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Mathematics of Aperiodic Order
Progress in Mathematics, 2015 Preface.- 1.M. Baake, M. Birkner and U. Grimm: Non-Periodic Systems with Continuous Diffraction Measures.- 2.S. Akiyama, M. Barge, V. Berthe, J.-Y. Lee and A. Siegel: On the Pisot Substitution Conjecture.- 3. L. Sadun: Cohomology of Hierarchical Tilings.- 4.J. Hunton: Spaces of Projection Method Patterns and their Cohomology.- 5.J.-B. Aujogue, M. Barge,
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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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Aperiodic Order and Quasicrystals: Spectral Properties
Annales Henri Poincaré, 2003Quasicrystals and other systems with aperiodic order are studied with respect to the nature of the spectrum of the associated Hamiltonians, using the framework of Delone to describe the aperiodic order. In the first part the paper is concerned with dicrete models. Delone sets with a topology and Delone dynamical systems are defined.
Lenz, Daniel, Stollmann, Peter
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Aperiodic Order in Nanoplasmonics
2013In this chapter, we review our work on the engineering of aperiodic order for nanoplasmonics device applications. In particular, we discuss the optical response of arrays of metallic nanoparticles with Fourier spectral features that interpolate in a tunable fashion between periodic crystals and disordered random media, referred to as Deterministic ...
Luca Dal Negro +5 more
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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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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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Aperiodic structures and notions of order and disorder
Philosophical Magazine, 2010The fabrication of artificial heterostructures is mainly based on substitution systems. We present simple ways to construct double-sided versions of the Fibonacci, Prouhet–Thue–Morse, paperfolding, period doubling and Golay–Rudin–Shapiro sequences. We also construct a generic instance of the two-dimensional Prouhet–Thue–Morse structure and explore its ...
S.I. Ben-Abraham, A. Quandt†
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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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