Quasicrystals And Discrete Geometry
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Quasicrystals And Discrete Geometry
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Author : Jiri Patera
language : en
Publisher: American Mathematical Soc.
Release Date : 1998-01-01
Quasicrystals And Discrete Geometry written by Jiri Patera 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 1998-01-01 with Science categories.
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
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.
Coverings Of Discrete Quasiperiodic Sets
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Author : Peter Kramer
language : en
Publisher: Springer
Release Date : 2003-07-01
Coverings Of Discrete Quasiperiodic Sets written by Peter Kramer and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-07-01 with Science categories.
In this up-to-date review and guide to most recent literature, the expert authors develop concepts related to quasiperiodic coverings and describe results. The text describes specific systems in 2 and 3 dimensions with many illustrations, and analyzes the atomic positions in quasicrystals.
From Quasicrystals To More Complex Systems
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Author : F. Axel
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29
From Quasicrystals To More Complex Systems written by F. Axel and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-29 with Mathematics categories.
This book is a collection of part of the written versions of the Physics Courses given at the Winter School "Order, Chance and Risk: Aperiodic Phenomena from Solid State to Finance" held at the Les Houches Center for Physics, between February 23 and March 6, 1998. The School gathered lecturers and participants from all over the world. On a thematic level, the content of the school can be viewed both as a continuation (aperiodic phenomena in solid state physics) and an extension (mathematical aspects of fmance and economy) of the previous "Beyond Quasicrystals", also held at Les Houches, March 7-18 1994 and published in the same ·series. One of its important goals was to promote in-depth concrete scientific exchanges between theoretical physicists, experimental physicists and mathematicians on the one hand, and on the other hand practitioners of the economico-fmancial sphere and specialists of financial mathematics. Therefore, besides the mathematical tools and concepts at work in theoretical descriptions, relevant experimental data were also presented together with methods allowing their interpretation. As a result of this choice, the School was stimulated by experimentalists and fmancial market operators who joined the theoretical physicists and mathematicians at the conference. The present volume deals with the theoretical and experimental studies on aperiodic solids with long range order, incommensurate phases, quasicrystals, glasses, and more complex systems (fractal, chaotic), while a second volume to appear in the same series is devoted to the finance and economy facet.
Mathematics Of Aperiodic Order
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Author : Johannes Kellendonk
language : en
Publisher: Birkhäuser
Release Date : 2015-06-05
Mathematics Of Aperiodic Order written by Johannes Kellendonk and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-06-05 with Mathematics categories.
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 Order Volume 1 A Mathematical Invitation
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Author : Michael Baake
language : en
Publisher: Cambridge University Press
Release Date : 2013-08-22
Aperiodic Order Volume 1 A Mathematical Invitation written by Michael Baake and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-08-22 with Mathematics categories.
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.
Aperiodic Order
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Author : Michael Baake
language : en
Publisher:
Release Date : 2013
Aperiodic Order written by Michael Baake and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013 with SCIENCE categories.
Geometry And Thermodynamics
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Author : J.C. Tolédano
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Geometry And Thermodynamics written by J.C. Tolédano and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.
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.
Discrete Geometry
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Author : Andras Bezdek
language : en
Publisher: CRC Press
Release Date : 2003-02-04
Discrete Geometry written by Andras Bezdek and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-02-04 with Mathematics categories.
Celebrating the work of Professor W. Kuperberg, this reference explores packing and covering theory, tilings, combinatorial and computational geometry, and convexity, featuring an extensive collection of problems compiled at the Discrete Geometry Special Session of the American Mathematical Society in New Orleans, Louisiana. Discrete Geometry analy
Polytopes And Discrete Geometry
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Author : Gabriel Cunningham
language : en
Publisher: American Mathematical Soc.
Release Date : 2021-04-06
Polytopes And Discrete Geometry written by Gabriel Cunningham 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 2021-04-06 with Education categories.
The papers showcase the breadth of discrete geometry through many new methods and results in a variety of topics. Also included are survey articles on some important areas of active research. This volume is aimed at researchers in discrete and convex geometry and researchers who work with abstract polytopes or string C C-groups. It is also aimed at early career mathematicians, including graduate students and postdoctoral fellows, to give them a glimpse of the variety and beauty of these research areas. Topics covered in this volume include: the combinatorics, geometry, and symmetries of convex polytopes; tilings; discrete point sets; the combinatorics of Eulerian posets and interval posets; symmetries of surfaces and maps on surfaces; self-dual polytopes; string C C-groups; hypertopes; and graph coloring.