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This study generalizes hyperuniformity disorder length to analyze extended particles, connecting particle shape and arrangement to spatial disorder. The findings enable precise quantification of hyperuniformity across various systems.

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Area of Science:

  • Statistical Physics
  • Materials Science
  • Computational Physics

Background:

  • Hyperuniformity quantifies deviations from typical disordered systems.
  • The hyperuniformity disorder length (h) analyzes volume fraction fluctuations in particle systems.
  • Existing methods are limited to point-like particles or specific measurement windows.

Purpose of the Study:

  • Generalize the hyperuniformity disorder length concept for extended particles.
  • Develop computational methods for analyzing spatial disorder in complex particle systems.
  • Establish a framework to quantify hyperuniformity based on particle shape and arrangement.

Main Methods:

  • Derived an expression for relative volume fraction variance considering particle and window volumes, and their overlap.
  • Developed computational methods for continuum and pixelated extended particles.
  • Analyzed exact results for special shapes and simulated Poisson patterns for other shapes.

Main Results:

  • Showed that for small windows, both particle shape and arrangement influence variance; for large windows, arrangement dominates scaling while shape sets proportionality.
  • Demonstrated translation of measured variance to hyperuniformity length spectra versus region size.
  • Validated the approach for non-overlapping particles and Einstein patterns with extended shapes.

Conclusions:

  • The generalized hyperuniformity disorder length provides a robust tool for characterizing spatial disorder in systems with extended particles.
  • This framework allows for a nuanced understanding of how particle geometry and arrangement collectively dictate system-level hyperuniformity.
  • The developed methods are applicable to diverse physical systems, from granular materials to soft matter, aiding in material design and analysis.