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On The Origin Of Crystallinity: A Lower Bound For The Regularity Radius Of Delone Sets, Igor A. Baburin, Mikhail M. Bouniaev, Nikolay Dolbilin, Nikolay Yu. Erokhovets, Alexey Garber, Sergey V. Krivovichev, Egon Schulte
On The Origin Of Crystallinity: A Lower Bound For The Regularity Radius Of Delone Sets, Igor A. Baburin, Mikhail M. Bouniaev, Nikolay Dolbilin, Nikolay Yu. Erokhovets, Alexey Garber, Sergey V. Krivovichev, Egon Schulte
School of Mathematical and Statistical Sciences Faculty Publications and Presentations
The mathematical conditions for the origin of long-range order or crystallinity in ideal crystals are one of the very fundamental problems of modern crystallography. It is widely believed that the (global) regularity of crystals is a consequence of `local order', in particular the repetition of local fragments, but the exact mathematical theory of this phenomenon is poorly known. In particular, most mathematical models for quasicrystals, for example Penrose tiling, have repetitive local fragments, but are not (globally) regular. The universal abstract models of any atomic arrangements are Delone sets, which are uniformly distributed discrete point sets in Euclidean d space. …