Results 11 to 20 of about 801,697 (279)

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   +4 more sources

Classification and statistics of cut and project sets [PDF]

Journal of the European Mathematical Society, 2023
We define Ratner-Marklof-Strombergsson measures. These are probability measures supported on cut-and-project sets in R^d (d > 1) which are invariant and ergodic for the action of the groups ASL_d(R) or SL_d(R).
Rühr, René, Weiss, Barak, Smilansky, Yotam   +2 more
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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.
Walton, James J., Koivusalo, Henna, Walton, James J, Walton, James   +3 more
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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
Koivusalo, Henna L L, Walton, Jamie, Koivusalo, Henna, Walton, James   +3 more
core   +7 more sources

Statistics of patterns in typical cut and project sets [PDF]

Ergodic Theory and Dynamical Systems, 2018
In this article pattern statistics of typical cubical cut and project sets are studied. We give estimates for the rate of convergence of appearances of patches to their asymptotic frequencies.
Julien, Antoine, HENNA KOIVUSALO, JAMES WALTON, ALAN HAYNES, Koivusalso, Henna, Koivusalo, Henna L L, Koivusalo, Henna, Walton, James, ANTOINE JULIEN, Haynes, Alan   +9 more
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On generalized self-similarities of cut-and-project sets [PDF]

Linear Algebra and its Applications, 2021
Masáková Z, Mazáč J, Pelantová E. On generalized self-similarities of cut-and-project sets. Linear Algebra and its Applications.
Masáková, Zuzana, Mazáč, Jan ; https://orcid.org/, Pelantová, Edita   +2 more
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On Helly Numbers for Crystals and Cut-And-Project Sets [PDF]

Studia Scientiarum Mathematicarum Hungarica
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 copies of a single lattice the Helly number does not exceed ...
Alexey Garber, Garber, Alexey
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Gaps problems and frequencies of patches in cut and project sets [PDF]

Mathematical Proceedings of the Cambridge Philosophical Society, 2016
We establish a connection between gaps problems in Diophantine approximation and the frequency spectrum of patches in cut and project sets with special windows.
Sadun, Lorenzo, Koivusalo, Henna L L, Koivusalo, Henna, Walton, James, Haynes, Alan   +4 more
core   +7 more sources

Construction of Crystallographic Tilings by the Cut-and-Project Method [PDF]

, 2021
Patterns of point sets and tilings were produced and studied for centuries in many cultures. At the border line of mathematics, crystallography, chemistry and physics the general opinion is that every construction for point sets has a counterpart for ...
Almutairi, Najat
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A characterization of linearly repetitive cut and project sets [PDF]

Nonlinearity, 2018
For the development of a mathematical theory which can be used to rigorously investigate physical properties of quasicrystals, it is necessary to understand regularity of patterns in special classes of aperiodic point sets in Euclidean space.
Alan Haynes, Henna Koivusalo, James Walton, Koivusalo, Henna L L, Koivusalo, Henna, Walton, James, Haynes, Alan   +6 more
core   +8 more sources