quasicrystals and geometry

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Quasicrystals And Geometry

Author : Marjorie Senechal
ISBN : 0521575419
Genre : Mathematics
File Size : 21. 97 MB
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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.

Quasicrystals A Primer 2nd Edition Dition En Anglais

Author : Christian Janot
ISBN : 0198565518
Genre : Science
File Size : 65. 67 MB
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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 weredissolved. This primer is intended to provide 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. Following the success of the first and second editions the opportunity has been taken to reprint the second edition in paperback at a more modest price.

Quasicrystals And Discrete Geometry

Author : Jiri Patera
ISBN : 0821871684
Genre : Science
File Size : 29. 82 MB
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Geometry And Thermodynamics

Author : J.C. Tolédano
ISBN : 9781461538165
Genre : Science
File Size : 65. 8 MB
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Distinct scientific communities are usually involved in the three fields of quasi-crystals, of liquid crystals, and of systems having modulated crystalline structures. However, in recent years, there has been a growing feeling that a number of common problems were encountered in the three fields. These comprise the need to recur to "exotic" spaces for describing the type of order of the atomic or molecular configurations of these systems (Euclidian "superspaces" of dimensions greater than 3, or 4-dimensional curved spaces); the recognition that one has to deal with geometrically frustrated systems, and also the occurence of specific excitations (static or dynamic) resulting from the continuous degeneracies of the stable structures considered. In the view of discussing these problems, aNA TO-Advance Research Workshop has assembled in Preveza (Greece), in september 1989,50 experts of the three considered fields (with an equal proportion of theorists and experimentalists). 35 hours of conferences and discussions have led to a more detailed evaluation of the similarities and of the differences in the approaches implemented in the studies of the three types of systems. The papers contained in this NATO-series book provide the substance of this workshop. The reader will find three types of papers. Some very short papers giving the main ideas stated on a subject. Papers comprising 8-10 pages which stick closely to the contents of the talks presented. Longer papers providing more extensively the background and results relative to a given topic. It is worth summarizing the principal outputs of the workshop.

Quasicrystals And Quasi Drivers

Author : Antony J. Bourdillon
ISBN : 9781438955896
Genre : Science
File Size : 84. 64 MB
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The Book Quasicrystals - quasi drivers - quasi everything. The book is in two parts: the first tells about one set of quasi drivers who are nameless; the second describes the chemical force that drives the structure of quasicrystals. Quasicrystals contained, for twenty five years, the most fundamental unsolved structural problem in condensed matter physics. The first problem in quasicrystals is whether the extraordinary data represent conventional Bragg diffraction. They don't because the order, n, is logarithmic instead of linear. The second problem is structural: it is not necessary to model with more than one unit cell. The patterns can be indexed and simulated using a single structural unit, as is normal in crystallography. The unit is the key driving force that creates logarithmic periodicity. Quasi science? Everything that suffers biased reviewing. Science may be censored in journals, but not on the new age internet. The book recommends more open, more responsible, more reliable and more realistic science, to engage with modern communications.


Author : D. P. DiVincenzo
ISBN : 9810241569
Genre : Science
File Size : 86. 49 MB
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Quasicrystals: The State of the Art has proven to be a useful introduction to quasicrystals for mathematicians, physicists, materials scientists, and students. The original intent was for the book to be a progress report on recent developments in the field. However, the authors took care to adopt a broad, pedagogical approach focusing on points of lasting value. Many subtle and beautiful aspects of quasicrystals are explained in this book (and nowhere else) in a way that is useful for both the expert and the student. In this second edition, some authors have appended short notes updating their essays. Two new chapters have been added. Chapter 16, by Goldman and Thiel, reviews the experimental progress since the first edition (1991) in making quasicrystals, determining their structure, and finding applications. In Chapter 17, Steinhardt discusses the quasi-unit cell picture, a promising, new approach for describing the structure and growth of quasicrystals in terms of a single, repeating, overlapping cluster of atoms.

Fractions Tilings And Geometry

Author : Bowen Kerins
ISBN : 9781470440640
Genre :
File Size : 63. 30 MB
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Designed for precollege teachers by a collaborative of teachers, educators, and mathematicians, Fractions, Tilings, and Geometry is based on a course offered in the Summer School Teacher Program at the Park City Mathematics Institute. The overall goal of the course is an introduction to non-periodic tilings in two dimensions and space-filling polyhedra. While the course does not address quasicrystals, it provides the underlying mathematics that is used in their study. Because of this goal, the course explores Penrose tilings, the irrationality of the golden ratio, the connections between tessellations and packing problems, and Voronoi diagrams in 2 and 3 dimensions. These topics all connect to precollege mathematics, either as core ideas (irrational numbers) or enrichment for standard topics in geometry (polygons, angles, and constructions). But this book isn't a “course” in the traditional sense. It consists of a carefully sequenced collection of problem sets designed to develop several interconnected mathematical themes. These materials provide participants with the opportunity for authentic mathematical discovery—participants build mathematical structures by investigating patterns, use reasoning to test and formalize their ideas, offer and negotiate mathematical definitions, and apply their theories and mathematical machinery to solve problems. Fractions, Tilings, and Geometry is a volume of the book series “IAS/PCMI—The Teacher Program Series” published by the American Mathematical Society. Each volume in this series covers the content of one Summer School Teacher Program year and is independent of the rest.

The Physics Of Quasicrystals

Author : P J Steinhardt
ISBN : 9789813103849
Genre : Science
File Size : 60. 87 MB
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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. Request Inspection Copy

Tilings And Patterns

Author : Branko Grünbaum
ISBN : 0716719983
Genre : Mathematics
File Size : 64. 61 MB
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Tilings and Patterns: An Introduction presents in convenient paperback form the first half of Tilings and Patterns. Omitting the more specialized material of the earlier volume, this abbreviated edition make's the authors' contributions to tiling theory and its practical applications accessible to a wide audience.

Directions In Mathematical Quasicrystals

Author : Michael Baake
ISBN : 9780821826294
Genre : Mathematics
File Size : 58. 33 MB
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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 Schrodinger operators with implications to transport theory, the characterization of spectra through gap-labeling, 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.

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