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Mathematical Problems Of Classical Nonlinear Electromagnetic Theory
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Book Synopsis Mathematical Problems of Classical Nonlinear Electromagnetic Theory by : Frederick Bloom
Download or read book Mathematical Problems of Classical Nonlinear Electromagnetic Theory written by Frederick Bloom and published by CRC Press. This book was released on 2020-11-29 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt: A survey of some problems of current interest in the realm of classical nonlinear electromagnetic theory.
Book Synopsis Mathematical Problems of Classical Nonlinear Electromagnetic Theory by : Frederick Bloom
Download or read book Mathematical Problems of Classical Nonlinear Electromagnetic Theory written by Frederick Bloom and published by CRC Press. This book was released on 2020-11-29 with total page 412 pages. Available in PDF, EPUB and Kindle. Book excerpt: A survey of some problems of current interest in the realm of classical nonlinear electromagnetic theory.
Book Synopsis Mathematical Methods of Electromagnetic Theory by : Kurt O. Friedrichs
Download or read book Mathematical Methods of Electromagnetic Theory written by Kurt O. Friedrichs and published by American Mathematical Soc.. This book was released on 2014-11-12 with total page 159 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text provides a mathematically precise but intuitive introduction to classical electromagnetic theory and wave propagation, with a brief introduction to special relativity. While written in a distinctive, modern style, Friedrichs manages to convey the physical intuition and 19th century basis of the equations, with an emphasis on conservation laws. Particularly striking features of the book include: (a) a mathematically rigorous derivation of the interaction of electromagnetic waves with matter, (b) a straightforward explanation of how to use variational principles to solve problems in electro- and magnetostatics, and (c) a thorough discussion of the central importance of the conservation of charge. It is suitable for advanced undergraduate students in mathematics and physics with a background in advanced calculus and linear algebra, as well as mechanics and electromagnetics at an undergraduate level. Apart from minor corrections to the text, the notation was updated in this edition to follow the conventions of modern vector calculus. Titles in this series are co-published with the Courant Institute of Mathematical Sciences at New York University.
Book Synopsis Neoclassical Theory of Electromagnetic Interactions by : Anatoli Babin
Download or read book Neoclassical Theory of Electromagnetic Interactions written by Anatoli Babin and published by Springer. This book was released on 2016-08-04 with total page 696 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this monograph, the authors present their recently developed theory of electromagnetic interactions. This neoclassical approach extends the classical electromagnetic theory down to atomic scales and allows the explanation of various non-classical phenomena in the same framework. While the classical Maxwell–Lorentz electromagnetism theory succeeds in describing the physical reality at macroscopic scales, it struggles at atomic scales. Here, quantum mechanics traditionally takes over to describe non-classical phenomena such as the hydrogen spectrum and de Broglie waves. By means of modifying the classical theory, the approach presented here is able to consistently explain quantum-mechanical effects, and while similar to quantum mechanics in some respects, this neoclassical theory also differs markedly from it. In particular, the newly developed framework omits probabilistic interpretations of the wave function and features a new fundamental spatial scale which, at the size of the free electron, is much larger than the classical electron radius and is relevant to plasmonics and emission physics. This book will appeal to researchers interested in advanced aspects of electromagnetic theory. Treating the classical approach in detail, including non-relativistic aspects and the Lagrangian framework, and comparing the neoclassical theory with quantum mechanics and the de Broglie–Bohm theory, this work is completely self-contained.
Book Synopsis Problems in Classical Electromagnetism by : Andrea Macchi
Download or read book Problems in Classical Electromagnetism written by Andrea Macchi and published by Springer. This book was released on 2017-12-10 with total page 454 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains 157 problems in classical electromagnetism, most of them new and original compared to those found in other textbooks. Each problem is presented with a title in order to highlight its inspiration in different areas of physics or technology, so that the book is also a survey of historical discoveries and applications of classical electromagnetism. The solutions are complete and include detailed discussions, which take into account typical questions and mistakes by the students. Without unnecessary mathematical complexity, the problems and related discussions introduce the student to advanced concepts such as unipolar and homopolar motors, magnetic monopoles, radiation pressure, angular momentum of light, bulk and surface plasmons, radiation friction, as well as to tricky concepts and ostensible ambiguities or paradoxes related to the classical theory of the electromagnetic field. With this approach the book is both a teaching tool for undergraduates in physics, mathematics and electric engineering, and a reference for students wishing to work in optics, material science, electronics, plasma physics.
Book Synopsis Classical Theory Of Electromagnetism (Third Edition) by : Di Bartolo Baldassare
Download or read book Classical Theory Of Electromagnetism (Third Edition) written by Di Bartolo Baldassare and published by World Scientific. This book was released on 2018-06-13 with total page 720 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Ill-posed Problems for Integrodifferential Equations in Mechanics and Electromagnetic Theory by : Frederick Bloom
Download or read book Ill-posed Problems for Integrodifferential Equations in Mechanics and Electromagnetic Theory written by Frederick Bloom and published by SIAM. This book was released on 1981-01-01 with total page 231 pages. Available in PDF, EPUB and Kindle. Book excerpt: Examines ill-posed, initial-history boundary-value problems associated with systems of partial-integrodifferential equations arising in linear and nonlinear theories of mechanical viscoelasticity, rigid nonconducting material dielectrics, and heat conductors with memory. Variants of two differential inequalities, logarithmic convexity, and concavity are employed. Ideas based on energy arguments, Riemann invariants, and topological dynamics applied to evolution equations are also introduced. These concepts are discussed in an introductory chapter and applied there to initial boundary value problems of linear and nonlinear diffusion and elastodynamics. Subsequent chapters begin with an explanation of the underlying physical theories.
Book Synopsis The Classical Theory of Fields by : Carl S. Helrich
Download or read book The Classical Theory of Fields written by Carl S. Helrich and published by Springer Science & Business Media. This book was released on 2012-01-11 with total page 445 pages. Available in PDF, EPUB and Kindle. Book excerpt: The study of classical electromagnetic fields is an adventure. The theory is complete mathematically and we are able to present it as an example of classical Newtonian experimental and mathematical philosophy. There is a set of foundational experiments, on which most of the theory is constructed. And then there is the bold theoretical proposal of a field-field interaction from James Clerk Maxwell. This textbook presents the theory of classical fields as a mathematical structure based solidly on laboratory experiments. Here the student is introduced to the beauty of classical field theory as a gem of theoretical physics. To keep the discussion fluid, the history is placed in a beginning chapter and some of the mathematical proofs in the appendices. Chapters on Green’s Functions and Laplace’s Equation and a discussion of Faraday’s Experiment further deepen the understanding. The chapter on Einstein’s relativity is an integral necessity to the text. Finally, chapters on particle motion and waves in a dispersive medium complete the picture. High quality diagrams and detailed end-of-chapter questions enhance the learning experience.
Book Synopsis Nonlinear and Inverse Problems in Electromagnetics by : L. Beilina
Download or read book Nonlinear and Inverse Problems in Electromagnetics written by L. Beilina and published by Springer. This book was released on 2018-07-19 with total page 145 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume provides academic discussion on the theory and practice of mathematical analysis of nonlinear and inverse problems in electromagnetics and their applications. From mathematical problem statement to numerical results, the featured articles provide a concise overview of comprehensive approaches to the solution of problems. Articles highlight the most recent research concerning reliable theoretical approaches and numerical techniques and cover a wide range of applications, including acoustics, electromagnetics, optics, medical imaging, and geophysics. The nonlinear and ill-posed nature of inverse problems and the challenges they present when developing new numerical methods are explained, and numerical verification of proposed new methods on simulated and experimental data is provided. Based on the special session of the same name at the 2017 Progress in Electromagnetics Research Symposium, this book offers a platform for interaction between theoretical and practical researchers and between senior and incoming members in the field.
Book Synopsis Electromagnetism by : Michael K. h. Kiessling
Download or read book Electromagnetism written by Michael K. h. Kiessling and published by Birkhauser. This book was released on 2007 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Electromagnetism of Continuous Media by : Mauro Fabrizio
Download or read book Electromagnetism of Continuous Media written by Mauro Fabrizio and published by Oxford University Press. This book was released on 2003-06-05 with total page 690 pages. Available in PDF, EPUB and Kindle. Book excerpt: The wide application of technologies in new mechanical, electronic and biomedical systems calls for materials and structures with non-conventional properties (e.g materials with 'memory'). Of equal importance is the understanding of the physical behaviour of these materials and consequently developing mathematical modelling techniques for prediction. This self contained text discusses the mathematical modelling used with these types of electromagnetic materials. It provides a carefully structured, coherent, and comprehensive treatment of electromagnetism of continuous media. The authors provide a systematic review of known subjects along with original results about thermodynamics of electromagnetic materials, well-posedness of initial boundary-value problems, variational settings, and wave propagation. Models of non-linear materials, non-local materials (superconductors), and hysteretic (magnetic) materials are also developed in detail.
Book Synopsis Shock Formation in Small-Data Solutions to 3D Quasilinear Wave Equations by : Jared Speck
Download or read book Shock Formation in Small-Data Solutions to 3D Quasilinear Wave Equations written by Jared Speck and published by American Mathematical Soc.. This book was released on 2016-12-07 with total page 544 pages. Available in PDF, EPUB and Kindle. Book excerpt: In 1848 James Challis showed that smooth solutions to the compressible Euler equations can become multivalued, thus signifying the onset of a shock singularity. Today it is known that, for many hyperbolic systems, such singularities often develop. However, most shock-formation results have been proved only in one spatial dimension. Serge Alinhac's groundbreaking work on wave equations in the late 1990s was the first to treat more than one spatial dimension. In 2007, for the compressible Euler equations in vorticity-free regions, Demetrios Christodoulou remarkably sharpened Alinhac's results and gave a complete description of shock formation. In this monograph, Christodoulou's framework is extended to two classes of wave equations in three spatial dimensions. It is shown that if the nonlinear terms fail to satisfy the null condition, then for small data, shocks are the only possible singularities that can develop. Moreover, the author exhibits an open set of small data whose solutions form a shock, and he provides a sharp description of the blow-up. These results yield a sharp converse of the fundamental result of Christodoulou and Klainerman, who showed that small-data solutions are global when the null condition is satisfied. Readers who master the material will have acquired tools on the cutting edge of PDEs, fluid mechanics, hyperbolic conservation laws, wave equations, and geometric analysis.
Book Synopsis Completeness of Root Functions of Regular Differential Operators by : Sasun Yakubov
Download or read book Completeness of Root Functions of Regular Differential Operators written by Sasun Yakubov and published by CRC Press. This book was released on 1993-12-20 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: The precise mathematical investigation of various natural phenomena is an old and difficult problem. This book is the first to deal systematically with the general non-selfadjoint problems in mechanics and physics. It deals mainly with bounded domains with smooth boundaries, but also considers elliptic boundary value problems in tube domains, i.e. in non-smooth domains. This volume will be of particular value to those working in differential equations, functional analysis, and equations of mathematical physics.
Book Synopsis The Classical Electromagnetic Field by : Leonard Eyges
Download or read book The Classical Electromagnetic Field written by Leonard Eyges and published by Courier Corporation. This book was released on 2012-06-11 with total page 452 pages. Available in PDF, EPUB and Kindle. Book excerpt: This excellent text covers a year's course. Topics include vectors D and H inside matter, conservation laws for energy, momentum, invariance, form invariance, covariance in special relativity, and more.
Book Synopsis Nonlinear Electromagnetics by : Piergiorgio Uslenghi
Download or read book Nonlinear Electromagnetics written by Piergiorgio Uslenghi and published by Elsevier. This book was released on 2012-12-02 with total page 437 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonlinear Electromagnetics is a collection of research papers from different areas of study related to the nonlinear phenomena in electromagnetism. The book, after giving a short introduction to some mathematical techniques for nonlinear problems, covers related topics such as the history of particle physics; a physical description of the spectral transform; solitons in randomly inhomogenous media; and localized wave fields in nonlinear dispersive media. Also covered in this book are topics such as non-linear plasma-wave interaction; Lagrangian methods; electromagnetic problems in composite materials in linear and nonlinear regimes; and stationary regimes in passive nonlinear methods. The text is recommended for physicists and engineers interested in the development and applications of nonlinear electromagnetic and the mathematical expressions behind it.
Book Synopsis Foundations of Classical Electrodynamics by : Friedrich W Hehl
Download or read book Foundations of Classical Electrodynamics written by Friedrich W Hehl and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 405 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book we display the fundamental structure underlying classical electro dynamics, i. e. , the phenomenological theory of electric and magnetic effects. The book can be used as a textbook for an advanced course in theoretical electrodynamics for physics and mathematics students and, perhaps, for some highly motivated electrical engineering students. We expect from our readers that they know elementary electrodynamics in the conventional (1 + 3)-dimensional form including Maxwell's equations. More over, they should be familiar with linear algebra and elementary analysis, in cluding vector analysis. Some knowledge of differential geometry would help. Our approach rests on the metric-free integral formulation of the conservation laws of electrodynamics in the tradition of F. Kottler (1922), E. Cartan (1923), and D. van Dantzig (1934), and we stress, in particular, the axiomatic point of view. In this manner we are led to an understanding of why the Maxwell equa tions have their specific form. We hope that our book can be seen in the classical tradition of the book by E. J. Post (1962) on the Formal Structure of Electro magnetics and of the chapter "Charge and Magnetic Flux" of the encyclopedia article on classical field theories by C. Truesdell and R. A. Toupin (1960), in cluding R. A. Toupin's Bressanone lectures (1965); for the exact references see the end of the introduction on page 11. .
Book Synopsis Mathematical Methods in Electromagnetism by : M Cessenat
Download or read book Mathematical Methods in Electromagnetism written by M Cessenat and published by World Scientific. This book was released on 1996-07-13 with total page 396 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides the reader with basic tools to solve problems of electromagnetism in their natural functional frameworks thanks to modern mathematical methods: integral surface methods, and also semigroups, variational methods, etc., well adapted to a numerical approach. As examples of applications of these tools and concepts, we solve several fundamental problems of electromagnetism, stationary or time-dependent: scattering of an incident wave by an obstacle, bounded or not, by gratings; wave propagation in a waveguide, with junctions and cascades. We hope that mathematical notions will allow a better understanding of modelization in electromagnetism and emphasize the essential features related to the geometry and nature of materials. Contents:Mathematical Modelling of the Electromagnetic Field in Continuous Media: Maxwell Equations and Constitutive RelationsMathematical Framework for ElectromagnetismStationary Scattering Problems with Bounded ObstaclesWaveguide ProblemsStationary Scattering Problems on Unbounded ObstaclesEvolution ProblemsAppendix — Differential Geometry for ElectromagnetismReferencesIndexNotations Readership: Applied mathematicians. keywords:Electromagnetism;Mathematical Modeling;Maxwell Equations;Variational Methods;Differential Geometry;Hodge Decomposition;Impedance Operators;Calderon Operators;Waveguides;Scattering;Outgoing Waves;Causal Problems “I would recommend it to anyone interested in the analysis or numerical analysis of Maxwell's equations for its up-to-date and extensive treatment of the problem.” SIAM Reviews
