular Networks: Optimality, Anisotropy and Disorder

- Materials Science, Physics
- 2018

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… Expand

Binary mixtures of charged colloids: a potential route to synthesize disordered hyperuniform materials.

- Materials Science, Medicine
- Physical chemistry chemical physics : PCCP
- 2018

This work studies the small-wavenumber behavior of the spectral density of binary mixtures of charged colloids in suspension and finds that at dimensionless temperatures below 0.05 and dimensionless inverse screening lengths below 1.0, the disordered systems become effectively hyperuniform. Expand

Designing disordered hyperuniform two-phase materials with novel physical properties

- Materials Science, Physics
- 2018

Abstract Heterogeneous materials consisting of different phases are ideally suited to achieve a broad spectrum of desirable bulk physical properties by combining the best features of the constituents… Expand

Methodology to construct large realizations of perfectly hyperuniform disordered packings.

- Physics, Medicine
- Physical review. E
- 2019

It is proved that the constructed packings with a polydispersity in size are perfectly hyperuniform in the infinite-sample-size limit, regardless of particle shapes, positions, and numbers per cell. Expand

Enhanced Pinning For Vortices in Hyperuniform Substrates and Emergent Hyperuniform Vortex States

- Physics
- 2016

Disordered hyperuniformity is a state of matter which has isotropic liquid like properties while simultaneously having crystalline like properties such as little variation in the density fluctuations… Expand

Exotic Ordered and Disordered Many-Particle Systems with Novel Properties

- Physics
- 2017

This dissertation presents studies on several statistical-mechanical problems, many of which involve exotic many-particle systems. In Chapter 2, we present an algorithm to generate Random Sequential… Expand

#### References

SHOWING 1-10 OF 146 REFERENCES

Disordered hyperuniform heterogeneous materials.

- Physics, Medicine
- Journal of physics. Condensed matter : an Institute of Physics journal
- 2016

New rigorous criteria that disordered hyperuniform two-phase heterogeneous materials must obey are derived and implications for the design of such novel amorphous materials are explored. Expand

Hyperuniformity in point patterns and two-phase random heterogeneous media

- Mathematics, Physics
- 2009

Hyperuniform point patterns are characterized by vanishing infinite-wavelength density fluctuations and encompass all crystal structures, certain quasiperiodic systems, and special disordered point… Expand

Diagnosing hyperuniformity in two-dimensional, disordered, jammed packings of soft spheres.

- Materials Science, Physics
- Physical review. E, Statistical, nonlinear, and soft matter physics
- 2015

Using video optical microscopy to study hyperuniformity phenomena in disordered two-dimensional jammed packings of soft spheres and a simple packing reconstruction algorithm that incorporates particle polydispersity to minimize the free volume, simulations show that hyper uniformity in finite-sized samples can be ascertained more accurately in direct space than in reciprocal space. Expand

Anomalous local coordination, density fluctuations, and void statistics in disordered hyperuniform many-particle ground states.

- Mathematics, Physics
- Physical review. E, Statistical, nonlinear, and soft matter physics
- 2011

The results explicitly demonstrate that disordered hyperuniform many-particle ground states, and therefore also point distributions, with substantial clustering can be constructed, and directly relate the local coordination structure of the point patterns to the distribution of the void space external to the particles. Expand

Inverse design of disordered stealthy hyperuniform spin chains

- Physics
- 2016

Positioned between crystalline solids and liquids, disordered many-particle systems which are stealthy and hyperuniform represent new states of matter that are endowed with novel physical and… Expand

Hyperuniformity, quasi-long-range correlations, and void-space constraints in maximally random jammed particle packings. II. Anisotropy in particle shape.

- Physics, Medicine
- Physical review. E, Statistical, nonlinear, and soft matter physics
- 2011

This work considers maximally random jammed packings of hard ellipses and superdisks and shows that these systems both possess vanishing infinite-wavelength local-volume-fraction fluctuations and quasi-long-range pair correlations scaling as r(-(d+1)) in d Euclidean dimensions. Expand

Ensemble Theory for Stealthy Hyperuniform Disordered Ground States

- Physics
- 2015

It has been shown numerically that systems of particles interacting with "stealthy" bounded, long-ranged pair potentials (similar to Friedel oscillations) have classical ground states that are,… Expand

Microstructure characterization and bulk properties of disordered two-phase media

- Physics
- 1986

A general formalism is developed to statistically characterize the microstructure of porous and other composite media composed of inclusions (particles) distributed throughout a matrix phase (which,… Expand

Equilibrium phase behavior and maximally random jammed state of truncated tetrahedra.

- Materials Science, Physics
- The journal of physical chemistry. B
- 2014

A Monte Carlo implementation of the adaptive-shrinking-cell (ASC) numerical scheme and free-energy calculations are employed to ascertain with high precision the equilibrium phase behavior of systems of congruent Archimedean truncated tetrahedra over the entire range of possible densities up to the maximal nearly space-filling density. Expand

Local density fluctuations, hyperuniformity, and order metrics.

- Mathematics, Physics
- Physical review. E, Statistical, nonlinear, and soft matter physics
- 2003

The purpose of this paper is to characterize certain fundamental aspects of local density fluctuations associated with general point patterns in any space dimension d, and to study the variance in the number of points contained within a regularly shaped window of arbitrary size to further illuminate the understanding of hyperuniform systems. Expand