Special Functions, KZ Type Equations, and Representation Theory
Special Functions, KZ Type Equations, and Representation Theory

Author: Aleksandr Nikolaevich Varchenko

Publisher: American Mathematical Soc.

Published: 2003

Total Pages: 130

ISBN-13: 0821828673

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The last twenty years have seen an active interaction between mathematics and physics. This book is devoted to one of the new areas which deals with mathematical structures related to conformal field theory and its sqs-deformations. In the book, the author discusses the interplay between Knizhnik-Zamolodchikov type equations, the Bethe ansatz method, representation theory, and geometry of multi-dimensional hypergeometric functions. This book aims to provide an introduction to the area and expose different facets of the subject. It contains constructions, discussions of notions, statements of main results, and illustrative examples. The exposition is restricted to the simplest case of the theory associated with the Lie algebra s\mathfrak{sl 2s. This book is intended for researchers and graduate students in mathematics and in mathematical physics, in particular to those interested in applications of special functions.

X-ray and Neutron Reflectivity
X-ray and Neutron Reflectivity

Author: Jean Daillant

Publisher: Springer

Published: 2008-11-19

Total Pages: 360

ISBN-13: 3540885889

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ways in which the magnetic interaction between neutrons and magnetic moments can yield information on the magnetization densities of thin ?lms and multilayers. I commend the organizers for having organized a group of expert lecturers to present this subject in a detailed but clear fashion, as the importance of the subject deserves. Argonne, IL S. K. Sinha Contents 1 The Interaction of X-Rays (and Neutrons) with Matter . . . . . . . . . . . . . . 1 F. de Bergevin 1. 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1. 2 Generalities and De?nitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1. 3 From the Scattering by an Object to the Propagation in a Medium . 14 1. 4 X-Rays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 1. 5 X-Rays: Anisotropic Scattering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 1. A Appendix: the Born Approximation . . . . . . . . . . . . . . . . . . . . . . . . . . 54 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 2 Statistical Aspects of Wave Scattering at Rough Surfaces . . . . . . . . . . . . 59 A. Sentenac and J. Daillant 2. 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 2. 2 Description of Randomly Rough Surfaces . . . . . . . . . . . . . . . . . . . . . 60 2. 3 Description of a Surface Scattering Experiment, Coherence Domains . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 2. 4 Statistical Formulation of the Diffraction Problem . . . . . . . . . . . . . . 72 2. 5 Statistical Formulation of the Scattered Intensity Under the Born Approximation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 3 Specular Re?ectivity from Smooth and Rough Surfaces . . . . . . . . . . . . . 85 A. Gibaud and G. Vignaud 3. 1 The Re?ected Intensity from an Ideally Flat Surface . . . . . . . . . . . . 85 3. 2 X-Ray Re?ectivity in Strati?ed Media . . . . . . . . . . . . . . . . . . . . . . . . 98 3. 3 From Dynamical to Kinematical Theory . . . . . . . . . . . . . . . . . . . . . . 107 3. 4 In?uence of the Roughness on the Matrix Coef?cients . . . . . . . . . . 111 3. A Appendix: The Treatment of Roughness in Specular Re?ectivity . . 113 3. B Appendix: Inversion of re?ectivity data . . . . . . . . . . . . . . . . . . . . . . .

Three-Dimensional Magnonics
Three-Dimensional Magnonics

Author: Gianluca Gubbiotti

Publisher: CRC Press

Published: 2019-07-10

Total Pages: 261

ISBN-13: 1000024547

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Magnonics, a research field that uses spin waves, collective excitations of ordered magnetic materials, or magnons (their quanta) as a tool for signal processing, communication, and computation, has rapidly grown during the past decade because of the low-energy consumption and potential compatibility with next-generation circuits beyond CMOS electronics. The interest in 3D magnonic nanostructures follows the latest trend in conventional electronics based on expansion from 2D planar to 3D vertically integrated structures. To remain on the same technological level, a similar expansion should be realized in magnonics. Following this trend, this book provides an overview of recent developments in the exploitation of the third dimension in magnonics, with special focus on the propagation of spin waves in layered magnonic crystals, spin textures, curved surfaces, 3D nano-objects, and cavity magnonics.

Dynamics of Rail Transit Tunnel Systems
Dynamics of Rail Transit Tunnel Systems

Author: Shunhua Zhou

Publisher: Academic Press

Published: 2019-04-15

Total Pages: 277

ISBN-13: 0128183837

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Dynamics of Rail Transit Tunnel Systems develops the dynamic theory of a rail transit tunnel system and provides research methods for the evaluation of long-term settlement of rail transit tunnels in soft soil, the service performance of tunnel structures, and the characterization of environmental vibration induced by trains. In recent years, a large number of rail transit tunnels have been constructed and put into operation, particularly in China. To evaluate the time-dependent degradation of tunnel structures and train-induced environmental vibration, a reliable model must be established to determine the dynamic response of a vehicle-track-tunnel-soil system, hence the introduction of this timely resource. - Provides full theoretical background to help the reader gain an in-depth understanding of the various methods used for dynamic analysis of a rail transit tunnel system - Develops the dynamics theory and method of a rail transit tunnel system under the context of challenging engineering problems - Presents methods for analyzing the dynamic responses of rail transit tunnel-soil systems - Looks at problems that need to be solved in the future and proposes potential directions for future research

Spin-orbit Coupling Effects in Two-Dimensional Electron and Hole Systems
Spin-orbit Coupling Effects in Two-Dimensional Electron and Hole Systems

Author: Roland Winkler

Publisher: Springer

Published: 2003-10-06

Total Pages: 228

ISBN-13: 3540366164

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The first part provides a general introduction to the electronic structure of quasi-two-dimensional systems with a particular focus on group-theoretical methods. The main part of the monograph is devoted to spin-orbit coupling phenomena at zero and nonzero magnetic fields. Throughout the book, the main focus is on a thorough discussion of the physical ideas and a detailed interpretation of the results. Accurate numerical calculations are complemented by simple and transparent analytical models that capture the important physics.