The Density Fingerprint of a Periodic Point Set



Edelsbrunner, Herbert, Heiss, Teresa, Kurlin, Vitaliy ORCID: 0000-0001-5328-5351, Smith, Philip and Wintraecken, Mathijs
(2021) The Density Fingerprint of a Periodic Point Set. In: 37th Symposium of Computational Geometry, 2021-6-7 - 2021-6-11, Buffalo.

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Abstract

Modeling a crystal as a periodic point set, we present a fingerprint consisting of density functions that facilitates the efficient search for new materials and material properties. We prove invariance under isometries, continuity, and completeness in the generic case, which are necessary features for the reliable comparison of crystals. The proof of continuity integrates methods from discrete geometry and lattice theory, while the proof of generic completeness combines techniques from geometry with analysis. The fingerprint has a fast algorithm based on Brillouin zones and related inclusion-exclusion formulae. We have implemented the algorithm and describe its application to crystal structure prediction.

Item Type: Conference or Workshop Item (Unspecified)
Additional Information: accepted for SoCG 2021
Uncontrolled Keywords: cs.CG, cs.CG, math.MG, 68U05, 51-08, 52-08, 51K99, 51E99
Divisions: Faculty of Science and Engineering > School of Electrical Engineering, Electronics and Computer Science
Depositing User: Symplectic Admin
Date Deposited: 26 Mar 2021 08:21
Last Modified: 18 Jan 2023 22:54
DOI: 10.4230/LIPIcs.SoCG.2021.32
Related URLs:
URI: https://livrepository.liverpool.ac.uk/id/eprint/3118160