Aperiodic Order: Volume 1, A Mathematical Invitation - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Aperiodic Order: Volume 1, A Mathematical Invitation write by Michael Baake. This book was released on 2013-08-22. Aperiodic Order: Volume 1, A Mathematical Invitation available in PDF, EPUB and Kindle. 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.
Aperiodic Order
Aperiodic Order - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Aperiodic Order write by Michael Baake. This book was released on 2013-08-22. Aperiodic Order available in PDF, EPUB and Kindle. A comprehensive introductory monograph on the theory of aperiodic order, with numerous illustrations and examples.
Mathematics of Aperiodic Order
Mathematics of Aperiodic Order - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Mathematics of Aperiodic Order write by Johannes Kellendonk. This book was released on 2015-06-05. Mathematics of Aperiodic Order available in PDF, EPUB and Kindle. What is order that is not based on simple repetition, that is, periodicity? How must atoms be arranged in a material so that it diffracts like a quasicrystal? How can we describe aperiodically ordered systems mathematically? Originally triggered by the – later Nobel prize-winning – discovery of quasicrystals, the investigation of aperiodic order has since become a well-established and rapidly evolving field of mathematical research with close ties to a surprising variety of branches of mathematics and physics. This book offers an overview of the state of the art in the field of aperiodic order, presented in carefully selected authoritative surveys. It is intended for non-experts with a general background in mathematics, theoretical physics or computer science, and offers a highly accessible source of first-hand information for all those interested in this rich and exciting field. Topics covered include the mathematical theory of diffraction, the dynamical systems of tilings or Delone sets, their cohomology and non-commutative geometry, the Pisot substitution conjecture, aperiodic Schrödinger operators, and connections to arithmetic number theory.
The Tiling Book
The Tiling Book - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook The Tiling Book write by Colin Adams. This book was released on 2023-08-28. The Tiling Book available in PDF, EPUB and Kindle. Tiling theory provides a wonderful opportunity to illustrate both the beauty and utility of mathematics. It has all the relevant ingredients: there are stunning pictures; open problems can be stated without having to spend months providing the necessary background; and there are both deep mathematics and applications. Furthermore, tiling theory happens to be an area where many of the sub-fields of mathematics overlap. Tools can be applied from linear algebra, algebra, analysis, geometry, topology, and combinatorics. As such, it makes for an ideal capstone course for undergraduates or an introductory course for graduate students. This material can also be used for a lower-level course by skipping the more technical sections. In addition, readers from a variety of disciplines can read the book on their own to find out more about this intriguing subject. This book covers the necessary background on tilings and then delves into a variety of fascinating topics in the field, including symmetry groups, random tilings, aperiodic tilings, and quasicrystals. Although primarily focused on tilings of the Euclidean plane, the book also covers tilings of the sphere, hyperbolic plane, and Euclidean 3-space, including knotted tilings. Throughout, the book includes open problems and possible projects for students. Readers will come away with the background necessary to pursue further work in the subject.
A Computational Non-commutative Geometry Program for Disordered Topological Insulators
A Computational Non-commutative Geometry Program for Disordered Topological Insulators - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook A Computational Non-commutative Geometry Program for Disordered Topological Insulators write by Emil Prodan. This book was released on 2017-03-17. A Computational Non-commutative Geometry Program for Disordered Topological Insulators available in PDF, EPUB and Kindle. This work presents a computational program based on the principles of non-commutative geometry and showcases several applications to topological insulators. Noncommutative geometry has been originally proposed by Jean Bellissard as a theoretical framework for the investigation of homogeneous condensed matter systems. Recently, this approach has been successfully applied to topological insulators, where it facilitated many rigorous results concerning the stability of the topological invariants against disorder.In the first part of the book the notion of a homogeneous material is introduced and the class of disordered crystals defined together with the classification table, which conjectures all topological phases from this class. The manuscript continues with a discussion of electrons’ dynamics in disordered crystals and the theory of topological invariants in the presence of strong disorder is briefly reviewed. It is shown how all this can be captured in the language of noncommutative geometry using the concept of non-commutative Brillouin torus, and a list of known formulas for various physical response functions is presented. In the second part, auxiliary algebras are introduced and a canonical finite-volume approximation of the non-commutative Brillouin torus is developed. Explicit numerical algorithms for computing generic correlation functions are discussed. In the third part upper bounds on the numerical errors are derived and it is proved that the canonical-finite volume approximation converges extremely fast to the thermodynamic limit. Convergence tests and various applications concludes the presentation.The book is intended for graduate students and researchers in numerical and mathematical physics.
