Random Scalar Fields and Hyperuniformity

Abstract

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 endowed with novel transport and optical properties. Recently, the hyperuniformity concept has been generalized to characterize scalar fields, two-phase media and random vector fields. In this paper, we devise methods to explicitly construct hyperuniform scalar fields. We investigate explicitly spatial patterns generated from Gaussian random fields, which have been used to model the microwave background radiation and heterogeneous materials, the Cahn-Hilliard equation for spinodal decomposition, and Swift-Hohenberg equations that have been used to model emergent pattern formation, including Rayleigh-B{\' e}nard convection. We show that the Gaussian random scalar fields can be constructed to be hyperuniform. We also numerically study the time evolution of spinodal decomposition patterns and demonstrate that these patterns are hyperuniform in the scaling regime. Moreover, we find that labyrinth-like patterns generated by the Swift-Hohenberg equation are effectively hyperuniform. We show that thresholding a hyperuniform Gaussian random field to produce a two-phase random medium tends to destroy the hyperuniformity of the progenitor scalar field. We then propose guidelines to achieve effectively hyperuniform two-phase media derived from thresholded non-Gaussian fields. Our investigation paves the way for new research directions to characterize the large-structure spatial patterns that arise in physics, chemistry, biology and ecology. Moreover, our theoretical results are expected to guide experimentalists to synthesize new classes of hyperuniform materials with novel physical properties via coarsening processes and using state-of-the-art techniques, such as stereolithography and 3D printing.

16 pages, 18 figures

References in corpus (28)

• Is Random Close Packing of Spheres Well Defined?
• Jammed Hard-Particle Packings: From Kepler to Bernal and Beyond
• Local Density Fluctuations, Hyperuniformity, and Order Metrics
• Designer disordered materials with large complete photonic band gaps
• Unexpected Density Fluctuations in Jammed Disordered Sphere Packings
• Avian photoreceptor patterns represent a disordered hyperuniform solution to a multiscale packing problem
• Isotropic Band Gaps and Freeform Waveguides Observed in Hyperuniform Disordered Photonic Solids
• Hyperuniformity of critical absorbing states
• Hyperuniformity in point patterns and two-phase random heterogeneous media
• Theoretical Model for Faraday Waves with Multiple-Frequency Forcing
• Classical Disordered Ground States: Super-Ideal Gases, and Stealth and Equi-Luminous Materials
• Hyperuniformity and its Generalizations
• Hyperuniform long-range correlations are a signature of disordered jammed hard-particle packings
• How a well-adapted immune system is organized
• Transport properties of heterogeneous materials derived from Gaussian random fields: Bounds and Simulation
• Photonic band gap in isotropic hyperuniform disordered solids with low dielectric contrast
• Ensemble Theory for Stealthy Hyperuniform Disordered Ground States
• Precise Algorithm to Generate Random Sequential Addition of Hard Hyperspheres at Saturation
• Out-of-equilibrium structures in strongly interacting Rydberg gases with dissipation
• Diagnosing hyperuniformity in two-dimensional disordered jammed-packings of soft spheres
• Suppressed compressibility at large scale in jammed packings of size disperse spheres
• Incompressibility of polydisperse random close packed colloidal particles
• Critical slowing down and hyperuniformity on approach to jamming
• Ground states of stealthy hyperuniform potentials: I. Entropically favored configurations
• Hyperuniformity, quasi-long-range correlations, and void-space constraints in maximally random jammed particle packings. I. Polydisperse spheres
• Disordered Hyperuniform Heterogeneous Materials
• Direct laser writing of three dimensional network structures as templates for disordered photonic materials
• Effect of Window Shape on the Detection of Hyperuniformity via the Local Number Variance

Cited by in corpus (38)

• Hyperuniform States of Matter
• Designing Disordered Hyperuniform Two-Phase Materials with Novel Physical Properties
• Ultrafast jamming of electrons into an amorphous entangled state
• Predicting permeability via statistical learning on higher-order microstructural information
• Hyperuniform monocrystalline structures by spinodal solid-state dewetting
• Nonlocal Effective Electromagnetic Wave Characteristics of Composite Media: Beyond the Quasistatic Regime
• Active phase separation: new phenomenology from non-equilibrium physics
• Precise algorithms to compute surface correlation functions of two-phase heterogeneous media and their applications
• Efficient light-trapping in ultrathin GaAs solar cells using quasi-random photonic crystals
• Hyperuniformity with no fine tuning in sheared sedimenting suspensions
• Methodology to Construct Large Realizations of Perfectly Hyperuniform Disordered Packings
• Quantum phase transition between hyperuniform density distributions
• Effective Elastic Wave Characteristics of Composite Media
• Theoretical Prediction of the Effective Dynamic Dielectric Constant of Disordered Hyperuniform Anisotropic Composites Beyond the Long-Wavelength Regime
• Classical many-particle systems with unique disordered ground states
• Quantum criticality in Ising chains with random hyperuniform couplings
• Engineering the reciprocal space for ultrathin GaAs solar cells
• Hyperuniform electron distributions controlled by electron interactions in quasicrystal
• Optimized Large Hyperuniform Binary Colloidal Suspensions in Two Dimensions
• Non-equilibrium dynamic hyperuniform states
• Enhancing (quasi-)long-range order in a two-dimensional driven crystal
• Hyperuniformity in phase ordering: the roles of activity, noise, and non-constant mobility
• Fast Generation of Spectrally-Shaped Disorder
• Characterizing the Hyperuniformity of Ordered and Disordered Two-Phase Media
• The structure factor of primes
• Characterization of Anisotropic Gaussian Random Fields by Minkowski Tensors
• Hyperuniformity in amorphous speckle patterns
• Hyperuniformity Order Metric of Barlow Packings
• Multiscale Physics-Informed Neural Networks for the Inverse Design of Hyperuniform Optical Materials
• Hyperuniform Density Distributions of Brownian Particles via Designer External Potentials
• Hyperuniformity in two-dimensional periodic and quasiperiodic point patterns
• Hyperuniform scalar random fields for lensless, multispectral imaging systems
• Singular density correlations in chiral active fluids in three dimensions
• Devitrification and Melting Dynamics in Vapor Deposited Water Ice
• Hyperuniformity of Weighted Particle Systems
• Inferring traits of hyperuniformity from local structures via persistent homology
• Theoretical Basis for Classifying Hyperuniform States of Two-Component Systems
• Germanium-based nearly hyperuniform nanoarchitectures by ion beam impact