Search Results

Documents authored by Heiss, Teresa

Document
DOI: 10.4230/LIPIcs.SoCG.2021.32
The Density Fingerprint of a Periodic Point Set

Authors: Herbert Edelsbrunner, Teresa Heiss, Vitaliy Kurlin, Philip Smith, and Mathijs Wintraecken

Published in: LIPIcs, Volume 189, 37th International Symposium on Computational Geometry (SoCG 2021)

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.
Cite as

Herbert Edelsbrunner, Teresa Heiss, Vitaliy Kurlin, Philip Smith, and Mathijs Wintraecken. The Density Fingerprint of a Periodic Point Set. In 37th International Symposium on Computational Geometry (SoCG 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 189, pp. 32:1-32:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

Copy BibTex To Clipboard

@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-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2021.32},
  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}
}
Questions / Remarks / Feedback
X

Feedback for Dagstuhl Publishing


Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail
© 2023-2024 Schloss Dagstuhl – LZI GmbH Imprint Privacy Contact