Introduction To The Mathematics Of Quasicrystals
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Introduction To The Mathematics Of Quasicrystals
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Author : Marko V. Jaric
language : en
Publisher: Elsevier
Release Date : 2012-12-02
Introduction To The Mathematics Of Quasicrystals written by Marko V. Jaric and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-02 with Science categories.
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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Author : Marko V. Jarić
language : en
Publisher:
Release Date : 1989
Introduction To The Mathematics Of Quasicrystals written by Marko V. Jarić and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989 with Crystallography, Mathematical categories.
1. A brief introduction to tilings / Marjorie Senechal--2. Tilings and quasicrystals : a non-local growth problem? / R. Penrose--3. Group theory of icosohedral quasicrystals / P. Kramer and R.W. Haase--4. Some local properties of the three-dimensional Penrose tilings / Andre Katz--5. Defects in quasicrystals / J. Bohsung and H.-R. Trebin.
Introduction To The Mathematics Of Quasicrystals
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Author : Marko V. Jarić
language : en
Publisher:
Release Date : 1989
Introduction To The Mathematics Of Quasicrystals written by Marko V. Jarić and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989 with Crystallography categories.
Introduction to the Mathematics of Quasicrystals ...
Directions In Mathematical Quasicrystals
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Author : Michael Baake
language : en
Publisher: American Mathematical Soc.
Release Date : 2000
Directions In Mathematical Quasicrystals written by Michael Baake and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Crystallography, Mathematical categories.
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.
Quasicrystals And Geometry
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Author : Marjorie Senechal
language : en
Publisher: CUP Archive
Release Date : 1996-09-26
Quasicrystals And Geometry written by Marjorie Senechal and has been published by CUP Archive this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996-09-26 with Mathematics categories.
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.
The Physics Of Quasicrystals
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Author : Paul J. Steinhardt
language : en
Publisher: World Scientific
Release Date : 1987
The Physics Of Quasicrystals written by Paul J. Steinhardt and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1987 with Science categories.
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.
Mathematical Theory Of Elasticity Of Quasicrystals And Its Applications
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Author : Tian-You Fan
language : en
Publisher: Springer
Release Date : 2016-09-20
Mathematical Theory Of Elasticity Of Quasicrystals And Its Applications written by Tian-You Fan and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-09-20 with Science categories.
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.
Introduction To Quasicrystals
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Author : Marko Jaric
language : en
Publisher: Elsevier
Release Date : 2012-12-02
Introduction To Quasicrystals written by Marko Jaric and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-02 with Science categories.
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.
Quasicrystals
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Author : Hans-Rainer Trebin
language : en
Publisher: John Wiley & Sons
Release Date : 2006-05-12
Quasicrystals written by Hans-Rainer Trebin and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-05-12 with Science categories.
Quasicrystals form a new state of solid matter beside the crystalline and the amorphous. The positions of the atoms are ordered, but with noncrystallographic rotational symmetries and in a nonperiodic way. The new structure induces unusual physical properties, promising interesting applications. This book provides a comprehensive and up-to-date review and presents most recent research results, achieved by a collaboration of physicists, chemists, material scientists and mathematicians within the Priority Programme "Quasicrystals: Structure and Physical Properties" of the Deutsche Forschungsgemeinschaft (DFG). Starting from metallurgy, synthesis and characterization, the authors carry on with structure and mathematical modelling. On this basis electronic, magnetic, thermal, dynamic and mechanical properties are dealt with and finally surfaces and thin films.
Crystalline Symmetries An Informal Mathematical Introduction
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Author : Marjorie Senechal
language : en
Publisher: CRC Press
Release Date : 1990
Crystalline Symmetries An Informal Mathematical Introduction written by Marjorie Senechal and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990 with Art categories.
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.