Results 11 to 20 of about 688,997 (292)
Gap structure of 1D cut and project Hamiltonians
Journal of Physics: Conference Series, 2017 We study the gap properties of nearest neighbors tight binding models on quasiperiodic chains. We argue that two kind of gaps should be distinguished: stable and transient. We show that stable gaps have a well defined quasiperiodic limit. We also show that there is a direct relation between the gap size and the gap label.
Jagannathan, Anuradha +2 more
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Equivalence classes of codimension-one cut-and-project nets [PDF]
Ergodic Theory and Dynamical Systems, 2014 We prove that in any totally irrational cut-and-project setup with codimension (internal space dimension) one, it is possible to choose sections (windows) in non-trivial ways so that the resulting sets are bounded displacement equivalent to lattices. Our proof demonstrates that for any irrational ${\it\alpha}$, regardless of Diophantine type, there is ...
Haynes, Alan
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ON SELF-SIMILARITIES OF CUT-AND-PROJECT SETS
Acta Polytechnica, 2017 Among the commonly used mathematical models of quasicrystals are Delone sets constructed using a cut-and-project scheme, the so-called cut-and-project sets.
Zuzana Masáková, Jan Mazáč
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On Helly Numbers for Crystals and Cut-And-Project Sets
Studia Scientiarum Mathematicarum Hungarica, 2017 We prove existence of Helly numbers for crystals and for cut-and-project sets with convex windows. Also we show that for a two-dimensional crystal consisting of 𝑘 copies of a single lattice the Helly number does not exceed 𝑘 + 6.
Garber, Alexey
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Pure point diffraction and cut and project schemes for measures: the smooth case
Mathematische Zeitschrift, 2006 30 ...
Lenz, Daniel, Richard, Christoph
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Image Sampling with Quasicrystals [PDF]
Symmetry, Integrability and Geometry: Methods and Applications, 2009 We investigate the use of quasicrystals in image sampling. Quasicrystals produce space-filling, non-periodic point sets that are uniformly discrete and relatively dense, thereby ensuring the sample sites are evenly spread out throughout the sampled image.
Mark Grundland +3 more
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Cut‐and‐project quasicrystals, lattices and dense forests [PDF]
Journal of the London Mathematical Society, 2022 This version includes a picture provided by the referee and a subsection relating the theory developed in this paper to the properties of twisted bilayer graphene in ...
Adiceam, Faustin +2 more
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Symplectic Cuts and Projection Quantization [PDF]
International Journal of Modern Physics D, 1999 The recently proposed projection quantization, which is a method to quantize particular subspaces of systems with known quantum theory, is shown to yield a genuine quantization in several cases. This may be inferred from exact results established within symplectic cutting.
Bojowald, Martin, Strobl, Thomas
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Cut and project sets with polytopal window II: linear repetitivity [PDF]
Transactions of the American Mathematical Society, 2022 In this paper we give a complete characterisation of linear repetitivity for cut and project schemes with convex polytopal windows satisfying a weak homogeneity condition. This answers a question of Lagarias and Pleasants from the 90s for a natural class of cut and project schemes which is large enough to cover almost all such polytopal schemes which ...
Koivusalo, Henna L L, Walton, Jamie
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Cut and project sets with polytopal window I: Complexity [PDF]
Ergodic Theory and Dynamical Systems, 2020 We calculate the growth rate of the complexity function for polytopal cut and project sets. This generalizes work of Julien where the almost canonical condition is assumed. The analysis of polytopal cut and project sets has often relied on being able to replace acceptance domains of patterns by so-called cut regions. Our results correct mistakes in the
HENNA KOIVUSALO, JAMES J. WALTON
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