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Disordered hyperuniform systems exhibit unique properties. This study quantifies structural differences in Voronoi networks, revealing that cell-area distributions and correlations can distinguish hyperuniform, nonhyperuniform, and antihyperuniform networks.

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Area of Science:

  • Physics
  • Materials Science
  • Statistical Mechanics

Background:

  • Disordered hyperuniform systems are exotic states of matter with suppressed density fluctuations but no long-range order.
  • Characterizing these systems is crucial for understanding their unique physical properties.
  • Voronoi networks offer a framework to analyze the structure of such systems.

Purpose of the Study:

  • To quantify and compare the structural properties of various nonhyperuniform and hyperuniform networks.
  • To investigate the utility of Voronoi cell-area distributions and correlation functions in distinguishing different network types.
  • To establish a quantitative method for classifying hyperuniformity in disordered systems.

Main Methods:

  • Generation of large 2D Voronoi networks (approx. 10,000 nodes) from diverse point processes: antihyperuniform HIP, nonhyperuniform Poisson and RSA, and hyperuniform (stealthy and non-stealthy).
  • Analysis of Voronoi-cell area distributions using metrics like mean, variance, skewness (γ1), and excess kurtosis (γ2).
  • Computation of Voronoi-area correlation functions C00(r) to assess spatial correlations.

Main Results:

  • Voronoi-cell area distributions varied significantly across network types, with HIP showing high skewness and kurtosis, Poisson and non-stealthy hyperuniform being Gaussian-like, and RSA and stealthy hyperuniform exhibiting negative excess kurtosis.
  • Voronoi-area correlation functions (C00(r)) effectively distinguished network types: HIP showed slow decay, Poisson/RSA had fast positive decay, and hyperuniform networks displayed strong anticorrelations (negative C00(r)).
  • Suppressed large-scale area fluctuations, indicated by negative C00(r), were confirmed as a hallmark of hyperuniformity.

Conclusions:

  • Voronoi-cell area distributions and their statistical moments provide distinct signatures for antihyperuniform, nonhyperuniform, and hyperuniform networks.
  • The Voronoi-area correlation function C00(r) serves as a robust quantitative indicator to differentiate these network classes.
  • These findings offer a pathway to quantitatively identify and characterize hyperuniformity in disordered many-particle systems.