On the origin of crystallinity: a lower bound for the regularity radius of Delone sets.

  title={On the origin of crystallinity: a lower bound for the regularity radius of Delone sets.},
  author={Igor A. Baburin and Mikhail Bouniaev and Nikolay P. Dolbilin and Nikolay Erokhovets and Alexey Garber and Sergey V. Krivovichev and Egon Schulte},
  journal={Acta crystallographica. Section A, Foundations and advances},
  volume={74 Pt 6},
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… 

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