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

Baake, Michael; Frettlöh, Dirk and Grimm, Uwe (2007). A radial analogue of Poisson's summation formula with applications to powder diffraction and pinwheel patterns. Journal of Geometry and Physics, 57(5) pp. 1331–1343.

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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.

Item Type: Journal Article
ISSN: 0393-0440
Keywords: Poisson�s summation formula; circular symmetry; powder diffraction; pinwheel patterns
Academic Unit/Department: Mathematics, Computing and Technology > Mathematics and Statistics
Mathematics, Computing and Technology
Item ID: 6610
Depositing User: Uwe Grimm
Date Deposited: 02 Feb 2007
Last Modified: 24 Feb 2016 08:10
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