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Spectral triples and characterization of aperiodic order
Proceedings of the London Mathematical Society, 2011J. Kellendonk, J. Savinien
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2013
Quasicrystals are non-periodic solids that were discovered in 1982 by Dan Shechtman, Nobel Prize Laureate in Chemistry 2011. The underlying mathematics, known as the theory of aperiodic order, is the subject of this comprehensive multi-volume series. This first volume provides a graduate-level introduction to the many facets of this relatively new area
Michael Baake, Uwe Grimm
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Quasicrystals are non-periodic solids that were discovered in 1982 by Dan Shechtman, Nobel Prize Laureate in Chemistry 2011. The underlying mathematics, known as the theory of aperiodic order, is the subject of this comprehensive multi-volume series. This first volume provides a graduate-level introduction to the many facets of this relatively new area
Michael Baake, Uwe Grimm
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Quantum dots in aperiodic order
Physica E: Low-dimensional Systems and Nanostructures, 1998Abstract We study numerically with a Green-function technique one-dimensional arrays of quantum dots with two different models. The arrays are ordered according to the Fibonacci, the Thue–Morse, and the Rudin–Shapiro sequences. As a comparison, results from a periodically ordered chain and also from a random chain are included.
Michael Hörnquist, Thomas Ouchterlony
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Phonons in aperiodically ordered layer systems
Surface Science, 2008Abstract We have studied the phonons in multilayer structures following different aperiodic sequences (Fibonacci, Thue–Morse, Period-Doubling) along the growth direction. We have employed a nearest-neighbor force constant model giving a reasonably realistic description of metal systems.
A. Montalbán +3 more
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Entropy in the context of aperiodic order
2021Entropy is a well-studied concept and the literature contains a vast amount of material on this concept in the context of actions of countable discrete amenable groups. In this thesis we extend several statements about entropy and topological pressure to the context of unimodular amenable groups.
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Faithful Loops for Aperiodic E-Ordered Monoids
2009One of the main objectives of the algebraic theory of regular languages concerns the classification of regular languages based on Eilenberg's variety theorem [10]. This theorem states that there exists a bijection between varieties of regular languages and varieties of finite monoids. For example, the variety of star-free regular languages (the closure
Martin Beaudry, François Lemieux
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The impact of aperiodic order on mathematics
Materials Science and Engineering: A, 2000Abstract Mathematics has been strongly influenced by problems arising from physics. The existence of quasicrystals as strongly ordered structures which cannot be periodic has raised various mathematical questions that have stimulated developments in the areas of discrete geometry, harmonic analysis, group theory and ergodic theory.
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Ferroelectric order in van der Waals layered materials
Nature Reviews Materials, 2022Pankaj Sharma, Jan Seidel
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