Baake, Michael and Grimm, Uwe
(2011).
*Zeitschrift für Kristallographie*, 226(9) pp. 711–725.

DOI (Digital Object Identifier) Link: | http://doi.org/10.1524/zkri.2011.1389 |
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Google Scholar: | Look up in Google Scholar |

## 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 |
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Copyright Holders: | 2011 Oldenbourg Wissenschaftsverlag |

ISSN: | 0044-2968 |

Keywords: | diffraction spectra; autocorrelation; fourier transform; homometry; entropy |

Academic Unit/Department: | Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics Faculty of Science, Technology, Engineering and Mathematics (STEM) |

Item ID: | 29673 |

Depositing User: | Uwe Grimm |

Date Deposited: | 06 Oct 2011 08:55 |

Last Modified: | 02 Aug 2016 14:05 |

URI: | http://oro.open.ac.uk/id/eprint/29673 |

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