Results 261 to 270 of about 688,997 (292)

Cut-and-project sequences and substitution rules

Ferroelectrics, 2001
Abstract We consider infinite words in a 3-letter alphabet which arise from the cut-and-project scheme based on quadratic unitary Pisot numbers. Such sequences may be considered as ternary generalizations of classical Sturmian sequences. We describe the complexity of such sequences and give a condition under which these generalized Sturmian sequences ...
Zuzana Masáková, Edita Pelantová
openaire   +1 more source

Inflation centres of the cut and project quasicrystals

Journal of Physics A: Mathematical and General, 1998
Cut-and-project quasicrystals which display golden ratio inflation symmetries are investigated. The subclass with convex window is exhaustively described with respect to the possible inflation centres, both internal and external to the point set. Also, the possible inflation factors themselves are determined and found to form a 1D quasicrystal.
Masáková, Zuzana, Patera, Jiří, Pelantová, Edita   +2 more
openaire   +2 more sources

Characterization of Cut-and-Project Sets Using a Binary Operation

Letters in Mathematical Physics, 2000
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Masáková, Zuzana, Pelantová, Edita, Svobodová, Milena   +2 more
openaire   +1 more source

Two‐scale cut‐and‐projection convergence; homogenization of quasiperiodic structures

Mathematical Methods in the Applied Sciences, 2017
We demonstrate how the problem of finding the effective property of quasiperiodic constitutive relations can be simplified to the periodic homogenization setting by transforming the original quasiperiodic material structure to a periodic heterogeneous material in a higher dimensional space.
Wellander, Niklas, Guenneau, Sébastien, Cherkaev, Elena   +2 more
openaire   +1 more source

S-convexity and cut-and-project sets

Ferroelectrics, 2001
Abstract Cut-and-project sets with convex acceptance window based on irrationalities τ = 1/2(1 + √5), β = 1 + √2, μ = 2 + √3 are models for experimentally observed quasicrystals-materials with diffraction patterns consisting of sharp Bragg peaks in crystalographically disallowed patterns.
openaire   +1 more source

Combining random number generators using cut and project sequences

Czechoslovak Journal of Physics, 2001
This paper discusses the use of aperiodic (binary or ternary) sequences in combining pseudorandom number generators (RNG). We introduce a method for combining two or three RNGs using cut and project sequences. This combination method produces aperiodic number sequences having no lattice structure. Theoretical results are announced.
Louis-Sébastien Guimond, Jiří Patera, Jan Patera   +2 more
openaire   +1 more source

Finite graphs associated with a cut-and-project set

Czechoslovak Journal of Physics, 2001
A chain of finite graphsGm can be associated with a cut-and-project set in a natural way [J. Phys. A: Math. Gen.33 (2000) 2917]. The chain of Schrodinger type operatorsHm we define in this short note, may be useful in the description of the physical properties of quasicrystals.
openaire   +1 more source

Substitution rules for aperiodic sequences of the cut and project type

Journal of Physics A: Mathematical and General, 2000
Summary: We consider one-dimensional aperiodic sequences arising from a cut-and-project scheme with quadratic unitary Pisot numbers \(\beta\). A construction of the substitution rule is described under rather general assumptions. It allows one to build a given cut-and-project sequence \(\Sigma_\beta(\Omega)\) starting from its arbitrary point.
Masáková, Zuzana, Patera, Jiří, Pelantová, Edita   +2 more
openaire   +2 more sources

Algebraic numbers and ammann bars in cut-and-project schemes

Ferroelectrics, 2001
Abstract Ammann bars have been observed in many quasicrystals and have a number of uses. However, they are a non-generic feature of cut-and-project sets with random placings of the physical and internal spaces relative to the lattice. I shall describe an intimate connexion between Ammann bars and the method of constructing a cut-and-project set from a ...
openaire   +1 more source

Quasiperiodic tilings: cut and projection

1999
openaire   +1 more source