Introduction to the Mathematics of Quasicrystals

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Publisher : Elsevier
ISBN 13 : 0323159478
Total Pages : 238 pages
Book Rating : 4.3/5 (231 download)

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Book Synopsis Introduction to the Mathematics of Quasicrystals by : Marko V. Jaric

Download or read book Introduction to the Mathematics of Quasicrystals written by Marko V. Jaric and published by Elsevier. This book was released on 2012-12-02 with total page 238 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduction to the Mathematics of Quasicrystals provides a pedagogical introduction to mathematical concepts and results necessary for a quantitative description or analysis of quasicrystals. This book is organized into five chapters that cover the three mathematical areas most relevant to quasicrystals, namely, the theory of almost periodic functions, the theory of aperiodic tilings, and group theory. Chapter 1 describes the aspects of the theory of tiling in two- and three-dimensional space that are important for understanding some of the ways in which "classical mathematical crystallography is being generalized; this process is to include possible models for aperiodic crystals. Chapter 2 examines the non-local nature of assembly "mistakes that might have significance to the quasicrystals growth. This chapter also describes how closely a physical quasicrystal might be able to approximate a three-dimensional version of tilings. Chapter 3 discusses the theoretical background and concepts of group theory of icosahedral quasicrystals. Chapter 4 presents the local properties of the three-dimensional Penrose tilings and their global construction is described through the projection method. This chapter emphasizes the relationship between quasiperiodic sets of points and quasiperiodic tiling. Chapter 5 explores the analysis of defects in quasicrystals and their kinetics, as well as some properties of the perfect system. This book is of great value to physicists, crystallographers, metallurgists, and beginners in the field of quasicrystals.

Introduction to the Mathematics of Quasicrystals

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Publisher :
ISBN 13 : 9780120406029
Total Pages : 276 pages
Book Rating : 4.4/5 (6 download)

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Book Synopsis Introduction to the Mathematics of Quasicrystals by : Marko V. Jarić

Download or read book Introduction to the Mathematics of Quasicrystals written by Marko V. Jarić and published by . This book was released on 1989 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduction to the Mathematics of Quasicrystals ...

Aperiodic Order: Volume 1, A Mathematical Invitation

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Publisher : Cambridge University Press
ISBN 13 : 1316184382
Total Pages : 548 pages
Book Rating : 4.3/5 (161 download)

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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.

Mathematical Theory of Elasticity of Quasicrystals and Its Applications

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Author :
Publisher : Springer
ISBN 13 : 9811019843
Total Pages : 462 pages
Book Rating : 4.8/5 (11 download)

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Book Synopsis Mathematical Theory of Elasticity of Quasicrystals and Its Applications by : Tian-You Fan

Download or read book Mathematical Theory of Elasticity of Quasicrystals and Its Applications written by Tian-You Fan and published by Springer. This book was released on 2016-09-20 with total page 462 pages. Available in PDF, EPUB and Kindle. Book excerpt: This interdisciplinary work on condensed matter physics, the continuum mechanics of novel materials, and partial differential equations, discusses the mathematical theory of elasticity and hydrodynamics of quasicrystals, as well as its applications. By establishing new partial differential equations of higher order and their solutions under complicated boundary value and initial value conditions, the theories developed here dramatically simplify the solution of complex elasticity problems. Comprehensive and detailed mathematical derivations guide readers through the work. By combining theoretical analysis and experimental data, mathematical studies and practical applications, readers will gain a systematic, comprehensive and in-depth understanding of condensed matter physics, new continuum mechanics and applied mathematics. This new edition covers the latest developments in quasicrystal studies. In particular, it pays special attention to the hydrodynamics, soft-matter quasicrystals, and the Poisson bracket method and its application in deriving hydrodynamic equations. These new sections make the book an even more useful and comprehensive reference guide for researchers working in Condensed Matter Physics, Chemistry and Materials Science.

Quasicrystals and Geometry

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Publisher : CUP Archive
ISBN 13 : 9780521575416
Total Pages : 310 pages
Book Rating : 4.5/5 (754 download)

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Book Synopsis Quasicrystals and Geometry by : Marjorie Senechal

Download or read book Quasicrystals and Geometry written by Marjorie Senechal and published by CUP Archive. This book was released on 1996-09-26 with total page 310 pages. Available in PDF, EPUB and Kindle. Book excerpt: This first-ever detailed account of quasicrystal geometry will be of great value to mathematicians at all levels with an interest in quasicrystals and geometry, and will also be of interest to graduate students and researchers in solid state physics, crystallography and materials science.

Crystallography of Quasicrystals

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Publisher : Springer Science & Business Media
ISBN 13 : 3642018998
Total Pages : 388 pages
Book Rating : 4.6/5 (42 download)

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Book Synopsis Crystallography of Quasicrystals by : Steurer Walter

Download or read book Crystallography of Quasicrystals written by Steurer Walter and published by Springer Science & Business Media. This book was released on 2009-08-26 with total page 388 pages. Available in PDF, EPUB and Kindle. Book excerpt: From tilings to quasicrystal structures and from surfaces to the n-dimensional approach, this book gives a full, self-contained in-depth description of the crystallography of quasicrystals. It aims not only at conveying the concepts and a precise picture of the structures of quasicrystals, but it also enables the interested reader to enter the field of quasicrystal structure analysis. Going beyond metallic quasicrystals, it also describes the new, dynamically growing field of photonic quasicrystals. The readership will be graduate students and researchers in crystallography, solid-state physics, materials science, solid- state chemistry and applied mathematics.

Crystalline Symmetries, An Informal Mathematical Introduction

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Publisher : CRC Press
ISBN 13 :
Total Pages : 160 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Crystalline Symmetries, An Informal Mathematical Introduction by : Marjorie Senechal

Download or read book Crystalline Symmetries, An Informal Mathematical Introduction written by Marjorie Senechal and published by CRC Press. This book was released on 1990 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt: Crystalline Symmetries: an informal mathematical introduction is a guided tour through the maze of mathematical models and classifications that are used today to describe the symmetries of crystals. The mathematical basis of crystallography and the interpretation of The International Tables for X-ray Crystallography are explained in a heuristic and accessible way. In addition to discussing standard crystals, a special feature of this book is the chapter on generalised crystals and the Penrose tile model for the kinds of generalised crystals known as quasicrystals. This fruitful interaction between pure mathematics (symmetry, tilings) and physics should prove invaluable to final year undergraduate/graduate physicists and materials scientists; the reader gets a flavour of the powerful coherence of a group theoretical approach to crystallography. Mathematicians interested in applications of group theory to physical science will also find this book useful.

Quasicrystals

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Publisher : CRC Press
ISBN 13 : 1351209132
Total Pages : 284 pages
Book Rating : 4.3/5 (512 download)

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Book Synopsis Quasicrystals by : Enrique Maciá-Barber

Download or read book Quasicrystals written by Enrique Maciá-Barber and published by CRC Press. This book was released on 2020-12-18 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt: promoting the very notion of quasiperiodic order, and to spur its physical implications and technological capabilities. It, therefore, explores the fundamental aspects of intermetallic, photonic, and phononic quasicrystals, as well as soft-matter quasicrystals, including their intrinsic physical and structural properties. In addition, it thoroughly discusses experimental data and related theoretical approaches to explain them, extending the standard treatment given in most current solid state physics literature. It also explores exciting applications in new technological devices of quasiperiodically ordered systems, including multilayered quasiperiodic systems, along with 2D and 3D designs, whilst outlining new frontiers in quasicrystals research. This book can be used as a reader-friendly introductory text for graduate students, in addition to senior scientists and researchers coming from the fields of physics, chemistry, materials science, and engineering. Key features: • Provides an updated and detailed introduction to the interdisciplinary field of quasicrystals in a tutorial style, considering both fundamental aspects and additional freedom degrees provided by designs based on quasiperiodically ordered materials. • Includes 50 fully worked out exercises with detailed solutions, motivating, and illustrating the different concepts and notions to provide readers with further learning opportunities. • Presents a complete compendium of the current state of the art knowledge of quasicrystalline matter, and outlines future next generation materials based on quasiperiodically ordered designs for their potential use in useful technological devices. Dr. Enrique Maciá-Barber is Professor of condensed matter physics at the Universidad Complutense de Madrid. His research interests include the thermoelectric properties of quasicrystals and DNA biophysics. In 2010 he received the RSEF- BBVA Foundation Excellence Physics Teaching Award. His book Aperiodic Structures in Condensed Matter: Fundamentals and Applications (CRC Press, Boca-Raton, 2009) is one of the Top Selling Physics Books according to YBP Library Services.

Directions in Mathematical Quasicrystals

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Publisher : American Mathematical Soc.
ISBN 13 : 0821826298
Total Pages : 389 pages
Book Rating : 4.8/5 (218 download)

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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.

Mathematics of Aperiodic Order

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Publisher : Birkhäuser
ISBN 13 : 3034809034
Total Pages : 438 pages
Book Rating : 4.0/5 (348 download)

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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 438 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.

Aperiodic Crystals

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Publisher : Oxford University Press, USA
ISBN 13 : 0198567774
Total Pages : 481 pages
Book Rating : 4.1/5 (985 download)

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Book Synopsis Aperiodic Crystals by : Ted Janssen

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.

The Physics of Quasicrystals

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Publisher : World Scientific
ISBN 13 : 9789971502270
Total Pages : 792 pages
Book Rating : 4.5/5 (22 download)

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Book Synopsis The Physics of Quasicrystals by : Paul J. Steinhardt

Download or read book The Physics of Quasicrystals written by Paul J. Steinhardt and published by World Scientific. This book was released on 1987 with total page 792 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book comprises an introductory lecture outlining the basic concepts and challenges in the field. This is followed by a collection of reprinted articles which are important in understanding the subject. The book will focus mainly on mathematical and physical foundations of the subject rather than experimental progress. By concentrating on theoretical topics, this volume has long-lasting as well as immediate value to physicists, crystallographers, metallurgists and mathematicians.

Aperiodic Order: Volume 2, Crystallography and Almost Periodicity

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Publisher : Cambridge University Press
ISBN 13 : 1108514499
Total Pages : 408 pages
Book Rating : 4.1/5 (85 download)

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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.

Quasicrystals

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Publisher : Oxford University Press, USA
ISBN 13 : 0199657408
Total Pages : 428 pages
Book Rating : 4.1/5 (996 download)

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Book Synopsis Quasicrystals by : Christian Janot

Download or read book Quasicrystals written by Christian Janot and published by Oxford University Press, USA. This book was released on 2012-10-18 with total page 428 pages. Available in PDF, EPUB and Kindle. Book excerpt: In 1984 physicists discovered a monster in the world of crystallography, a structure that appeared to contain five-fold symmetry axes, which cannot exist in strictly periodic structures. Such quasi-periodic structures became known as quasicrystals. A previously formulated theory in terms of higher dimensional space groups was applied to them and new alloy phases were prepared which exhibited the properties expected from this model more closely. Thus many of the early controversies were dissolved. In 2011, the Nobel Prize for Chemistry was awarded to Dan Shechtman for the discovery of quasicrystals. This primer provides a descriptive approach to the subject for those coming to it for the first time. The various practical, experimental, and theoretical topics are dealt with in an accessible style. The book is completed by problem sets and there is a computer program that generates a Penrose lattice.

New Geometries for New Materials

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Publisher : Cambridge University Press
ISBN 13 : 0521861047
Total Pages : 9 pages
Book Rating : 4.5/5 (218 download)

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Book Synopsis New Geometries for New Materials by : Eric A. Lord

Download or read book New Geometries for New Materials written by Eric A. Lord and published by Cambridge University Press. This book was released on 2006-09-21 with total page 9 pages. Available in PDF, EPUB and Kindle. Book excerpt: This 2006 book presents the geometrical ideas of structure at the atomic level that are being developed and integrated into materials science. Emphasis is placed on the intuitive understanding of geometrical principles through illustrations not detailed computation. This book will appeal to those working in crystallography, solid-state science and materials science.

Quasicrystals

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Publisher : Springer Science & Business Media
ISBN 13 : 3662050285
Total Pages : 575 pages
Book Rating : 4.6/5 (62 download)

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Book Synopsis Quasicrystals by : J.-B. Suck

Download or read book Quasicrystals written by J.-B. Suck and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 575 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book provides an introduction to all aspects of the physics of quasicrystals. The chapters, each written by an expert in this field, cover quasiperiodic tilings and the modeling of the atomic structure of quasicrystals. The electronic density of states and the calculation of the electronic structure play a key role in this introduction, as does an extensive discussion of the atomic dynamics. The study of defects in quasicrystals by high resolution electron microscopy and the computer simulations of defects and fracture in decorated tilings are important subjects for the application of these aperiodic crystals.

A Guide to Distribution Theory and Fourier Transforms

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Publisher : World Scientific
ISBN 13 : 9789812384300
Total Pages : 238 pages
Book Rating : 4.3/5 (843 download)

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Book Synopsis A Guide to Distribution Theory and Fourier Transforms by : Robert S. Strichartz

Download or read book A Guide to Distribution Theory and Fourier Transforms written by Robert S. Strichartz and published by World Scientific. This book was released on 2003 with total page 238 pages. Available in PDF, EPUB and Kindle. Book excerpt: This important book provides a concise exposition of the basic ideas of the theory of distribution and Fourier transforms and its application to partial differential equations. The author clearly presents the ideas, precise statements of theorems, and explanations of ideas behind the proofs. Methods in which techniques are used in applications are illustrated, and many problems are included. The book also introduces several significant recent topics, including pseudodifferential operators, wave front sets, wavelets, and quasicrystals. Background mathematical prerequisites have been kept to a minimum, with only a knowledge of multidimensional calculus and basic complex variables needed to fully understand the concepts in the book.A Guide to Distribution Theory and Fourier Transforms can serve as a textbook for parts of a course on Applied Analysis or Methods of Mathematical Physics, and in fact it is used that way at Cornell.