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Characterizing pixel and point patterns with a hyperuniformity disorder length.

A T Chieco1, R Dreyfus2, D J Durian1

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Summary
This summary is machine-generated.

We introduce a new metric, the hyperuniformity disorder length (h), to quantify density fluctuations in particle systems. This length (h) measures particle distribution within a window, offering a novel way to characterize disorder.

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Area of Science:

  • Statistical Mechanics
  • Materials Science
  • Computational Physics

Background:

  • Characterizing disorder in particle systems is crucial for understanding material properties.
  • Traditional methods often rely on spectral analysis of density fluctuations.
  • A new real-space metric is needed to complement existing techniques.

Purpose of the Study:

  • Introduce and define the hyperuniformity disorder length (h) as a new metric for quantifying disorder.
  • Investigate the behavior of h in various simulated 2D particle patterns.
  • Propose a new spectroscopic approach based on h(L) versus L.

Main Methods:

  • Simulated 2D pixel patterns representing different particle configurations (binomial, vacancy, Einstein).
  • Calculation of the hyperuniformity disorder length (h) based on particle distribution near window boundaries.
  • Analysis of h(L) behavior across different window sizes (L) and particle densities.

Main Results:

  • Exact result h=L/2 for binomial patterns with long-range fluctuations.
  • Vacancy patterns show h dependent on fraction of removed particles (f) and dimensions (d).
  • Einstein patterns exhibit a constant h at large L, related to particle displacement.

Conclusions:

  • The hyperuniformity disorder length (h) effectively quantifies disorder in particle systems.
  • The proposed 'hyperuniformity disorder length spectroscopy' offers a complementary real-space analysis method.
  • This approach provides new insights into the structure and properties of disordered materials.