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Hyperuniformity on spherical surfaces.

Ariel G Meyra1,2, Guillermo J Zarragoicoechea1,3, Alberto L Maltz4

  • 1IFLYSIB (UNLP, CONICET), 59 No. 789, B1900BTE La Plata, Argentina.

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Summary
This summary is machine-generated.

This study characterizes hyperuniform point distributions on spherical surfaces. Analyzing local density fluctuations reveals how window size helps identify hyperuniform patterns in curved spaces.

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Area of Science:

  • Statistical Physics
  • Materials Science
  • Geometry

Background:

  • Hyperuniformity describes materials with suppressed large-scale density fluctuations.
  • Most research focuses on Euclidean spaces, neglecting curved surfaces.
  • Real-world systems like avian retina photoreceptors exist on curved surfaces.

Purpose of the Study:

  • To characterize hyperuniform point distributions on spherical surfaces.
  • To extend hyperuniformity studies to curved geometries.
  • To investigate density fluctuations in ordered and disordered systems on spheres.

Main Methods:

  • Analyzing local particle number variance within spherical caps.
  • Examining regular, uniform, and fluid particle distributions.
  • Investigating interactions via Lennard-Jones, dipole-dipole, and charge-charge potentials.

Main Results:

  • The scaling of local number variance with window size effectively characterizes hyperuniformity.
  • Demonstrated applicability to various point distributions on spherical surfaces.
  • Established a method for identifying hyperuniformity in curved spaces.

Conclusions:

  • Local density fluctuations can characterize hyperuniformity on spherical surfaces.
  • This work bridges the gap between Euclidean and curved space hyperuniformity.
  • Provides a framework for studying hyperuniform systems in non-Euclidean geometries.