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Mathematics Of Aperiodic Order
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Book Synopsis Aperiodic Order: Volume 1, A Mathematical Invitation by : Michael Baake
Download or read book Aperiodic Order: Volume 1, A Mathematical Invitation written by Michael Baake and published by Cambridge University Press. This book was released on 2013-08-22 with total page 548 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis The Mathematics of Long-Range Aperiodic Order by : R.V. Moody
Download or read book The Mathematics of Long-Range Aperiodic Order written by R.V. Moody and published by Springer. This book was released on 2010-12-15 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: THEOREM: Rotational symmetries of order greater than six, and also five-fold rotational symmetry, are impossible for a periodic pattern in the plane or in three-dimensional space. The discovery of quasicrystals shattered this fundamental 'law', not by showing it to be logically false but by showing that periodicity was not synonymous with long-range order, if by 'long-range order' we mean whatever order is necessary for a crystal to produce a diffraction pat tern with sharp bright spots. It suggested that we may not know what 'long-range order' means, nor what a 'crystal' is, nor how 'symmetry' should be defined. Since 1984, solid state science has been under going a veritable K uhnian revolution. -M. SENECHAL, Quasicrystals and Geometry Between total order and total disorder He the vast majority of physical structures and processes that we see around us in the natural world. On the whole our mathematics is well developed for describing the totally ordered or totally disordered worlds. But in reality the two are rarely separated and the mathematical tools required to investigate these in-between states in depth are in their infancy.
Book Synopsis Mathematics of Aperiodic Order by : Johannes Kellendonk
Download or read book Mathematics of Aperiodic Order written by Johannes Kellendonk and published by Birkhäuser. This book was released on 2015-06-05 with total page 428 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Aperiodic Order written by Michael Baake and published by Cambridge University Press. This book was released on 2013-08-22 with total page 548 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive introductory monograph on the theory of aperiodic order, with numerous illustrations and examples.
Book Synopsis Aperiodic Order: Volume 2, Crystallography and Almost Periodicity by : Michael Baake
Download or read book Aperiodic Order: Volume 2, Crystallography and Almost Periodicity written by Michael Baake and published by Cambridge University Press. This book was released on 2017-11-02 with total page 408 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quasicrystals are non-periodic solids that were discovered in 1982 by Dan Shechtman, Nobel Prize Laureate in Chemistry 2011. The mathematics that underlies this discovery or that proceeded from it, known as the theory of Aperiodic Order, is the subject of this comprehensive multi-volume series. This second volume begins to develop the theory in more depth. A collection of leading experts, among them Robert V. Moody, cover various aspects of crystallography, generalising appropriately from the classical case to the setting of aperiodically ordered structures. A strong focus is placed upon almost periodicity, a central concept of crystallography that captures the coherent repetition of local motifs or patterns, and its close links to Fourier analysis. The book opens with a foreword by Jeffrey C. Lagarias on the wider mathematical perspective and closes with an epilogue on the emergence of quasicrystals, written by Peter Kramer, one of the founders of the field.
Download or read book Aperiodic Order written by Michael Baake and published by Cambridge University Press. This book was released on 2013 with total page 407 pages. Available in PDF, EPUB and Kindle. Book excerpt: The second volume in a series exploring the mathematics of aperiodic order. Covers various aspects of crystallography.
Book Synopsis Aperiodic Order: Volume 2, Crystallography and Almost Periodicity by : Michael Baake
Download or read book Aperiodic Order: Volume 2, Crystallography and Almost Periodicity written by Michael Baake and published by Cambridge University Press. This book was released on 2017-11-02 with total page 407 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quasicrystals are non-periodic solids that were discovered in 1982 by Dan Shechtman, Nobel Prize Laureate in Chemistry 2011. The mathematics that underlies this discovery or that proceeded from it, known as the theory of Aperiodic Order, is the subject of this comprehensive multi-volume series. This second volume begins to develop the theory in more depth. A collection of leading experts, among them Robert V. Moody, cover various aspects of crystallography, generalising appropriately from the classical case to the setting of aperiodically ordered structures. A strong focus is placed upon almost periodicity, a central concept of crystallography that captures the coherent repetition of local motifs or patterns, and its close links to Fourier analysis. The book opens with a foreword by Jeffrey C. Lagarias on the wider mathematical perspective and closes with an epilogue on the emergence of quasicrystals, written by Peter Kramer, one of the founders of the field.
Book Synopsis Directions in Mathematical Quasicrystals by : Michael Baake
Download or read book Directions in Mathematical Quasicrystals written by Michael Baake and published by American Mathematical Soc.. This book was released on 2000 with total page 389 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume includes twelve solicited articles which survey the current state of knowledge and some of the open questions on the mathematics of aperiodic order. A number of the articles deal with the sophisticated mathematical ideas that are being developed from physical motivations. Many prominent mathematical aspects of the subject are presented, including the geometry of aperiodic point sets and their diffractive properties, self-affine tilings, the role of $C*$-algebras in tiling theory, and the interconnections between symmetry and aperiodic point sets. Also discussed are the question of pure point diffraction of general model sets, the arithmetic of shelling icosahedral quasicrystals, and the study of self-similar measures on model sets. From the physical perspective, articles reflect approaches to the mathematics of quasicrystal growth and the Wulff shape, recent results on the spectral nature of aperiodic Schrödinger operators with implications to transport theory, the characterization of spectra through gap-labelling, and the mathematics of planar dimer models. A selective bibliography with comments is also provided to assist the reader in getting an overview of the field. The book will serve as a comprehensive guide and an inspiration to those interested in learning more about this intriguing subject.
Download or read book Aperiodic Crystals written by Ted Janssen and published by Oxford University Press, USA. This book was released on 2007-05-24 with total page 481 pages. Available in PDF, EPUB and Kindle. Book excerpt: Most materials and crystals have an atomic structure which is described by a regular stacking of a microscopic fundamental unit, the unit cell. However, there are also many well ordered materials without such a unit cell. This book deals with the structure determination and a discussion of the main special properties of these materials.
Book Synopsis Topology of Tiling Spaces by : Lorenzo Adlai Sadun
Download or read book Topology of Tiling Spaces written by Lorenzo Adlai Sadun and published by American Mathematical Soc.. This book was released on 2008 with total page 131 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This book is an introduction to the topology of tiling spaces, with a target audience of graduate students who wish to learn about the interface of topology with aperiodic order. It isn't a comprehensive and cross-referenced tome about everything having to do with tilings, which would be too big, too hard to read, and far too hard to write! Rather, it is a review of the explosion of recent work on tiling spaces as inverse limits, on the cohomology of tiling spaces, on substitution tilings and the role of rotations, and on tilings that do not have finite local complexity. Powerful computational techniques have been developed, as have new ways of thinking about tiling spaces." "The text contains a generous supply of examples and exercises."--BOOK JACKET.
Book Synopsis 2019-20 MATRIX Annals by : Jan de Gier
Download or read book 2019-20 MATRIX Annals written by Jan de Gier and published by Springer Nature. This book was released on 2021-02-10 with total page 803 pages. Available in PDF, EPUB and Kindle. Book excerpt: MATRIX is Australia’s international and residential mathematical research institute. It facilitates new collaborations and mathematical advances through intensive residential research programs, each 1-4 weeks in duration. This book is a scientific record of the ten programs held at MATRIX in 2019 and the two programs held in January 2020: · Topology of Manifolds: Interactions Between High and Low Dimensions · Australian-German Workshop on Differential Geometry in the Large · Aperiodic Order meets Number Theory · Ergodic Theory, Diophantine Approximation and Related Topics · Influencing Public Health Policy with Data-informed Mathematical Models of Infectious Diseases · International Workshop on Spatial Statistics · Mathematics of Physiological Rhythms · Conservation Laws, Interfaces and Mixing · Structural Graph Theory Downunder · Tropical Geometry and Mirror Symmetry · Early Career Researchers Workshop on Geometric Analysis and PDEs · Harmonic Analysis and Dispersive PDEs: Problems and Progress The articles are grouped into peer-reviewed contributions and other contributions. The peer-reviewed articles present original results or reviews on a topic related to the MATRIX program; the remaining contributions are predominantly lecture notes or short articles based on talks or activities at MATRIX.
Book Synopsis Illustrating Mathematics by : Diana Davis
Download or read book Illustrating Mathematics written by Diana Davis and published by American Mathematical Soc.. This book was released on 2020-10-16 with total page 171 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is for anyone who wishes to illustrate their mathematical ideas, which in our experience means everyone. It is organized by material, rather than by subject area, and purposefully emphasizes the process of creating things, including discussions of failures that occurred along the way. As a result, the reader can learn from the experiences of those who came before, and will be inspired to create their own illustrations. Topics illustrated within include prime numbers, fractals, the Klein bottle, Borromean rings, tilings, space-filling curves, knot theory, billiards, complex dynamics, algebraic surfaces, groups and prime ideals, the Riemann zeta function, quadratic fields, hyperbolic space, and hyperbolic 3-manifolds. Everyone who opens this book should find a type of mathematics with which they identify. Each contributor explains the mathematics behind their illustration at an accessible level, so that all readers can appreciate the beauty of both the object itself and the mathematics behind it.
Book Synopsis Ergodic Theory and Dynamical Systems in their Interactions with Arithmetics and Combinatorics by : Sébastien Ferenczi
Download or read book Ergodic Theory and Dynamical Systems in their Interactions with Arithmetics and Combinatorics written by Sébastien Ferenczi and published by Springer. This book was released on 2018-06-15 with total page 434 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book concentrates on the modern theory of dynamical systems and its interactions with number theory and combinatorics. The greater part begins with a course in analytic number theory and focuses on its links with ergodic theory, presenting an exhaustive account of recent research on Sarnak's conjecture on Möbius disjointness. Selected topics involving more traditional connections between number theory and dynamics are also presented, including equidistribution, homogenous dynamics, and Lagrange and Markov spectra. In addition, some dynamical and number theoretical aspects of aperiodic order, some algebraic systems, and a recent development concerning tame systems are described.
Book Synopsis The Second Kind of Impossible by : Paul Steinhardt
Download or read book The Second Kind of Impossible written by Paul Steinhardt and published by Simon & Schuster. This book was released on 2020-01-07 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt: *Shortlisted for the 2019 Royal Society Insight Investment Science Book Prize* One of the most fascinating scientific detective stories of the last fifty years, an exciting quest for a new form of matter. “A riveting tale of derring-do” (Nature), this book reads like James Gleick’s Chaos combined with an Indiana Jones adventure. When leading Princeton physicist Paul Steinhardt began working in the 1980s, scientists thought they knew all the conceivable forms of matter. The Second Kind of Impossible is the story of Steinhardt’s thirty-five-year-long quest to challenge conventional wisdom. It begins with a curious geometric pattern that inspires two theoretical physicists to propose a radically new type of matter—one that raises the possibility of new materials with never before seen properties, but that violates laws set in stone for centuries. Steinhardt dubs this new form of matter “quasicrystal.” The rest of the scientific community calls it simply impossible. The Second Kind of Impossible captures Steinhardt’s scientific odyssey as it unfolds over decades, first to prove viability, and then to pursue his wildest conjecture—that nature made quasicrystals long before humans discovered them. Along the way, his team encounters clandestine collectors, corrupt scientists, secret diaries, international smugglers, and KGB agents. Their quest culminates in a daring expedition to a distant corner of the Earth, in pursuit of tiny fragments of a meteorite forged at the birth of the solar system. Steinhardt’s discoveries chart a new direction in science. They not only change our ideas about patterns and matter, but also reveal new truths about the processes that shaped our solar system. The underlying science is important, simple, and beautiful—and Steinhardt’s firsthand account is “packed with discovery, disappointment, exhilaration, and persistence...This book is a front-row seat to history as it is made” (Nature).
Book Synopsis Mathematics as a Tool by : Johannes Lenhard
Download or read book Mathematics as a Tool written by Johannes Lenhard and published by Springer. This book was released on 2017-04-04 with total page 285 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book puts forward a new role for mathematics in the natural sciences. In the traditional understanding, a strong viewpoint is advocated, on the one hand, according to which mathematics is used for truthfully expressing laws of nature and thus for rendering the rational structure of the world. In a weaker understanding, many deny that these fundamental laws are of an essentially mathematical character, and suggest that mathematics is merely a convenient tool for systematizing observational knowledge. The position developed in this volume combines features of both the strong and the weak viewpoint. In accordance with the former, mathematics is assigned an active and even shaping role in the sciences, but at the same time, employing mathematics as a tool is taken to be independent from the possible mathematical structure of the objects under consideration. Hence the tool perspective is contextual rather than ontological. Furthermore, tool-use has to respect conditions like suitability, efficacy, optimality, and others. There is a spectrum of means that will normally differ in how well they serve particular purposes. The tool perspective underlines the inevitably provisional validity of mathematics: any tool can be adjusted, improved, or lose its adequacy upon changing practical conditions.
Download or read book Miles of Tiles written by Charles Radin and published by American Mathematical Soc.. This book was released on 1999 with total page 134 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Miles of Tiles" is a mathematics lesson for middle school classes requiring students to calculate the number and cost of tiles needed to cover the floor of the classroom. This lesson includes Internet activities. "Miles of Tiles" is presented as a service of the Link-to-Learn Professional Development Project of Pennsylvania, a state-sponsored educational technology initiative.
Book Synopsis Quasicrystals and Discrete Geometry by : Jiri Patera
Download or read book Quasicrystals and Discrete Geometry written by Jiri Patera and published by American Mathematical Soc.. This book was released on 1998-01-01 with total page 306 pages. Available in PDF, EPUB and Kindle. Book excerpt: Comprising the proceedings of the fall 1995 semester program arranged by The Fields Institute at the U. of Toronto, Ontario, Canada, this volume contains eleven contributions which address ordered aperiodic systems realized either as point sets with the Delone property or as tilings of a Euclidean space. This collection of articles aims to bring into the mainstream of mathematics and mathematical physics this developing field of study integrating algebra, geometry, Fourier analysis, number theory, crystallography, and theoretical physics. Annotation copyrighted by Book News, Inc., Portland, OR
