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math.MG2025
Continuous invariant-based asymmetries of periodic crystals quantify deviations from higher symmetry
Surya Majumder, Daniel Widdowson, Yury Elkin +4
Ideal symmetry is known to break down under almost any noise. One measure of asymmetry in a periodic crystal is the relative multiplicity Z' of geometrically non-equivalent units.…
math.MG2022★ 8 cited
Recognition of near-duplicate periodic patterns by continuous metrics with approximation guarantees
Olga Anosova, Daniel Widdowson, Vitaliy Kurlin
This paper rigorously solves the challenging problem of recognizing periodic patterns under rigid motion in Euclidean geometry. The 3-dimensional case is practically important for…