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A Brief History of Aperiodic Crystals: 1962–2012 Read chapter Read first chapter

2013 | OriginalPaper | Chapter

5. Some Comments on the Inverse Problem of Pure Point Diffraction

Authors : Venta Terauds, Michael Baake

Published in: Aperiodic Crystals

Publisher: Springer Netherlands

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Abstract

In a recent paper arXiv:​1111.​3617, Lenz and Moody presented a method for constructing families of real solutions to the inverse problem for a given pure point diffraction measure. Applying their technique and discussing some possible extensions, we present, in a non-technical manner, some examples of homometric structures.

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previous chapter Magic Numbers in the Discrete Tomography of Cyclotomic Model Sets
next chapter Well-Rounded Sublattices and Coincidence Site Lattices
Literature
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Grimm U, Baake M (2008) Homometric point sets and inverse problems. Z Kristallogr 223:777–781 CrossRef
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Grünbaum FA, Moore CC (1995) The use of higher-order invariants in the determination of generalized Patterson cyclotomic sets. Acta Crystallogr, Ser A 51:310–323 CrossRef
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Hof A (1995) On diffraction by aperiodic structures. Commun Math Phys 169:25–43 CrossRef
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Hof A (1995) Diffraction by aperiodic structures. In: Moody RV (ed) The mathematics of long-range aperiodic order. NATO ASI series C, vol 489. Kluwer, Dordrecht, pp 239–268
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Terauds V (2013) The inverse problem of pure point diffraction—examples and open questions, in preparation
Metadata
Title
Some Comments on the Inverse Problem of Pure Point Diffraction
Authors
Venta Terauds
Michael Baake
Copyright Year
2013
Publisher
Springer Netherlands
Book
Aperiodic Crystals

Print ISBN: 978-94-007-6430-9

Electronic ISBN: 978-94-007-6431-6

Copyright Year: 2013

DOI
https://doi.org/10.1007/978-94-007-6431-6_5

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