Average minimum distances of periodic point sets – foundational invariants for mapping periodic crystals

نویسندگان

چکیده

The fundamental model of any solid crystalline material (crystal) at the atomic scale is a periodic point set. strongest natural equivalence crystals rigid motion or isometry that preserves all inter-atomic distances. Past comparisons structures often used manual thresholds, symmetry groups and reduced cells, which are discontinuous under perturbations thermal vibrations atoms. This work defines infinite sequence continuous invariants (Average Minimum Distances) to progressively capture distances between neighbors. asymptotic behaviour new theoretically proved in dimensions for wide class sets including non-periodic. proposed near linear time algorithm identified different world's largest Cambridge Structural Database within few hours on modest desktop. ultra fast speed continuity provide rigorous foundations continuously parameterise space as high-dimensional extension Mendeleev's table elements.

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ژورنال

عنوان ژورنال: Match

سال: 2021

ISSN: ['0340-6253']

DOI: https://doi.org/10.46793/match.87-3.529w