Results 21 to 30 of about 612,349 (305)
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. In one dimension, prototypical mathematical models for quasicrystals are provided by Sturmian sequences and by ...
Alan Haynes +2 more
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On generalized self-similarities of cut-and-project sets [PDF]
Linear Algebra and its Applications, 2019 Cut-and-project sets $ \subset\mathbb{R}^n$ represent one of the types of uniformly discrete relatively dense sets. They arise by projection of a section of a higher-dimensional lattice to a suitably oriented subspace. Cut-and-project sets find application in solid state physics as mathematical models of atomic positions in quasicrystals, the ...
Zuzana Masáková +2 more
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Cut-and-project quasicrystals, lattices, and dense forests [PDF]
Journal of the London Mathematical Society, 2019 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 ...
Faustin Adiceam +2 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 of cut and project schemes which is large enough to cover almost all such polytopal schemes which ...
Henna Koivusalo, James Walton
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Classification and statistics of cut and project sets
Journal of the European Mathematical Society, 2020 We define Ratner–Marklof–Strömbergsson measures (following Marklof and Strömbergsson (2014)). These are probability measures supported on cut-and-project sets in \smash{\mathbb{R}^d} (d \geq 2) which are invariant and ...
René Rühr +2 more
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SYMPLECTIC CUTS AND PROJECTION QUANTIZATION FOR NON-HOLONOMIC CONSTRAINTS [PDF]
International Journal of Modern Physics D, 2003 Projection quantization, which is a method to quantize systems with non-holonomic constraints like the condition Det q > 0 in general relativity, is shown to coincide with a reduced phase space quantization in a class of cases which is specified in the main text.
Martin Bojowald, Thomas Strobl
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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. We also give bounds for repetitivity and repulsivity functions. The proofs use ideas and tools developed in discrepancy theory.
Koivusalo, Henna L L +3 more
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Asymmetries of Cut-and-Project Sets and Related Tilings
Interdisciplinary Information Sciences, 2009 In order to characterize the (a)symmetries of cut-and-project sets, we prove the following: any cut-and-project set with the two projections being injective on the lattice is fixed by an affine transformation if and only if (1) the window restricted on the projection of the lattice is fixed by another affine transformation, and (2) both affine ...
Shinji Iizuka +2 more
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Complexity and cohomology for cut-and-projection tilings [PDF]
Ergodic Theory and Dynamical Systems, 2009 AbstractWe consider a subclass of tilings: the tilings obtained by cut-and-projection. Under somewhat standard assumptions, we show that the natural complexity function has polynomial growth. We compute its exponentαin terms of the ranks of certain groups which appear in the construction. We give bounds forα. These computations apply to some well-known
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Non-Local Game of Life in 2D Quasicrystals
Crystals, 2018 On a two-dimensional quasicrystal, a Penrose tiling, we simulate for the first time a game of life dynamics governed by non-local rules. Quasicrystals have inherently non-local order since any local patch, the emperor, forces the existence of a large ...
Fang Fang +3 more
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