Baake, Michael; Frettlöh, Dirk and Grimm, Uwe
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|DOI (Digital Object Identifier) Link:||https://doi.org/10.1016/j.geomphys.2006.10.009|
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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|
|Keywords:||Poissonï¿½s summation formula; circular symmetry; powder diffraction; pinwheel patterns|
|Academic Unit/School:||Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics
Faculty of Science, Technology, Engineering and Mathematics (STEM)
|Depositing User:||Uwe Grimm|
|Date Deposited:||02 Feb 2007|
|Last Modified:||01 Dec 2016 04:37|
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