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Diffraction of a model set with complex windows

Baake, Michael and Grimm, Uwe (2019). Diffraction of a model set with complex windows. Journal of Physics: Conference Series (In Press).

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Abstract

The well-known plastic number substitution gives rise to a ternary inflation tiling of the real line whose inflation factor is the smallest Pisot-Vijayaraghavan number. The corresponding dynamical system has pure point spectrum, and the associated control point sets can be described as regular model sets whose windows in two-dimensional internal space are Rauzy fractals with a complicated structure. Here, we calculate the resulting pure point diffraction measure via a Fourier matrix cocycle, which admits a closed formula for the Fourier transform of the Rauzy fractals, via a rapidly converging infinite product.

Item Type: Journal Item
ISSN: 1742-6596
Project Funding Details:
Funded Project NameProject IDFunding Body
Lyapunov Exponents and Spectral Properties of Aperiodic StructuresEP/S010335/1EPSRC (Engineering and Physical Sciences Research Council)
Academic Unit/School: Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics
Faculty of Science, Technology, Engineering and Mathematics (STEM)
Related URLs:
Item ID: 61757
Depositing User: Uwe Grimm
Date Deposited: 11 Jun 2019 13:01
Last Modified: 06 Sep 2019 19:52
URI: http://oro.open.ac.uk/id/eprint/61757
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