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Baake, Michael and Grimm, Uwe
(2020).
DOI: https://doi.org/10.1107/S2053273320007421
Abstract
Tilings based on the cut-and-project method are key model systems for the description of aperiodic solids. Typically, quantities of interest in crystallography involve averaging over large patches, and are well defined only in the infinite-volume limit. In particular, this is the case for autocorrelation and diffraction measures. For cut-and-project systems, the averaging can conveniently be transferred to internal space, which means dealing with the corresponding windows. In this topical review, this is illustrated by the example of averaged shelling numbers for the Fibonacci tiling, and the standard approach to the diffraction for this example is recapitulated. Further, recent developments are discussed for cut-and-project structures with an inflation symmetry, which are based on an internal counterpart of the renormalization cocycle. Finally, a brief review is given of the notion of hyperuniformity, which has recently gained popularity, and its application to aperiodic structures.
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About
- Item ORO ID
- 71195
- Item Type
- Journal Item
- ISSN
- 2053-2733
- Project Funding Details
-
Funded Project Name Project ID Funding Body Lyapunov Exponents and Spectral Properties of Aperiodic Structures EP/S010335/1 EPSRC - Keywords
- quasicrystals; projection method; inflation rules; diffraction; hyperuniformity
- Academic Unit or School
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Faculty of Science, Technology, Engineering and Mathematics (STEM)
Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics - Copyright Holders
- © 2020 Michael Baake, © 2020 Uwe Grimm
- Related URLs
- Depositing User
- Uwe Grimm