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Robust minimal matching rules for quasicrystals
Author(s) -
Kalugin Pavel,
Katz André
Publication year - 2019
Publication title -
acta crystallographica section a
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.742
H-Index - 83
ISSN - 2053-2733
DOI - 10.1107/s2053273319008180
Subject(s) - quasicrystal , quasiperiodic function , matching (statistics) , set (abstract data type) , computer science , pattern matching , diffraction , data mining , algorithm , mathematics , physics , artificial intelligence , geometry , optics , mathematical analysis , programming language , statistics
A unified framework is proposed for dealing with matching rules of quasiperiodic patterns, relevant for both tiling models and real‐world quasicrystals. The approach is intended for extraction and validation of a minimal set of matching rules, directly from the phased diffraction data. The construction yields precise values for the spatial density of distinct atomic positions and tolerates the presence of defects in a robust way.