License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.SoCG.2021.32
URN: urn:nbn:de:0030-drops-138310
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2021/13831/
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Edelsbrunner, Herbert ; Heiss, Teresa ; Kurlin, Vitaliy ; Smith, Philip ; Wintraecken, Mathijs

The Density Fingerprint of a Periodic Point Set

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LIPIcs-SoCG-2021-32.pdf (3 MB)

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.

BibTeX - Entry

@InProceedings{edelsbrunner_et_al:LIPIcs.SoCG.2021.32,
  author =	{Edelsbrunner, Herbert and Heiss, Teresa and Kurlin, Vitaliy and Smith, Philip and Wintraecken, Mathijs},
  title =	{{The Density Fingerprint of a Periodic Point Set}},
  booktitle =	{37th International Symposium on Computational Geometry (SoCG 2021)},
  pages =	{32:1--32:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-184-9},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{189},
  editor =	{Buchin, Kevin and Colin de Verdi\`{e}re, \'{E}ric},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2021/13831},
  URN =		{urn:nbn:de:0030-drops-138310},
  doi =		{10.4230/LIPIcs.SoCG.2021.32},
  annote =	{Keywords: Lattices, periodic sets, isometries, Dirichlet-Voronoi domains, Brillouin zones, bottleneck distance, stability, continuity, crystal database}
}

Keywords: Lattices, periodic sets, isometries, Dirichlet-Voronoi domains, Brillouin zones, bottleneck distance, stability, continuity, crystal database
Collection: 37th International Symposium on Computational Geometry (SoCG 2021)
Issue Date: 2021
Date of publication: 02.06.2021

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