Results 11 to 20 of about 612,349 (305)
ON SELF-SIMILARITIES OF CUT-AND-PROJECT SETS [PDF]
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
doaj +3 more sources
Gap structure of 1D cut and project Hamiltonians [PDF]
Journal of Physics: Conference Series, 2016 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.
Jagannathan, Anuradha +2 more
core +4 more sources
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 to lattices.
Haynes, Alan
core +4 more sources
On Helly number for crystals and cut-and-project sets
Studia Scientiarum Mathematicarum Hungarica, 2017 We prove existence of finite Helly numbers for crystals and for cut-and-project sets with convex windows; also we prove exact bound of $k+6$ for the Helly number of a crystal consisting of $k$ copies of a single lattice.
Garber, Alexey
core +2 more sources
A short guide to pure point diffraction in cut-and-project sets [PDF]
Journal of Physics A: Mathematical and Theoretical, 2017 We briefly review the diffraction of quasicrystals and then give an elementary alternative proof of the diffraction formula for regular cut-and-project sets, which is based on Bochner's theorem from Fourier analysis. This clarifies a common view that the
Richard, Christoph, Strungaru, Nicolae
core +4 more sources
Weighted $1\times1$ cut-and-project sets in bounded distance to a lattice [PDF]
Discrete & Computational Geometry, 2018 Recent results of Grepstad and Lev are used to show that weighted cut-and-project sets with one-dimensional physical space and one-dimensional internal space are bounded distance equivalent to some lattice if the weight function $h$ is continuous on the ...
Frettlöh, Dirk, Garber, Alexey
core +4 more sources
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 Walton
openalex +7 more sources
Pure point diffraction and cut and project schemes for measures: The smooth case [PDF]
Mathematische Zeitschrift, 2006 We present cut and project formalism based on measures and continuous weight functions of sufficiently fast decay. The emerging measures are strongly almost periodic.
A. Córdoba +25 more
core +3 more sources
The Meyer property of cut-and-project sets [PDF]
Journal of Physics A: Mathematical and General, 2004 Summary: We consider cut-and-project sets \(\Sigma(\Omega)\) with compact acceptance window \(\Omega\subset\mathbb{R}^d\). It is known that \(\Sigma(\Omega)\) satisfies the Meyer property, i.e., it is a Delone set and there exists a finite set \(F\) such that \(\Sigma(\Omega)-\Sigma (\Omega)\subset \Sigma(\Omega) +F\). The investigation of the set \(F\)
Ľubomíra Balková +2 more
openalex +4 more sources