On the Scattering of Electromagnetic Waves by Perfectly Conducting Bodies Moving in Vacuum. Part 6. Manifolds in Euclidean Spaces, Regularity Properties of Domains PDF Download
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Author: A. G. Dallas Publisher: ISBN: Category : Languages : en Pages : 190
Book Description
Various standard results concerning manifolds in euclidean spaces, coordinate systems, and functions defined on such manifolds are developed and organized. For example, conditions are identified under which the image of a manifold is again a manifold. A development of Lebesgue measure and integration on a manifold is presented. Included is a change-of-variables formula for the transformation of an integral over a manifold to integration over a second manifold suitably related to the first. Classes of regular domains are defined. Special attention is given to those regular domains possessing a Holder-continuous exterior unit normal field, or Lyapunov domains. Slightly modifying the standard presentations, geometric and analytic properties of the boundary of a Lyapunov domain are derived, including the identification of certain canonical tangent-plane coordinate systems. (Author).
Author: A. G. Dallas Publisher: ISBN: Category : Languages : en Pages : 190
Book Description
Various standard results concerning manifolds in euclidean spaces, coordinate systems, and functions defined on such manifolds are developed and organized. For example, conditions are identified under which the image of a manifold is again a manifold. A development of Lebesgue measure and integration on a manifold is presented. Included is a change-of-variables formula for the transformation of an integral over a manifold to integration over a second manifold suitably related to the first. Classes of regular domains are defined. Special attention is given to those regular domains possessing a Holder-continuous exterior unit normal field, or Lyapunov domains. Slightly modifying the standard presentations, geometric and analytic properties of the boundary of a Lyapunov domain are derived, including the identification of certain canonical tangent-plane coordinate systems. (Author).
Author: A. G. Dallas Publisher: ISBN: Category : Languages : en Pages : 310
Book Description
The problem of determining the scattered electromagnetic field produced when an initially quiescent incident field impinges upon a perfectly conducting body moving and deforming in vacuum is originally formulated as an initial-boundary-value problem for Maxwell's equations in a noncylindrical exterior domain in space-time. The motion and deformation of the scatterer are allowed to be fairly general, the essential hypotheses being that the boundry of its space-time track is smooth and can be mapped and smoothly onto a cylinder, while the speeds of points on the body must remain less than that of light in vacuum. Within this setting, uniqueness theorems are proven for various initial-boundary-value problems for a system of generalized Maxwell equations (in particular, for the scattering problem), and for the scalar wave equation, in noncylindrical domains.
Author: Franck Assous Publisher: Springer ISBN: 3319708422 Category : Mathematics Languages : en Pages : 460
Book Description
This book presents an in-depth treatment of various mathematical aspects of electromagnetism and Maxwell's equations: from modeling issues to well-posedness results and the coupled models of plasma physics (Vlasov-Maxwell and Vlasov-Poisson systems) and magnetohydrodynamics (MHD). These equations and boundary conditions are discussed, including a brief review of absorbing boundary conditions. The focus then moves to well‐posedness results. The relevant function spaces are introduced, with an emphasis on boundary and topological conditions. General variational frameworks are defined for static and quasi-static problems, time-harmonic problems (including fixed frequency or Helmholtz-like problems and unknown frequency or eigenvalue problems), and time-dependent problems, with or without constraints. They are then applied to prove the well-posedness of Maxwell’s equations and their simplified models, in the various settings described above. The book is completed with a discussion of dimensionally reduced models in prismatic and axisymmetric geometries, and a survey of existence and uniqueness results for the Vlasov-Poisson, Vlasov-Maxwell and MHD equations. The book addresses mainly researchers in applied mathematics who work on Maxwell’s equations. However, it can be used for master or doctorate-level courses on mathematical electromagnetism as it requires only a bachelor-level knowledge of analysis.
Author: Alexander Altland Publisher: Cambridge University Press ISBN: 0521769752 Category : Science Languages : en Pages : 785
Book Description
This primer is aimed at elevating graduate students of condensed matter theory to a level where they can engage in independent research. Topics covered include second quantisation, path and functional field integration, mean-field theory and collective phenomena.
Author: Karl Johan Åström Publisher: Princeton University Press ISBN: 069121347X Category : Technology & Engineering Languages : en Pages :
Book Description
The essential introduction to the principles and applications of feedback systems—now fully revised and expanded This textbook covers the mathematics needed to model, analyze, and design feedback systems. Now more user-friendly than ever, this revised and expanded edition of Feedback Systems is a one-volume resource for students and researchers in mathematics and engineering. It has applications across a range of disciplines that utilize feedback in physical, biological, information, and economic systems. Karl Åström and Richard Murray use techniques from physics, computer science, and operations research to introduce control-oriented modeling. They begin with state space tools for analysis and design, including stability of solutions, Lyapunov functions, reachability, state feedback observability, and estimators. The matrix exponential plays a central role in the analysis of linear control systems, allowing a concise development of many of the key concepts for this class of models. Åström and Murray then develop and explain tools in the frequency domain, including transfer functions, Nyquist analysis, PID control, frequency domain design, and robustness. Features a new chapter on design principles and tools, illustrating the types of problems that can be solved using feedback Includes a new chapter on fundamental limits and new material on the Routh-Hurwitz criterion and root locus plots Provides exercises at the end of every chapter Comes with an electronic solutions manual An ideal textbook for undergraduate and graduate students Indispensable for researchers seeking a self-contained resource on control theory
Author: Diego Dalvit Publisher: Springer Science & Business Media ISBN: 364220287X Category : Science Languages : en Pages : 465
Book Description
Casimir effects serve as primary examples of directly observable manifestations of the nontrivial properties of quantum fields, and as such are attracting increasing interest from quantum field theorists, particle physicists, and cosmologists. Furthermore, though very weak except at short distances, Casimir forces are universal in the sense that all material objects are subject to them. They are thus also an increasingly important part of the physics of atom-surface interactions, while in nanotechnology they are being investigated not only as contributors to ‘stiction’ but also as potential mechanisms for actuating micro-electromechanical devices. While the field of Casimir physics is expanding rapidly, it has reached a level of maturity in some important respects: on the experimental side, where most sources of imprecision in force measurements have been identified as well as on the theoretical side, where, for example, semi-analytical and numerical methods for the computation of Casimir forces between bodies of arbitrary shape have been successfully developed. This book is, then, a timely and comprehensive guide to the essence of Casimir (and Casimir-Polder) physics that will have lasting value, serving the dual purpose of an introduction and reference to the field. While this volume is not intended to be a unified textbook, but rather a collection of largely independent chapters written by prominent experts in the field, the detailed and carefully written articles adopt a style that should appeal to non-specialist researchers in the field as well as to a broader audience of graduate students.
Author: Sandro Salsa Publisher: Springer ISBN: 3319150936 Category : Mathematics Languages : en Pages : 714
Book Description
The book is intended as an advanced undergraduate or first-year graduate course for students from various disciplines, including applied mathematics, physics and engineering. It has evolved from courses offered on partial differential equations (PDEs) over the last several years at the Politecnico di Milano. These courses had a twofold purpose: on the one hand, to teach students to appreciate the interplay between theory and modeling in problems arising in the applied sciences, and on the other to provide them with a solid theoretical background in numerical methods, such as finite elements. Accordingly, this textbook is divided into two parts. The first part, chapters 2 to 5, is more elementary in nature and focuses on developing and studying basic problems from the macro-areas of diffusion, propagation and transport, waves and vibrations. In turn the second part, chapters 6 to 11, concentrates on the development of Hilbert spaces methods for the variational formulation and the analysis of (mainly) linear boundary and initial-boundary value problems.
Author: B. Andrei Bernevig Publisher: Princeton University Press ISBN: 1400846730 Category : Science Languages : en Pages : 264
Book Description
This graduate-level textbook is the first pedagogical synthesis of the field of topological insulators and superconductors, one of the most exciting areas of research in condensed matter physics. Presenting the latest developments, while providing all the calculations necessary for a self-contained and complete description of the discipline, it is ideal for graduate students and researchers preparing to work in this area, and it will be an essential reference both within and outside the classroom. The book begins with simple concepts such as Berry phases, Dirac fermions, Hall conductance and its link to topology, and the Hofstadter problem of lattice electrons in a magnetic field. It moves on to explain topological phases of matter such as Chern insulators, two- and three-dimensional topological insulators, and Majorana p-wave wires. Additionally, the book covers zero modes on vortices in topological superconductors, time-reversal topological superconductors, and topological responses/field theory and topological indices. The book also analyzes recent topics in condensed matter theory and concludes by surveying active subfields of research such as insulators with point-group symmetries and the stability of topological semimetals. Problems at the end of each chapter offer opportunities to test knowledge and engage with frontier research issues. Topological Insulators and Topological Superconductors will provide graduate students and researchers with the physical understanding and mathematical tools needed to embark on research in this rapidly evolving field.
Author: A. G. Dallas
Author: A. G. Dallas
Author: 
Author: A. G. Dallas
Author: 
Author: Franck Assous
Author: Alexander Altland
Author: Karl Johan Åström
Author: Diego Dalvit
Author: Sandro Salsa
Author: B. Andrei Bernevig