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Pair correlation function based on Voronoi topology.

Vasco M Worlitzer1, Gil Ariel1, Emanuel A Lazar1

  • 1Department of Mathematics, Bar Ilan University, Ramat Gan 5290002, Israel.

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|January 20, 2024
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Summary
This summary is machine-generated.

This study introduces a discrete Voronoi pair correlation function (PCF) to reveal local particle arrangements missed by the standard averaged PCF. This new method enhances structural analysis in diverse physical systems.

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Area of Science:

  • Statistical Mechanics
  • Materials Science
  • Complex Systems

Background:

  • The pair correlation function (PCF) is a standard tool for analyzing particle systems.
  • However, the averaged nature of the PCF can obscure critical local structural details.
  • These hidden details can significantly influence macroscopic system properties.

Purpose of the Study:

  • To develop a discrete version of the PCF that captures local topological configurations.
  • To overcome the limitations of the traditional averaged PCF in discerning subtle structural differences.
  • To provide a more sensitive method for analyzing particle arrangements in various physical systems.

Main Methods:

  • Utilizing Voronoi topology to define local interparticle relationships.
  • Developing a discrete pair correlation function based on Voronoi tessellations.
  • Applying the Voronoi PCF to analyze crystalline, hyperuniform, and active systems.

Main Results:

  • The Voronoi PCF effectively highlights local interparticle topological configurations.
  • Demonstrated sensitivity to structural differences in crystalline and hyperuniform systems.
  • Revealed clustering and giant number fluctuations in active systems.

Conclusions:

  • The discrete Voronoi PCF offers a powerful alternative to the traditional PCF for detailed structural analysis.
  • This method enhances the understanding of complex physical systems by revealing hidden local order.
  • The Voronoi PCF is applicable to a wide range of simulated and experimental data.