Solid-Angle Nearest-Neighbor Method for Size-Disperse Systems of Spheres

TL;DR

This paper introduces SANNR, an improved solid-angle neighbor detection method that accurately identifies neighbors in size-disperse particle systems, outperforming existing methods in complex mixtures and phase analysis.

Contribution

SANNR extends the SANN algorithm by incorporating particle radii, enabling robust neighbor detection in size-disperse systems, with demonstrated advantages over Voronoi, Laguerre, and SANN methods.

Findings

SANNR closely matches Laguerre tessellation in size-sensitive neighbor detection.

SANNR improves local order detection in crystallization simulations.

SANNR maintains geometric continuity while incorporating size information.

Abstract

Identifying nearest neighbors accurately is essential in particle-based simulations, from analyzing local structure to detecting phase transitions. While parameter-free methods such as Voronoi tessellation and the solid-angle nearest-neighbor (SANN) algorithm are effective in monodisperse systems, they become less reliable in mixtures with large size disparities. We introduce SANNR, a generalization of SANN that incorporates particle radii into the solid-angle criterion for robust, size-sensitive neighbor detection. We compare SANNR against Voronoi, Laguerre, and SANN in binary and size-disperse sphere mixtures. Using Wasserstein distance metrics, we show that SANNR closely matches size-aware Laguerre tessellation while preserving the geometric continuity of SANN. Applied to the crystallization of the complex AB$_{13}$ phase, SANNR improves detection of local bond-orientational order and better captures the emergence of global symmetry. SANNR thus offers a smooth, parameter-free, and extensible framework for neighbor detection in polydisperse and multicomponent systems.