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.
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.
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.
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 687 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.
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 452 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.
Download or read book Problems in Classical Electromagnetism written by Andrea Macchi and published by Springer Nature. This book was released on 2023-05-29 with total page 587 pages. Available in PDF, EPUB and Kindle. Book excerpt: This second edition adds 46 new problems, for a total of 203. The solutions to certain “old” problems have been revised for improved clarity, in response to questions and comments from our students (second-year students in the Master’s in Physics program). Each problem is given a title indicating its relation to the various areas of physics or technology. By tackling the problems presented here, students are gently introduced to advanced topics such as unipolar and homopolar motors, magnetic monopoles, radiation pressure, angular momentum of light, bulk and surface plasmons, and radiation friction. We also address a number of tricky concepts and apparent ambiguities and paradoxes encountered in the classical theory of electromagnetism, with a particular focus on conservation laws and transformation properties between different frames of reference. At the same time, the book can be used as an introduction to applications of classical electromagnetism including cutting-edge topics like plasmonics, metamaterials, and light-driven propulsion. While unnecessary mathematical complexity is avoided, the new edition also provides a few introductory examples concerning elegant and powerful solution techniques. Hopefully the second edition offers an even better teaching tool for undergraduates in physics, mathematics, and electric engineering, and a valuable reference guide for students planning to work in optics, material science, electronics, and plasma physics.
Download or read book Incompressible Bipolar and Non Newtonian Viscous Fluid Flow written by Hamid Bellout and published by Springer Science & Business Media. This book was released on 2013-11-19 with total page 583 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of incompressible multipolar viscous fluids is a non-Newtonian model of fluid flow, which incorporates nonlinear viscosity, as well as higher order velocity gradients, and is based on scientific first principles. The Navier-Stokes model of fluid flow is based on the Stokes hypothesis, which a priori simplifies and restricts the relationship between the stress tensor and the velocity. By relaxing the constraints of the Stokes hypothesis, the mathematical theory of multipolar viscous fluids generalizes the standard Navier-Stokes model. The rigorous theory of multipolar viscous fluids is compatible with all known thermodynamical processes and the principle of material frame indifference; this is in contrast with the formulation of most non-Newtonian fluid flow models which result from ad hoc assumptions about the relation between the stress tensor and the velocity. The higher-order boundary conditions, which must be formulated for multipolar viscous flow problems, are a rigorous consequence of the principle of virtual work; this is in stark contrast to the approach employed by authors who have studied the regularizing effects of adding artificial viscosity, in the form of higher order spatial derivatives, to the Navier-Stokes model. A number of research groups, primarily in the United States, Germany, Eastern Europe, and China, have explored the consequences of multipolar viscous fluid models; these efforts, and those of the authors, which are described in this book, have focused on the solution of problems in the context of specific geometries, on the existence of weak and classical solutions, and on dynamical systems aspects of the theory. This volume will be a valuable resource for mathematicians interested in solutions to systems of nonlinear partial differential equations, as well as to applied mathematicians, fluid dynamicists, and mechanical engineers with an interest in the problems of fluid mechanics.
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:
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.
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.
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.
Download or read book Solved Problems in Classical Electromagnetism written by J. Pierrus and published by Oxford University Press. This book was released on 2018-08-02 with total page 649 pages. Available in PDF, EPUB and Kindle. Book excerpt: Classical electromagnetism - one of the fundamental pillars of physics - is an important topic for all types of physicists from the theoretical to the applied. The subject is widely recognized to be one of the most challenging areas of the physics curriculum, both for students to learn and for lecturers to teach. Although textbooks on electromagnetism are plentiful, hardly any are written in the question-and-answer style format adopted in this book. It contains nearly 300 worked questions and solutions in classical electromagnetism, and is based on material usually encountered during the course of a standard university physics degree. Topics covered include some of the background mathematical techniques, electrostatics, magnetostatics, elementary circuit theory, electrodynamics, electromagnetic waves and electromagnetic radiation. For the most part the book deals with the microscopic theory, although we also introduce the important subject of macroscopic electromagnetism as well. Nearly all questions end with a series of comments whose purpose is to stimulate inductive reasoning and reach various important conclusions arising from the problem. Occasionally, points of historical interest are also mentioned. Both analytical and numerical techniques are used in obtaining and analyzing solutions. All computer calculations are performed with MathematicaCO® and the relevant code is provided in a notebook; either in the solution or the comments.
Download or read book Hyperbolic Conservation Laws in Continuum Physics written by Constantine M. Dafermos and published by Springer Science & Business Media. This book was released on 2006-01-16 with total page 636 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a lucid and authoritative exposition of the mathematical theory of hyperbolic system laws. The second edition contains a new chapter recounting exciting recent developments on the vanishing viscosity method. Numerous new sections introduce newly derived results. From the reviews: "The author is known as one of the leading experts in the field. His masterly written book is, surely, the most complete exposition in the subject of conservations laws." --Zentralblatt MATH
Download or read book Systems of Nonlinear Hyperbolic Equations Associated with Problems of Classical Electromagnetic Theory written by Frederick Bloom and published by . This book was released on 1982 with total page 34 pages. Available in PDF, EPUB and Kindle. Book excerpt: A survey is given of nonlinear phenomena in classical electromagnetic theory with the emphasis on singularity development in nonlinear materials and electromagnetic shock wave formation in nonlinear distributed parameter transmission lines. As influences on shock wave formation the author considers the mechanisms of anisotropy, nonlinear conduction, dispersion and relaxation. (Author).
Download or read book Interpretation of Classical Electromagnetism written by G. Rosser and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 443 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this book is to interpret all the laws of classical electromagnetism in a modern coherent way. In a typical undergraduate course using vector analysis, the students finally end up with Maxwell's equations, when they are often exhausted after a very long course, in which full discussions are properly given of the full range of applications of individual laws, each of which is important in its own right. As a result, many students do not appreciate how limited is the experimental evidence on the basis of which Maxwell's equations are normally developed and they do not always appre ciate the underlying unity of classical electromagnetism, before they go on to graduate courses in which Maxwell's equations are taken as axiomatic. This book is designed to be used between such an undergraduate course and graduate courses. It is written by an experimental physicist and is intended to be used by physicists, electrical engineers and applied mathematicians.
Download or read book Introduction to the Mathematical Physics of Nonlinear Waves written by Minoru Fujimoto and published by Morgan & Claypool Publishers. This book was released on 2014-03-01 with total page 217 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonlinear physics is a well-established discipline in physics today, and this book offers a comprehensive account of the basic soliton theory and its applications. Although primarily mathematical, the theory for nonlinear phenomena in practical environment
Download or read book Basic Mathematical Research for Electromagnetic Theory written by Morris Kline and published by . This book was released on 1958 with total page 28 pages. Available in PDF, EPUB and Kindle. Book excerpt: The objective of the research under this contract was to explore mathematical problems which arise in the field of theoretical electromagnetics, or to anticipate mathematical needs or methodology for electromagnetic problems. The Division of Electromagnetic Research has been tackling electromagnetic problems for a number of years and has found that many investigations have been hampered by the lack of available mathematical information or of methods.
