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

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dc.creatorBaake, Michael
dc.creatorFrettlöh, Dirk
dc.creatorGrimm, Uwe
dc.date2006-10-12
dc.date.accessioned2026-07-07T07:43:18Z
dc.date.available2026-07-07T07:43:18Z
dc.descriptionDiffraction 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.
dc.description16 pages, 8 figures
dc.identifierhttps://arxiv.org/abs/math/0610408
dc.identifierhttp://arxiv.org/abs/math/0610408
dc.identifierJournal of Geometry and Physics 57 (2007) 1331-1343
dc.identifierdoi:10.1016/j.geomphys.2006.10.009
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/122773
dc.subjectSpectral Theory
dc.subjectMetric Geometry
dc.subject46F12, 78A45, 52C23
dc.titleA radial analogue of Poisson's summation formula with applications to powder diffraction and pinwheel patterns
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