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arXiv · 1907.07017

Modulated crystals and almost periodic measures

Jeong-Yup Lee·Daniel Lenz·Christoph Richard·Bernd Sing·Nicolae Strungaru
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Abstract

Modulated crystals and quasicrystals can simultaneously be described as modulated quasicrystals, a class of point sets introduced by de Bruijn in 1987. With appropriate modulation functions, modulated quasicrystals themselves constitute a substantial subclass of strongly almost periodic point measures. We re-analyse these structures using methods from modern mathematical diffraction theory, thereby providing a coherent view over that class. Similarly to de Bruijn's analysis, we find stability with respect to almost periodic modulations.

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Jeong-Yup Lee, Daniel Lenz, Christoph Richard, Bernd Sing, Nicolae Strungaru. 2019-07-16. Modulated crystals and almost periodic measures. https://doi.org/10.1007/s11005-020-01337-2

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