Download or read book Eigenfunctions of the Curl Operator Rotationally Invariant Helmholtz Theorem and Applications to Electromagnetic Theory and Fluid Dynamics written by H. E. Moses and published by . This book was released on 1970 with total page 60 pages. Available in PDF, EPUB and Kindle. Book excerpt: Air Force Requirements, such as the knowledge of the upper atmosphere environment of vehicles and the knowledge of the propagation characteristics of radio and radar signals, require the solutions of the equations of motion of fluid dynamics and of electromagnetic theory which are often very complicated. This report presents a new mathematical approach to the obtaining of such solutions. The vector field is represented in such a form that new techniques may be used to find the appropriate solutions. Some problems of fluid dynamics and electromagnetic theory are solved as an illustration of the new approach. In this report, eigenfunctions of the curl operator are introduced. The expansion of vector fields in terms of these eigenfunctions leads to a decomposition of such fields into three modes, one of which corresponds to an irrotational vector field, and two of which correspond to rotational circularly polarized vector fields of opposite signs of polarization. Under a rotation of coordinates, the three modes which are introduced in this fashion remain invariant. Hence the Helmholtz decomposition of vector fields has been introduced in an irreducible, rotationally invariant form. These expansions enable one to handle the curl and divergence operators simply. As illustrations of the use of the curl eigenfunctions, four problems are solved.
Download or read book Eigenfunctions of the Curl Operator Rotationally Invariant Helmholtz Theorem and Applications to Electromagnetic Theory and Fluid Dynamics written by H. E. Moses and published by . This book was released on 1970 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Air Force Requirements, such as the knowledge of the upper atmosphere environment of vehicles and the knowledge of the propagation characteristics of radio and radar signals, require the solutions of the equations of motion of fluid dynamics and of electromagnetic theory which are often very complicated. This report presents a new mathematical approach to the obtaining of such solutions. The vector field is represented in such a form that new techniques may be used to find the appropriate solutions. Some problems of fluid dynamics and electromagnetic theory are solved as an illustration of the new approach. In this report, eigenfunctions of the curl operator are introduced. The expansion of vector fields in terms of these eigenfunctions leads to a decomposition of such fields into three modes, one of which corresponds to an irrotational vector field, and two of which correspond to rotational circularly polarized vector fields of opposite signs of polarization. Under a rotation of coordinates, the three modes which are introduced in this fashion remain invariant. Hence the Helmholtz decomposition of vector fields has been introduced in an irreducible, rotationally invariant form. These expansions enable one to handle the curl and divergence operators simply. As illustrations of the use of the curl eigenfunctions, four problems are solved.
Download or read book Scattering And Biomedical Engineering Modeling And Applications Proceedings Of The Fifth International Workshop On Mathematical Methods In Scattering Theory And Biomedical Technology written by Dimitrios I Fotiadis and published by World Scientific. This book was released on 2002-08-01 with total page 472 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume deals with scattering theory, applied mathematics, modeling and biomedical engineering. Most of the papers describe mathematical methods, numerical solutions and models for well-known problems in those areas.The proceedings have been selected for coverage in:• Index to Scientific & Technical Proceedings (ISTP CDROM version / ISI Proceedings)
Download or read book Turbulence in Fluids written by Marcel Lesieur and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 520 pages. Available in PDF, EPUB and Kindle. Book excerpt: Turbulence is a dangerous topic which is often at the origin of serious fights in the scientific meetings devoted to it since it represents extremely different points of view, all of which have in common their complexity, as well as an inability to solve the problem. It is even difficult to agree on what exactly is the problem to be solved. Extremely schematically, two opposing points of view have been ad vocated during these last twenty years: the first one is "statistical", and tries to model the evolution of averaged quantities of the flow. This com munity, which has followed the glorious trail of Taylor and Kolmogorov, believes in the phenomenology of cascades, and strongly disputes the possibility of any coherence or order associated to turbulence. On the other bank of the river stands the "coherence among chaos" community, which considers turbulence from a purely deterministic po int of view, by studying either the behaviour of dynamical systems, or the stability of flows in various situations. To this community are also associated the experimentalists who seek to identify coherent structures in shear flows.
Download or read book Electromagnetic and Optical Pulse Propagation 2 written by Kurt E. Oughstun and published by Springer Science & Business Media. This book was released on 2010-07-23 with total page 841 pages. Available in PDF, EPUB and Kindle. Book excerpt: Electromagnetic & Optical Pulse Propagation presents a detailed, systematic treatment of the time-domain electromagnetics with application to the propagation of transient electromagnetic fields (including ultrawideband signals and ultrashort pulses) in homogeneous, isotropic media which exhibit both temporal frequency dispersion and attenuation. The development is mathematically rigorous with strict adherence to the fundamental physical principle of causality. Approximation methods are based upon mathematically well-defined asymptotic techniques that are based upon the saddle point method. A detailed description is given of the asymptotic expansions used. Meaningful exercises are given throughout the text to help the reader‘s understanding of the material, making the book a useful graduate level text in electromagnetic wave theory for both physics, electrical engineering and materials science programs. Both students and researchers alike will obtain a better understanding of time domain electromagnetics as it applies to electromagnetic radiation and wave propagation theory with applications to ground and foliage penetrating radar, medical imaging, communications, and the health and safety issues associated with ultrawideband pulsed fields. Volume 2 presents a detailed asymptotic description of plane wave pulse propagation in dielectric, conducting, and semiconducting materials as described by the classical Lorentz model of dielectric resonance, the Rocard-Powles-Debys model of orientational polarization, and the Drude model of metals. The rigorous description of the signal velocity of a pulse in a dispersive material is presented in connection with the question of superluminal pulse propagation.
Download or read book Bibliography with Abstracts of AFCRL Publications from 1 October to 31 December 1971 written by Air Force Cambridge Research Laboratories (U.S.) and published by . This book was released on 1972 with total page 158 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Advances in Applied Mechanics written by and published by Academic Press. This book was released on 1996-05-09 with total page 385 pages. Available in PDF, EPUB and Kindle. Book excerpt: This highly acclaimed series provides survey articles on the present state and future direction of research in important branches of applied mechanics.
Download or read book Scientific and Technical Aerospace Reports written by and published by . This book was released on 1970 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Mathematical Physics with Differential Equations written by Yisong Yang and published by Oxford University Press. This book was released on 2023-07-27 with total page 593 pages. Available in PDF, EPUB and Kindle. Book excerpt: Traditional literature in mathematical physics is clustered around classical mechanics, especially fluids and elasticity. This book reflects the modern development of theoretical physics in the areas of field theories: classical, quantum, and gravitational, in which differential equations play essential roles and offer powerful insight. Yang here presents a broad range of fundamental topics in theoretical and mathematical physics based on the viewpoint of differential equations. The subject areas covered include classical and quantum many-body problems, thermodynamics, electromagnetism, magnetic monopoles, special relativity, gauge field theories, general relativity, superconductivity, vortices and other topological solitons, and canonical quantization of fields, for which knowledge and use of linear and nonlinear differential equations are essential for comprehension. Much emphasis is given to the mathematical and physical content offering an appreciation of the interplay of mathematics and theoretical physics from the viewpoint of differential equations. Advanced methods and techniques of modern nonlinear functional analysis are kept to a minimum and each chapter is supplemented with a collection of exercises of varied depths making it an ideal resource for students and researchers alike.
Download or read book A Friendly Guide to Wavelets written by Gerald Kaiser and published by Springer Science & Business Media. This book was released on 1994-08-01 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is designed as a textbook for an introductory course on wavelet analysis and time-frequency analysis aimed at graduate students or advanced undergraduates in science and engineering. It can also be used as a self-study or reference book by practicing researchers in signal analysis and related areas. Since the expected audience is not presumed to have a high level of mathematical background, much of the needed analytical machinery is developed from the beginning. The only prerequisites for the first eight chapters are matrix theory, Fourier series, and Fourier integral transforms. Each of these chapters ends with a set of straightforward exercises designed to drive home the concepts just covered, and the many graphics should further facilitate absorption.
Download or read book Report on Research at AFCRL written by Air Force Cambridge Research Laboratories (U.S.) and published by . This book was released on 1970 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Mathematical Analysis of Deterministic and Stochastic Problems in Complex Media Electromagnetics written by G. F. Roach and published by Princeton University Press. This book was released on 2012-03-04 with total page 399 pages. Available in PDF, EPUB and Kindle. Book excerpt: Electromagnetic complex media are artificial materials that affect the propagation of electromagnetic waves in surprising ways not usually seen in nature. Because of their wide range of important applications, these materials have been intensely studied over the past twenty-five years, mainly from the perspectives of physics and engineering. But a body of rigorous mathematical theory has also gradually developed, and this is the first book to present that theory. Designed for researchers and advanced graduate students in applied mathematics, electrical engineering, and physics, this book introduces the electromagnetics of complex media through a systematic, state-of-the-art account of their mathematical theory. The book combines the study of well posedness, homogenization, and controllability of Maxwell equations complemented with constitutive relations describing complex media. The book treats deterministic and stochastic problems both in the frequency and time domains. It also covers computational aspects and scattering problems, among other important topics. Detailed appendices make the book self-contained in terms of mathematical prerequisites, and accessible to engineers and physicists as well as mathematicians.
Download or read book SIAM Journal on Applied Mathematics written by Society for Industrial and Applied Mathematics and published by . This book was released on 1966 with total page 690 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contains research articles on mathematical methods and their applications in the physical, engineering, biological, and medical sciences.
Download or read book Vertical Shear Modes in Inertial Waves on a Rotating Earth written by Harry E. Moses and published by . This book was released on 1970 with total page 26 pages. Available in PDF, EPUB and Kindle. Book excerpt: Knowledge and understanding of upper atmospheric winds (air motions) are important elements in the design and operation of vehicles traversing this regime. This report describes mathematically some of these air motions and relates them to observations made using chemical trails. (Author).
Download or read book Force free Magnetic Fields Curl Eigenfunctions and the Sphere in Transform Space with Applications to Fluid Dynamics and Electromagnetic Theory written by Malcolm A. MacLeod and published by . This book was released on 1993 with total page 36 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Reduced Stress Tensor and Dissipation and the Transport of Lamb Vector written by Jie-Zhi Wu and published by . This book was released on 1996 with total page 20 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Proceedings written by and published by . This book was released on 1993 with total page 706 pages. Available in PDF, EPUB and Kindle. Book excerpt: Publishes research papers in the mathematical and physical sciences. Continues: Proceedings of the Royal Society of London. Series A, Mathematical and physical sciences. Continued by: Proceedings. Mathematical, physical, and engineering sciences.
