Inflation versus projection sets in aperiodic systems: the role of the window in averaging and diffraction

Baake M, Grimm U (2020)
Acta crystallographica. Section A, Foundations and advances 76( 5): 559-570.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Baake, MichaelUniBi; Grimm, Uwe
Abstract / Bemerkung
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. open access.
Erscheinungsjahr
2020
Zeitschriftentitel
Acta crystallographica. Section A, Foundations and advances
Band
76
Ausgabe
5
Seite(n)
559-570
ISSN
2053-2733
Page URI
https://pub.uni-bielefeld.de/record/2945768

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Baake M, Grimm U. Inflation versus projection sets in aperiodic systems: the role of the window in averaging and diffraction. Acta crystallographica. Section A, Foundations and advances. 2020;76( 5):559-570.
Baake, M., & Grimm, U. (2020). Inflation versus projection sets in aperiodic systems: the role of the window in averaging and diffraction. Acta crystallographica. Section A, Foundations and advances, 76( 5), 559-570. doi:10.1107/S2053273320007421
Baake, M., and Grimm, U. (2020). Inflation versus projection sets in aperiodic systems: the role of the window in averaging and diffraction. Acta crystallographica. Section A, Foundations and advances 76, 559-570.
Baake, M., & Grimm, U., 2020. Inflation versus projection sets in aperiodic systems: the role of the window in averaging and diffraction. Acta crystallographica. Section A, Foundations and advances, 76( 5), p 559-570.
M. Baake and U. Grimm, “Inflation versus projection sets in aperiodic systems: the role of the window in averaging and diffraction”, Acta crystallographica. Section A, Foundations and advances, vol. 76, 2020, pp. 559-570.
Baake, M., Grimm, U.: Inflation versus projection sets in aperiodic systems: the role of the window in averaging and diffraction. Acta crystallographica. Section A, Foundations and advances. 76, 559-570 (2020).
Baake, Michael, and Grimm, Uwe. “Inflation versus projection sets in aperiodic systems: the role of the window in averaging and diffraction”. Acta crystallographica. Section A, Foundations and advances 76. 5 (2020): 559-570.
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2020-10-29T20:00:00Z

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