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Multiresolution of quasicrystal diffraction spectra
Gazeau J.-P.
Acta Crystallographica Section A: Foundations of Crystallography 65 (2009) 466-489 - http://hal.in2p3.fr/in2p3-00185505
Physique/Physique des Hautes Energies - Théorie
Multiresolution of quasicrystal diffraction spectra
J.-P. Gazeau1
1 :  APC - UMR 7164 - AstroParticule et Cosmologie
http://www.apc.univ-paris7.fr/
CNRS : UMR7164 – IN2P3 – Observatoire de Paris – Université Paris VII - Paris Diderot – CEA : DSM/IRFU
APC - UMR 7164, Université Paris Diderot, 10 rue Alice Domon et Léonie Duquet, case postale 7020, F-75205 Paris Cedex 13
France
APC - THEORIE
Abstract: A method for analyzing and classifying two-dimensional pure point diffraction spectra (i.e. a set of Bragg peaks) of certain self-similar structures with scaling factor [beta] > 1, such as quasicrystals, is presented. The two-dimensional pure point diffraction spectrum [Pi] is viewed as a point set in the complex plane in which each point is assigned a positive number, its Bragg intensity. Then, by using a nested sequence of self-similar subsets called [beta]-lattices, we implement a multiresolution analysis of the spectrum [Pi]. This analysis yields a partition of [Pi] simultaneously in geometry, in scale and in intensity (the 'fingerprint' of the spectrum, not of the diffracting structure itself). The method is tested through numerical explorations of pure point diffraction spectra of various mathematical structures and also with the diffraction pattern of a realistic model of a quasicrystal.

Articles dans des revues avec comité de lecture
2009
Acta Crystallographica Section A: Foundations of Crystallography (Acta Crystallogr A)
Publisher International Union of Crystallography
ISSN 0108-7673 
65
466-489