771 citations · 12.9k across the 162 of their papers we have counts for
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Generating large disordered stealthy hyperuniform systems with ultra-high accuracy to determine their physical properties
Peter K. Morse, Jaeuk Kim, Paul J. Steinhardt +1
Hyperuniform many-particle systems are characterized by a structure factor that is precisely zero as ; and stealthy hyperuniform systems…
Realizability of Iso- Processes via Effective Pair Interactions
Haina Wang, Frank H. Stillinger, Salvatore Torquato
An outstanding problem in statistical mechanics is the determination of whether prescribed functional forms of the pair correlation function [or equivalently, structure fa…
Exclusion Volumes of Convex Bodies in High Space Dimensions: Applications to Virial Coefficients and Continuum Percolation
Salvatore Torquato, Yang Jiao
Using the concepts of mixed volumes and quermassintegrals of convex geometry, we derive an exact formula for the exclusion volume for a general convex body that applies in any spac…
Local Number Fluctuations in Hyperuniform and Nonhyperuniform Systems: Higher-Order Moments and Distribution Functions
Salvatore Torquato, Jaeuk Kim, Michael A. Klatt
The local number variance associated with a spherical sampling window of radius enables a classification of many-particle systems in -dimensional Euclidean space according t…
Nearest-Neighbor Functions for Disordered Stealthy Hyperuniform Many-Particle Systems
Timothy M. Middlemas, Salvatore Torquato
Disordered stealthy many-particle systems in are exotic states of matter that suppress single scattering events for a finite range of wavenumbers around the origin i…
Characterizing the Hyperuniformity of Ordered and Disordered Two-Phase Media
Jaeuk Kim, Salvatore Torquato
The hyperuniformity concept provides a unified means to classify all perfect crystals, perfect quasicrystals, and exotic amorphous states of matter according to their capacity to s…
Realizable hyperuniform and nonhyperuniform particle configurations with targeted spectral functions via effective pair interactions
Ge Zhang, Salvatore Torquato
The capacity to identify realizable many-body configurations associated with targeted functional forms for the pair correlation function or its corresponding structure fac…
Cloaking the Underlying Long-Range Order of Randomly Perturbed Lattices
Michael A. Klatt, Jaeuk Kim, Salvatore Torquato
Random, uncorrelated displacements of particles on a lattice preserve the hyperuniformity of the original lattice, that is, normalized density fluctuations vanish in the limit of i…
Hyperuniformity Order Metric of Barlow Packings
Timothy M. Middlemas, Frank H. Stillinger, Salvatore Torquato
The concept of hyperuniformity has been a useful tool in the study of large-scale density fluctuations in systems ranging across the natural and mathematical sciences. One can rank…
Hyperuniformity and anti-hyperuniformity in one-dimensional substitution tilings
Erdal C. Oğuz, Joshua E. S. Socolar, Paul J. Steinhardt +1
We consider the scaling properties characterizing the hyperuniformity (or anti-hyperuniformity) of long wavelength fluctuations in a broad class of one-dimensional substitution til…
Basic Understanding of Condensed Phases of Matter via Packing Models
Salvatore Torquato
Packing problems have been a source of fascination for millenia and their study has produced a rich literature that spans numerous disciplines. Investigations of hard-particle pack…
Uncovering Multiscale Order in the Prime Numbers via Scattering
S. Torquato, G. Zhang, M. de Courcy-Ireland
The prime numbers have been a source of fascination for millenia and continue to surprise us. Motivated by the hyperuniformity concept, which has attracted recent attention in phys…
The structure factor of primes
Ge Zhang, Fausto Martelli, Salvatore Torquato
Although the prime numbers are deterministic, they can be viewed, by some measures, as pseudo-random numbers. In this article, we numerically study the pair statistics of the prime…
Hyperuniform States of Matter
Salvatore Torquato
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…
Disordered hyperuniformity in two-component non-additive hard disk plasmas
E. Lomba, J. J. Weis, S. Torquato
We study the behavior of a two-component plasma made up of non-additive hard disks with a logarithmic Coulomb interaction. Due to the Coulomb repulsion, long-wavelength total densi…
Characterization of Maximally Random Jammed Sphere Packings. III. Transport and Electromagnetic Properties via Correlation Functions
Michael A. Klatt, Salvatore Torquato
In the first two papers of this series, we characterized the structure of maximally random jammed (MRJ) sphere packings across length scales by computing a variety of different cor…
Large-scale structure and hyperuniformity of amorphous ices
Fausto Martelli, Salvatore Torquato, Nicolas Giovambattista +1
We investigate the large-scale structure of amorphous ices and transitions between their different forms by quantifying their large-scale density fluctuations. Specifically, we sim…
Can exotic disordered "stealthy" particle configurations tolerate arbitrarily large holes?
G. Zhang, F. H. Stillinger, S. Torquato
The probability of finding a spherical cavity or "hole" of arbitrarily large size in typical disordered many-particle systems in the infinite-size limit (e.g., equilibrium liquid s…
Hyperuniformity of Quasicrystals
Erdal C. Oğuz, Joshua E. S. Socolar, Paul J. Steinhardt +1
Hyperuniform systems, which include crystals, quasicrystals and special disordered systems, have attracted considerable recent attention, but rigorous analyses of the hyperuniformi…
Structural characterization and statistical-mechanical model of epidermal patterns
Duyu Chen, Wen Yih Aw, Danelle Devenport +1
In proliferating epithelia of mammalian skin, cells of irregular polygonal-like shapes pack into complex nearly flat two-dimensional structures that are pliable to deformations. In…
The Weyl-Heisenberg ensemble: hyperuniformity and higher Landau levels
Luís Daniel Abreu, João M. Pereira, José Luis Romero +1
Weyl-Heisenberg ensembles are a class of determinantal point processes associated with the Schrödinger representation of the Heisenberg group. Hyperuniformity characterizes a state…
Effect of Window Shape on the Detection of Hyperuniformity via the Local Number Variance
Jaeuk Kim, Salvatore Torquato
Hyperuniform many particle systems in d-dimensional space, which includes crystals, quasicrystals, and some exotic disordered systems, are characterized by an anomalous suppression…
Characterization of Maximally Random Jammed Sphere Packings: II. Correlation Functions and Density Fluctuations
Michael A. Klatt, Salvatore Torquato
In the first paper of this series, we introduced Voronoi correlation functions to characterize the structure of maximally random jammed (MRJ) sphere packings across length scales.…
Static Structural Signatures of Nearly Jammed Disordered and Ordered Hard-Sphere Packings: Direct Correlation Function
Steven Atkinson, Frank H. Stillinger, Salvatore Torquato
Dynamical signatures are known to precede jamming in hard-particle systems, but static structural signatures have proven more elusive. The observation that compressing hard-particl…