A radial analogue of Poisson's summation formula with applications to powder diffraction and pinwheel patterns

Baake M, Frettlöh D, Grimm U (2007)
JOURNAL OF GEOMETRY AND PHYSICS 57(5): 1331-1343.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Abstract / Bemerkung
Diffraction images with continuous rotation symmetry arise from amorphous systems, but also from regular crystals when investigated by powder diffraction. On the theoretical side, pinwheel patterns and their higher dimensional generalisations display such symmetries as well, in spite of being perfectly ordered. We present first steps and results towards a general frame to investigate such systems, with emphasis on statistical properties that are helpful to understand and compare the diffraction images. An alternative substitution rule for the pinwheel tiling, with two different prototiles, permits the derivation of several combinatorial and spectral properties of this still somewhat enigmatic example. These results are compared with properties of the square lattice and its powder diffraction. (c) 2006 Michael Baake. Published by Elsevier B.V. All rights reserved.
Stichworte
powder diffraction; pinwheel patterns; Poisson's summation formula; circular symmetry
Erscheinungsjahr
2007
Zeitschriftentitel
JOURNAL OF GEOMETRY AND PHYSICS
Band
57
Ausgabe
5
Seite(n)
1331-1343
ISSN
0393-0440
Page URI
https://pub.uni-bielefeld.de/record/1595778

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Baake M, Frettlöh D, Grimm U. A radial analogue of Poisson's summation formula with applications to powder diffraction and pinwheel patterns. JOURNAL OF GEOMETRY AND PHYSICS. 2007;57(5):1331-1343.
Baake, M., Frettlöh, D., & Grimm, U. (2007). A radial analogue of Poisson's summation formula with applications to powder diffraction and pinwheel patterns. JOURNAL OF GEOMETRY AND PHYSICS, 57(5), 1331-1343. https://doi.org/10.1016/j.geomphys.2006.10.009
Baake, M., Frettlöh, D., and Grimm, U. (2007). A radial analogue of Poisson's summation formula with applications to powder diffraction and pinwheel patterns. JOURNAL OF GEOMETRY AND PHYSICS 57, 1331-1343.
Baake, M., Frettlöh, D., & Grimm, U., 2007. A radial analogue of Poisson's summation formula with applications to powder diffraction and pinwheel patterns. JOURNAL OF GEOMETRY AND PHYSICS, 57(5), p 1331-1343.
M. Baake, D. Frettlöh, and U. Grimm, “A radial analogue of Poisson's summation formula with applications to powder diffraction and pinwheel patterns”, JOURNAL OF GEOMETRY AND PHYSICS, vol. 57, 2007, pp. 1331-1343.
Baake, M., Frettlöh, D., Grimm, U.: A radial analogue of Poisson's summation formula with applications to powder diffraction and pinwheel patterns. JOURNAL OF GEOMETRY AND PHYSICS. 57, 1331-1343 (2007).
Baake, Michael, Frettlöh, Dirk, and Grimm, Uwe. “A radial analogue of Poisson's summation formula with applications to powder diffraction and pinwheel patterns”. JOURNAL OF GEOMETRY AND PHYSICS 57.5 (2007): 1331-1343.

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