Download or read book Aperiodic Order and Spectral Properties written by Michael Baake and published by . This book was released on 2017 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book On the Spectral Properties of Quasicrystals and Other Deterministic Aperiodic Structures written by Bibek Kafle and published by . This book was released on 2013 with total page 73 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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.
Download or read book Optics of Aperiodic Structures written by Luca Dal Negro and published by CRC Press. This book was released on 2013-12-21 with total page 512 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Download or read book The Mathematics of Long Range Aperiodic Order written by R.V. Moody and published by Springer. This book was released on 1997-03-31 with total page 556 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Aperiodic Order 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: A comprehensive introductory monograph on the theory of aperiodic order, with numerous illustrations and examples.
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.
Download or read book Dynamical And Complex Systems written by Shaun Bullett and published by World Scientific. This book was released on 2016-12-22 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book leads readers from a basic foundation to an advanced level understanding of dynamical and complex systems. It is the perfect text for graduate or PhD mathematical-science students looking for support in topics such as applied dynamical systems, Lotka-Volterra dynamical systems, applied dynamical systems theory, dynamical systems in cosmology, aperiodic order, and complex systems dynamics.Dynamical and Complex Systems is the fifth volume of the LTCC Advanced Mathematics Series. This series is the first to provide advanced introductions to mathematical science topics to advanced students of mathematics. Edited by the three joint heads of the London Taught Course Centre for PhD Students in the Mathematical Sciences (LTCC), each book supports readers in broadening their mathematical knowledge outside of their immediate research disciplines while also covering specialized key areas.
Download or read book Quasicrystals written by Hans-Rainer Trebin and published by John Wiley & Sons. This book was released on 2006-05-12 with total page 668 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Quasicrystals written by Enrique Maciá-Barber and published by CRC Press. This book was released on 2020-12-17 with total page 403 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an interdisciplinary guide to quasicrystals, the 2011 Nobel Prize in Chemistry winning topic, by presenting an up-to-date and detailed introduction to the many fundamental aspects and applications of quasicrystals science. It reviews the most characteristic features of the peculiar geometric order underlying their structure and their reported intrinsic physical properties, along with their potential for specific applications. The role of quasiperiodic order in science and technology is also examined by focusing on the new design capabilities provided by this novel ordering of matter. This book is specifically devoted to 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.
Download or read book Analysis and Geometry on Graphs and Manifolds written by Matthias Keller and published by Cambridge University Press. This book was released on 2020-08-20 with total page 493 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book addresses the interplay between several rapidly expanding areas of mathematics. Suitable for graduate students as well as researchers, it provides surveys of topics linking geometry, spectral theory and stochastics.
Download or read book Aperiodic Structures in Condensed Matter written by Enrique Macia Barber and published by CRC Press. This book was released on 2008-11-21 with total page 457 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
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.
Download or read book Fields Networks Computational Methods and Systems in Modern Electrodynamics written by Peter Russer and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: On June 1St 2004 the Faculty of Electrical Engineering and Information Technology of the Technische Universitat Miinchen bestowed the degree of the doctor honoris causa to Leopold B. Felsen, for extraordinary achievements in the theory of electromag netic fields. On this occasion on June 1St and 2nd 2004 at the Technische Universitat Miinchen a symposium on "Fields, Networks, Computational Methods, and Systems: A Modern View of Engineering Electrodynamics" in honor of Leopold B. Felsen was organized. The symposium topic focused on an important area of Leopold Felsen research interests and, as the title emphasizes, on a modern view of applied Electro dynamics. While the fundamental physical laws of electrodynamics are well known, research in this field is experiencing a steady continuous growth. The problem -solving approaches of, say, twenty years ago may seem now fairly obsolete since considerable progress has been made in the meantime. In this monograph we collect samples of present day state of the art in dealing with electromagnetic fields, their network theory representation, their computation and, finally, on system applications. The network formulation of field problems can improve the problem formulation and also contribute to the solution methodology. Network theory systematic approaches for circuit analysis are based on the separation of the circuit into the connection circuit and the circuit elements. Many applications in science and technology rely on computations of the electromagnetic field in either man-made or natural complex structures.
Download or read book Light Localisation and Lasing written by Mher Ghulinyan and published by Cambridge University Press. This book was released on 2015 with total page 261 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents research on quasi-random and random photonic systems for graduate students and researchers in optics, photonics and optical engineering.
Download or read book Waves in Complex Media written by Luca Dal Negro and published by . This book was released on 2022-05-04 with total page 714 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a clear and interdisciplinary introduction to the structural and scattering properties of complex photonic media, focusing on deterministic aperiodic structures and their conceptual roots in geometry and number theory. It integrates important results and recent developments into a coherent and physically consistent story, balanced between mathematical designs, scattering and optical theories, and engineering device applications. The book includes discussions of emerging device applications in metamaterials and nano-optics technology. Both academia and industry will find the book of interest as it develops the underlying physical and mathematical background in partnership with engineering applications, providing a perspective on both fundamental optical sciences and photonic device technology. Emphasizing the comprehension of physical concepts and their engineering implications over the more formal developments, this is an essential introduction to the stimulating and fast-growing field of aperiodic optics and complex photonics.
Download or read book Plasmonics Theory and Applications written by Tigran V. Shahbazyan and published by Springer Science & Business Media. This book was released on 2014-01-09 with total page 581 pages. Available in PDF, EPUB and Kindle. Book excerpt: This contributed volume summarizes recent theoretical developments in plasmonics and its applications in physics, chemistry, materials science, engineering, and medicine. It focuses on recent advances in several major areas of plasmonics including plasmon-enhanced spectroscopies, light scattering, many-body effects, nonlinear optics, and ultrafast dynamics. The theoretical and computational methods used in these investigations include electromagnetic calculations, density functional theory calculations, and nonequilibrium electron dynamics calculations. The book presents a comprehensive overview of these methods as well as their applications to various current problems of interest.
