Solid-Angle Nearest-Neighbor Method for Size-Disperse Systems of Spheres
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| Format: | Preprint |
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2025
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| _version_ | 1866913993218588672 |
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| author | Varela-Rosales, Nydia Roxana Engel, Michael |
| author_facet | Varela-Rosales, Nydia Roxana Engel, Michael |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2508_11220 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Solid-Angle Nearest-Neighbor Method for Size-Disperse Systems of Spheres Varela-Rosales, Nydia Roxana Engel, Michael Soft Condensed Matter Computational Physics 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. |
| title | Solid-Angle Nearest-Neighbor Method for Size-Disperse Systems of Spheres |
| topic | Soft Condensed Matter Computational Physics |
| url | https://arxiv.org/abs/2508.11220 |