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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.
Physical Review. E
|October 3, 2019
Summary
This study characterizes hyperuniform point distributions on spherical surfaces. Analyzing local density fluctuations reveals how window size helps identify hyperuniform patterns in curved spaces.
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.
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