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Kraemer AS, Sanders DP. Embedding quasicrystals in a periodic cell: dynamics in quasiperiodic structures. Phys Rev Lett. 2013;111(12):125501doi: 10.1103/PhysRevLett.111.125501.
Kraemer, A. S., & Sanders, D. P. (2013). Embedding quasicrystals in a periodic cell: dynamics in quasiperiodic structures. Physical review letters, 111(12), 125501. https://doi.org/10.1103/PhysRevLett.111.125501
Kraemer, Atahualpa S, and Sanders, David P. "Embedding quasicrystals in a periodic cell: dynamics in quasiperiodic structures." Physical review letters vol. 111,12 (2013): 125501. doi: https://doi.org/10.1103/PhysRevLett.111.125501
Kraemer AS, Sanders DP. Embedding quasicrystals in a periodic cell: dynamics in quasiperiodic structures. Phys Rev Lett. 2013 Sep 20;111(12):125501. doi: 10.1103/PhysRevLett.111.125501. Epub 2013 Sep 18. PMID: 24093274.
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Phys Rev Lett. 2013 Sep 20;111(12):125501. doi: 10.1103/PhysRevLett.111.125501. Epub 2013 Sep 18.

Embedding quasicrystals in a periodic cell: dynamics in quasiperiodic structures.

Physical review letters

Atahualpa S Kraemer, David P Sanders

Affiliations

  1. Departamento de Física, Facultad de Ciencias, Universidad Nacional Autónoma de México, Ciudad Universitaria, México D.F. 04510, Mexico.

PMID: 24093274 DOI: 10.1103/PhysRevLett.111.125501

Abstract

We introduce a construction to "periodize" a quasiperiodic lattice of obstacles, i.e., embed it into a unit cell in a higher-dimensional space, reversing the projection method used to form quasilattices. This gives an algorithm for simulating dynamics, as well as a natural notion of uniform distribution, in quasiperiodic structures. It also shows the generic existence of channels, where particles travel without colliding, up to a critical obstacle radius, which we calculate for a Penrose tiling. As an application, we find superdiffusion in the presence of channels, and a subdiffusive regime when obstacles overlap.

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