Pair correlation function based on Voronoi topology

TL;DR

This paper introduces a discrete pair correlation function based on Voronoi topology that captures local structural differences in particle arrangements, providing more detailed insights than traditional averaged PCF.

Contribution

It presents a novel Voronoi topology-based discrete PCF that enhances the analysis of local particle arrangements in various physical systems.

Findings

Effective in distinguishing crystalline, hyperuniform, and active systems.

Highlights local topological configurations missed by traditional PCF.

Applicable to both simulated and experimental data.

Abstract

The pair correlation function (PCF) has proven an effective tool for analyzing many physical systems due to its simplicity and its applicability to simulated and experimental data. However, as an averaged quantity, the PCF can fail to capture subtle structural differences in particle arrangements, even when those differences can have a major impact on system properties. Here, we use Voronoi topology to introduce a discrete version of the PCF that highlights local inter-particle topological configurations. The advantages of the Voronoi PCF are demonstrated in several examples including crystalline, hyperuniform, and active systems showing clustering and giant number fluctuations.