Quasi-periodic Tiling with Multiplicity: A Lattice Enumeration Approach
نویسندگان
چکیده
منابع مشابه
Quasi-periodic Tiling with Multiplicity: A Lattice Enumeration Approach
The k-tiling problem is the problem of covering R with translates of a convex polytope P using a discrete multiset Λ of translation vectors. Thus, every point in R is covered exactly k times, except possibly for the boundary of P and its translates. In this paper, we study the k-tiling problem when the tiling set Λ is a finite union of translated lattices. This is motivated by the work of Kolou...
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Recently, a tiling derived from the well-known 2D quasi-periodic octagonal tiling has been introduced. In this letter, we show that in the framework of a tight-binding model, the electronic spectrum of this nontrivial tiling can be derived. The integrated density of state is singular and can be a devil staircase, there can be a finite or infinite number of gaps, whereas the measure of the spect...
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ژورنال
عنوان ژورنال: Discrete & Computational Geometry
سال: 2015
ISSN: 0179-5376,1432-0444
DOI: 10.1007/s00454-015-9713-y