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Author: Michael Baake
Publisher: Cambridge University Press
ISBN: 1108514499
Category : Mathematics
Languages : en
Pages : 408
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Book Description
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.
Author: Michael Baake
Publisher: Cambridge University Press
ISBN: 1108514499
Category : Mathematics
Languages : en
Pages : 408
Get Book Here
Book Description
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.
Author: Michael Baake
Publisher: Cambridge University Press
ISBN: 1316184382
Category : Mathematics
Languages : en
Pages : 548
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Book Description
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.
Author: Johannes Kellendonk
Publisher: Birkhäuser
ISBN: 3034809034
Category : Mathematics
Languages : en
Pages : 438
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Book Description
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.
Author: Enrique Macia Barber
Publisher: CRC Press
ISBN: 1420068288
Category : Science
Languages : en
Pages : 457
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Book Description
One of the Top Selling Physics Books according to YBP Library ServicesOrder can be found in all the structures unfolding around us at different scales, including in the arrangements of matter and in energy flow patterns. Aperiodic Structures in Condensed Matter: Fundamentals and Applications focuses on a special kind of order referred to as aperiod
Author: Ted Janssen
Publisher: Oxford University Press, USA
ISBN: 0198567774
Category : Science
Languages : en
Pages : 481
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Book Description
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.
Author: R.V. Moody
Publisher: Springer
ISBN: 0792345061
Category : Mathematics
Languages : en
Pages : 556
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Book Description
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.
Author: Lorenzo Adlai Sadun
Publisher: American Mathematical Soc.
ISBN: 0821847279
Category : Mathematics
Languages : en
Pages : 131
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Book Description
"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.
Author: Marko Jaric
Publisher: Elsevier
ISBN: 0323140645
Category : Science
Languages : en
Pages : 296
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Book Description
Aperiodicity and Order, Volume 1: Introduction to Quasicrystals deals with various aperiodic types of order in quasicrystals as well as the basic physics of quasicrystalline order and materials. Questions about the nature of order and the order of nature are addressed. This volume is comprised of six chapters; the first of which introduces the reader to icosahedral coordination in metallic crystals, with emphasis on the structural principles of metallic materials that are crystalline and may be expected to carry over to aperiodic materials. The discussion then turns to short- and long-range icosahedral orders in glass, crystals, and quasicrystals. The origins of icosahedral order are explained, and the physical properties of icosahedral materials are described. The chapters that follow focus on the metallurgy of quasicrystals, the crystallography of ideal icosahedral crystals, and stability and deformations in quasicrystalline solids. The book concludes with a discussion on symmetry, elasticity, and hydrodynamics in quasiperiodic structures. A pedagogical review of continuum elastic-hydrodynamic theory for quasicrystals and related structures is presented. This book is intended primarily as an introduction for new students in the field and as a reference for active researchers.
Author: Michael Baake
Publisher: American Mathematical Soc.
ISBN: 0821826298
Category : Mathematics
Languages : en
Pages : 389
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Book Description
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.
Author: Luca Dal Negro
Publisher: CRC Press
ISBN: 9814463094
Category : Science
Languages : en
Pages : 512
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Book Description
This book presents state-of-the-art contributions from a number of leading experts that actively work worldwide in the rapidly growing, highly interdisciplinary, and fascinating fields of aperiodic optics and complex photonics. Edited by Luca Dal Negro, a prominent researcher in these areas of optical science, the book covers the fundamental, compu
