Aperiodic order . Volume 1 A mathematical invitation / / Michael Baake, Uwe Grimm [[electronic resource]]

• Autore: Baake Michael
• Pubblicazione: Cambridge : , : Cambridge University Press, , 2013
• Edizione: 1st ed.
• Descrizione fisica: 1 online resource (xvi, 531 pages) : digital, PDF file(s)
• Disciplina: 548.7
• Soggetto topico: Aperiodic tilings; Quasicrystals - Mathematics
• Persona (resp. second.): GrimmUwe
• Note generali: Title from publisher's bibliographic system (viewed on 05 Oct 2015).
• Nota di bibliografia: Includes bibliographical references and index.
• Nota di contenuto: Cover; Half-title; Series information; Title page; Copyright information; Table of contents; Foreword; Preface; Chapter 1 Introduction; Chapter 2 Preliminaries; 2.1. Point sets; 2.2. Voronoi and Delone cells; 2.3. Groups; 2.4. Perron-Frobenius theory; 2.5. Number-theoretic tools; Chapter 3 Lattices and Crystals; 3.1. Periodicity and lattices; 3.2. The crystallographic restriction; 3.3. Root lattices; 3.4. Minkowski embedding; Chapter 4 Symbolic Substitutions and Inflations; 4.1. Substitution rules; 4.2. Hulls and their properties; 4.3. Symmetries, invariant measures and ergodicity ; 4.4. Metallic means sequences4.5. Period doubling and paper folding; 4.6. Thue-Morse substitution; 4.7. Rudin-Shapiro and Kolakoski sequences; 4.8. Complexity and further directions; 4.9. Block substitutions; Chapter 5 Patterns and Tilings; 5.1. Patterns and local indistinguishability; 5.2. Local derivability; 5.3. Repetitivity and finite local complexity; 5.4. Geometric hull; 5.5. Proximality; 5.6. Symmetry and inflation; 5.7. Local rules; Chapter 6 Inflation Tilings; 6.1. Ammann-Beenker tilings; 6.2. Penrose tilings and their relatives; 6.3. Square triangle and shield tilings ; 6.4. Planar tilings with integer inflation multiplier6.5. Examples of non-Pisot tilings; 6.6. Pinwheel tilings; 6.7. Tilings in higher dimensions; 6.8. Colourful examples; Chapter 7 Projection Method and Model Sets; 7.1. Silver mean chain via projection; 7.2. Cut and project schemes and model sets; 7.3. Cyclotomic model sets; 7.4. Icosahedral model sets and beyond; 7.5. Alternative constructions; Chapter 8 Fourier Analysis and Measures; 8.1. Fourier series; 8.2. Almost periodic functions; 8.3. Fourier transform of functions; 8.4. Fourier transform of distributions ; 8.5. Measures and their decomposition8.6. Fourier transform of measures; 8.7. Fourier-Stieltjes coefficients of measures on S1; 8.8. Volume averaged convolutions; Chapter 9 Diffraction; 9.1. Mathematical diffraction theory; 9.2. Poisson's summation formula and perfect crystals; 9.3. Autocorrelation and diffraction of the silver mean chain; 9.4. Autocorrelation and diffraction of regular model sets; 9.5. Pure point diffraction of weighted Dirac combs; 9.6. Homometric point sets; Chapter 10 Beyond Model Sets; 10.1. Diffraction of the Thue-Morse chain ; 10.2. Diffraction of the Rudin-Shapiro chain10.3. Diffraction of lattice subsets; 10.4. Visible lattice points; 10.5. Extension to Meyer sets; Chapter 11 Random Structures; 11.1. Probabilistic preliminaries; 11.2. Bernoulli systems; 11.3. Renewal processes on the line; 11.4. Point processes from random matrix theory; 11.5. Lattice systems with interaction; 11.6. Random tilings; Appendix A The Icosahedral Group; Appendix B The Dynamical Spectrum; References; List of Definitions; List of Examples; List of Remarks; Index
• Sommario/riassunto: 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 of mathematics. Special attention is given to methods from algebra, discrete geometry and harmonic analysis, while the main focus is on topics motivated by physics and crystallography. In particular, the authors provide a systematic exposition of the mathematical theory of kinematic diffraction. Numerous illustrations and worked-out examples help the reader to bridge the gap between theory and application. The authors also point to more advanced topics to show how the theory interacts with other areas of pure and applied mathematics.
• Titolo autorizzato: Aperiodic order
• ISBN: 1-316-18318-1; 1-316-18367-X; 1-316-18377-7; 1-316-18448-X; 1-316-18473-0; 1-316-18403-X; 1-139-02525-2
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910828054403321
• Lo trovi qui: Univ. Federico II
• Serie: Encyclopedia of mathematics and its applications ; ; v. 149.