Related papers: Quantifying the Long-Range Structure of Foams and …
We introduce the concept of a hyperuniformity disorder length that controls the variance of volume fraction fluctuations for randomly placed windows of fixed size. In particular, fluctuations are determined by the average number of…
We investigate the short, medium, and long-range structure of soft disk configurations for a wide range of area fractions and simulation protocols by converting the real-space spectrum of volume fraction fluctuations for windows of width…
We study the Voronoi and void statistics of super-homogeneous (or hyperuniform) point patterns in which the infinite-wavelength density fluctuations vanish. Super-homogeneous or hyperuniform point patterns arise in one-component plasmas,…
The concept of a hyperuniformity disorder length $h$ was recently introduced for analyzing volume fraction fluctuations for a set of measuring windows. This length permits a direct connection to the nature of disorder in the spatial…
We study the variance in the number of points contained within a window $\Omega$ of arbitrary size, and to further illuminate our understanding of {\it hyperuniform} systems, i.e., point patterns that do not possess long-wavelength…
Hyperuniform materials, characterized by their suppressed density fluctuations and vanishing structure factors as the wave number approaches zero, represent a unique state of matter that straddles the boundary between order and randomness.…
We provide numerical constructions of one-dimensional hyperuniform many-particle distributions that exhibit unusual clustering and asymptotic local number density fluctuations growing more slowly than the volume of an observation window but…
Hyperuniform point patterns are characterized by vanishing infinite wavelength density fluctuations and encompass all crystal structures, certain quasi-periodic systems, and special disordered point patterns. This article generalizes the…
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 suppress large-scale density fluctuations. While the…
A spatial distribution is hyperuniform if it has local density fluctuations that vanish in the limit of long length scales. Hyperuniformity is a well known property of both crystals and quasicrystals. Of recent interest, however, is…
We consider the Voronoi diagram generated by $n$ i.i.d. $\mathbb{R}^{d}$-valued random variables with an arbitrary underlying probability density function $f$ on $\mathbb{R}^{d}$, and analyse the asymptotic behaviours of certain geometric…
Studies of disordered heterogeneous media and galaxy cosmology share a common goal: analyzing the distribution of particles at `microscales' to predict physical properties at `macroscales', whether for a liquid, composite material, or…
We explore quantitative descriptors that herald when a many-particle system in $d$-dimensional Euclidean space $\mathbb{R}^d$ approaches a hyperuniform state as a function of the relevant control parameter. We establish quantitative…
Hyperuniformity characterizes a state of matter for which density fluctuations diminish towards zero at the largest length scales. However, the task of determining whether or not an experimental system is hyperuniform is experimentally…
Hyperuniform particle arrangements are characterized by a local number variance that grows more slowly than the volume of the observation window. We generalize this concept to describe particle systems in which particles carry weights:…
Disordered hyperuniform many-particle systems are recently discovered exotic states of matter, characterized by a complete suppression of normalized infinite-wavelength density fluctuations and lack of conventional long-range order. Here,…
Connecting the collective behavior of disordered systems with local structure on the particle scale is an important challenge, for example in granular and glassy systems. Compounding complexity, in many scientific and industrial…
Disordered hyperuniform packings are unusual amorphous states of two-phase materials that are endowed with exotic physical properties. Such hyperuniform systems are characterized by an anomalous suppression of volume-fraction fluctuations…
We introduce a general, efficient method to completely describe the topology of individual grains, bubbles, and cells in three-dimensional polycrystals, foams, and other multicellular microstructures. This approach is applied to a pair of…
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.…