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Diffraction of limit periodic point sets

Citation

Baake, M and Grimm, U, Diffraction of limit periodic point sets, Philosophical Magazine, 91, (19-21) pp. 2661-2670. ISSN 1478-6435 (2011) [Refereed Article]


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Copyright Statement

Copyright 2011 Taylor & Francis

DOI: doi:10.1080/14786435.2010.508447

Abstract

Limit periodic point sets are aperiodic structures with pure point diffraction supported on a countably, but not finitely generated Fourier module that is based on a lattice and certain integer multiples of it. Examples are cut and project sets with p-adic internal spaces. We illustrate this by explicit results for the diffraction measures of two examples with 2-adic internal spaces. The first and well-known example is the period doubling sequence in one dimension, which is based on the period doubling substitution rule. The second example is a weighted planar point set that is derived from the classic chair tiling in the plane. It can be described as a fixed point of a block substitution rule.

Item Details

Item Type:Refereed Article
Keywords:diffraction; autocorrelation; limit periodicity; substitution systems; integer inflation factors; pure point measures
Research Division:Mathematical Sciences
Research Group:Pure Mathematics
Research Field:Operator Algebras and Functional Analysis
Objective Division:Expanding Knowledge
Objective Group:Expanding Knowledge
Objective Field:Expanding Knowledge in the Mathematical Sciences
Author:Baake, M (Professor Michael Baake)
Author:Grimm, U (Professor Uwe Grimm)
ID Code:77997
Year Published:2011
Web of Science® Times Cited:7
Deposited By:Mathematics and Physics
Deposited On:2012-06-12
Last Modified:2017-03-16
Downloads:0

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