Hyperuniformity on spherical surfaces

Abstract

In this work we present a study on the characterization of ordered and disordered hyperuniform point distributions on spherical surfaces. In spite of the extensive literature on disordered hyperuniform systems in Euclidean geometries, to date few works have dealt with the problem of hyperuniformity in curved spaces. As a matter of fact, some systems that display disordered hyperuniformity, like the space distribution of photoreceptors in avian retina, actually occur on curved surfaces. Here we will focus on the local particle number variance and its dependence on the size of the sampling window (which we take to be a spherical cap) for regular and uniform point distributions, as well as for equilibrium configurations of fluid particles interacting through Lennard-Jones, dipole-dipole and charge-charge potentials. We will show how the scaling of the local number variance enables the characterization of hyperuniform point patterns also on spherical surfaces.

References in corpus (25)

• Local Density Fluctuations, Hyperuniformity, and Order Metrics
• Designer disordered materials with large complete photonic band gaps
• Hyperuniform States of Matter
• 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
• Transport Phase Diagram and Anderson Localization in Hyperuniform Disordered Photonic Materials
• How a well-adapted immune system is organized
• An icosahedron-based method for pixelizing the celestial sphere
• Hyperuniform density fluctuations and diverging dynamic correlations in periodically driven colloidal suspensions
• Emergent hyperuniformity in periodically-driven emulsions
• Out-of-equilibrium structures in strongly interacting Rydberg gases with dissipation
• Designing Disordered Hyperuniform Two-Phase Materials with Novel Physical Properties
• Fractionalization of Interstitials in Curved Colloidal Crystals
• QMC designs: optimal order Quasi Monte Carlo Integration schemes on the sphere
• Transport, Geometrical and Topological Properties of Stealthy Disordered Hyperuniform Two-Phase Systems
• Two diverging length scales in the structure of jammed packings
• Hyperuniformity with no fine tuning in sheared sedimenting suspensions
• Disordered hyperuniformity in two-component non-additive hard disk plasmas
• Hyperuniform point sets on the sphere: deterministic constructions
• Disordered multihyperuniformity derived from binary plasmas
• Classical many-particle systems with unique disordered ground states
• Spherical structure factor and classification of hyperuniformity on the sphere
• Correlations and hyperuniformity in the avalanche size of the Oslo Model

Cited by in corpus (5)

• Hyperuniform point sets on the sphere: probabilistic aspects
• A minimal statistical-mechanical model for multihyperuniform patterns in avian retina
• The most uniform distribution of points on the sphere
• Global order parameters for particle distributions on the sphere
• Correlation functions in mixtures with energetically favoured nearest-neighbours of different kind: a size-asymmetric case