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Kinematic diffraction from a mathematical viewpoint

Baake, Michael and Grimm, Uwe (2011). Kinematic diffraction from a mathematical viewpoint. Zeitschrift für Kristallographie, 226(9) pp. 711–725.

DOI (Digital Object Identifier) Link: http://dx.doi.org/10.1524/zkri.2011.1389
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Abstract

Mathematical diffraction theory is concerned with the analysis of the diffraction image of a given structure and the corresponding inverse problem of structure determination. In recent years, the understanding of systems with continuous and mixed spectra has improved considerably. Simultaneously, their relevance has grown in practice as well. In this context, the phenomenon of homometry shows various unexpected new facets. This is particularly so for systems with stochastic components.
After an introduction to the mathematical tools, we briefly discuss pure point spectra, based on the Poisson summation formula for lattice Dirac combs. This provides an elegant approach to the diffraction formulas of infinite crystals and quasicrystals. We continue by considering classic deterministic examples with singular or absolutely continuous diffraction spectra. In particular, we recall an isospectral family of structures with continuously varying entropy. We close with a summary of more recent results on the diffraction of dynamical systems of algebraic or stochastic origin.

Item Type: Journal Article
Copyright Holders: 2011 Oldenbourg Wissenschaftsverlag
ISSN: 0044-2968
Keywords: diffraction spectra; autocorrelation; fourier transform; homometry; entropy
Academic Unit/Department: Mathematics, Computing and Technology > Mathematics and Statistics
Item ID: 29673
Depositing User: Uwe Grimm
Date Deposited: 06 Oct 2011 08:55
Last Modified: 30 Nov 2012 16:52
URI: http://oro.open.ac.uk/id/eprint/29673
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