The Density Fingerprint of a Periodic Point Set. arXiv:2104.11046
Preprint, arXiv:2104.11046 [cs.CG] (2021).
Summary: 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.
MSC:
| 68U05 | Computer graphics; computational geometry (digital and algorithmic aspects) |
| 51-08 | Computational methods for problems pertaining to geometry |
| 52-08 | Computational methods for problems pertaining to convex and discrete geometry |
| 51K99 | Distance geometry |
| 51E99 | Finite geometry and special incidence structures |
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