Baake, Michael; Frettlöh, Dirk and Grimm, Uwe
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|DOI (Digital Object Identifier) Link:||https://doi.org/10.1080/14786430601057953|
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Pinwheel patterns and their higher dimensional generalizations display continuous circular or spherical symmetries in spite of being perfectly ordered. The same symmetries show up in the corresponding diffraction images. Interestingly, they also arise from amorphous systems, and also from regular crystals when investigated by powder diffraction. We present first steps and results towards a general framework to investigate such systems, with emphasis on statistical properties that are helpful to understand and compare the diffraction images. We concentrate on properties that are accessible via an alternative substitution rule for the pinwheel tiling, based on two different prototiles. Due to striking similarities, we compare our results with a toy model for the powder diffraction of the square lattice.
|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:||22 Jun 2007|
|Last Modified:||29 Nov 2016 19:21|
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