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Variational Principles in Dynamics and Quantum Theory
Par Wolfgang Yourgrau, Stanley Mandelstam. 1968
Concentrating upon applications that are most relevant to modern physics, this valuable book surveys variational principles and examines their relationship…
to dynamics and quantum theory. Stressing the history and theory of these mathematical concepts rather than the mechanics, the authors provide many insights into the development of quantum mechanics and present much hard-to-find material in a remarkably lucid, compact form.After summarizing the historical background from Pythagoras to Francis Bacon, Professors Yourgrau and Mandelstram cover Fermat's principle of least time, the principle of least action of Maupertuis, development of this principle by Euler and Lagrange, and the equations of Lagrange and Hamilton. Equipped by this thorough preparation to treat variational principles in general, they proceed to derive Hamilton's principle, the Hamilton-Jacobi equation, and Hamilton's canonical equations.An investigation of electrodynamics in Hamiltonian form covers next, followed by a resume of variational principles in classical dynamics. The authors then launch into an analysis of their most significant topics: the relation between variational principles and wave mechanics, and the principles of Feynman and Schwinger in quantum mechanics. Two concluding chapters extend the discussion to hydrodynamics and natural philosophy.Professional physicists, mathematicians, and advanced students with a strong mathematical background will find this stimulating volume invaluable reading. Extremely popular in its hardcover edition, this volume will find even wider appreciation in its first fine inexpensive paperbound edition.Electromagnetic Fields and Waves
Par Vladimir Rojansky. 1971
Intended for advanced undergraduate and graduate students, this well-known and popular textbook provides an introduction to the physical principles, mathematical…
apparatus, and typical applications of classical electromagnetic theory. Beginning with the notion of scalar fields, Professor Rojansky leads the student through vectors and vector fields, the laws of Ohm, Joule, Coulomb, and Faraday, static electricity, and continues all the way to Maxwell's equations for bodies at rest, and to examples of electromagnetic waves. A particularly useful feature of the book is the author's introduction and explanation of the necessary mathematics as he goes along, rather than presuming student understanding. Although an extensive background is not necessary, a general knowledge of physics and calculus is a prerequisite. Throughout the book, the development of each topic is explicit and unhurried, an approach intended to avoid basic misconceptions that lead to major misunderstandings later on. Short exercises help the student test his grasp of the material, and the text is studded with diagrams and illustrations that supplement the content and elucidate many hard-to-visualize concepts. The book ends at a point where the use of Maxwell's equations in several important problems has been illustrated, and students are prepared to proceed to a variety of further topics. Professor Rojansky brings many years of experience both as a teacher and a scientist (including ten years of advanced research at TRW Space Technologies Laboratories) to this lucid discussion of the fundamentals of electromagnetic fields and waves. His extensive pedagogical background enables him to communicate difficult concepts with great clarity.The Theory of Sound, Volume One
Par J. W. Rayleigh. 1945
The Nobel Laureate's classic sums up all research in the field prior to 1877, then presents Rayleigh's own original contributions.Volume…
One covers harmonic vibrations, systems with one degree of freedom, vibrating systems in general, transverse vibrations of strings, longitudinal and torsional vibrations of bars, vibrations of membranes and plates, curved shells and plates, and electrical vibrations.Theory of Electromagnetic Wave Propagation
Par Charles Herach Papas. 1988
While there are so many books on general electromagnetic theory for graduate-level students, there are significantly fewer that concentrate on…
the radiation aspects as does this well-known work. Interfacing physics and electrical engineering, Dr. Papas's clearly written text discusses highly important topics in the theory of electromagnetic wave propagation and antennas in a way that reveals the inherent simplicity of the basic ideas and their logical development from the Maxwell field equation.Chapter 1: Maxwell's field equations and those parts of electromagnetic field theory necessary for understanding the remainder of the book.Chapter 2: How the dyadic Green's function can be used to compute radiation from monochromatic sources.Chapter 3: Problems of radiation emitted by wire antennas and antenna arrays from the viewpoint of analysis and synthesis.Chapter 4: Two methods of expanding a radiation field in multiples -- one based on the Taylor expansion of the Helmholtz integrals and the other, on all expansion in spherical waves.Chapter 5: Wave aspects of radio-astronomical antenna theory.Chapter 6: Theory of electromagnetic wave propagation in a plasma medium describing the behavior of an antenna immersed in such a medium.Chapter 7: Covariance of Maxwell's equations in material media and its application to phenomena such as the Doppler effect.By unifying various topics under the single mantle of electromagnetic theory, Professor Papas has made the contents of this book easy to learn and convenient to teach. In addition, the book assembles much data previously available only in scattered research literature. The result is a superb graduate-level text that can also lend itself to self-instruction by researchers.Elementary Wave Optics
Par Robert H. Webb. 1997
This undergraduate textbook presents thorough coverage of the standard topics of classical optics and optical instrument design; it also offers…
significant details regarding the concepts of modern optics. Its survey of the mathematical tools of optics grants students insights into the physical principles of quantum mechanics.Two principal concepts occur throughout: a treatment of scattering from real scatterers (leading to Huygens' principles, diffraction theory, the index of refraction, and related topics); and the difference between coherent and noncoherent wave phenomena. Examinations of superimposition of field amplitudes and detection of intensities recur throughout the book.This highly physical approach is augmented by extensive appendixes of mathematical details. Two sets of problems appear at the end of each chapter and form a crucial part of the exposition. One set consists of well-tested problems with detailed solutions, paired with similar problems without supplied solutions. The other set contains short, easier exercises, filling the more conventional role of end-of-chapter problems.Plasma Confinement
Par J. D. Meiss, R. D. Hazeltine. 1992
Detailed and authoritative, this volume examines the essential physics underlying international research in magnetic confinement fusion. It offers readable, thorough…
accounts of the fundamental concepts behind methods of confining plasma at or near thermonuclear conditions. Designed for a one- or two-semester graduate-level course in plasma physics, it also represents a valuable reference for professional physicists in controlled fusion and related disciplines.Strain Gradient Plasticity-Based Modeling of Damage and Fracture
Par Emilio Martínez Pañeda. 2018
This book provides a comprehensive introduction to numerical modeling of size effects in metal plasticity. The main classes of strain…
gradient plasticity formulations are described and efficiently implemented in the context of the finite element method. A robust numerical framework is presented and employed to investigate the role of strain gradients on structural integrity assessment. The results obtained reveal the need of incorporating the influence on geometrically necessary dislocations in the modeling of various damage mechanisms. Large gradients of plastic strain increase dislocation density, promoting strain hardening and elevating crack tip stresses. This stress elevation is quantified under both infinitesimal and finite deformation theories, rationalizing the experimental observation of cleavage fracture in the presence of significant plastic flow. Gradient-enhanced modeling of crack growth resistance, hydrogen diffusion and environmentally assisted cracking highlighted the relevance of an appropriate characterization of the mechanical response at the small scales involved in crack tip deformation. Particularly promising predictions are attained in the field of hydrogen embrittlement. The research has been conducted at the Universities of Cambridge, Oviedo, Luxembourg, and the Technical University of Denmark, in a collaborative effort to understand, model and optimize the mechanical response of engineering materials.Optics and Optical Instruments: An Introduction
Par B K Johnson. 1960
This book illustrates basic practical applications of optical principle. Working models of telescopes, microscopes, photographic lenses, and optical projection systems…
are diagrammed and explained in full, as are the basic experiments for determining accuracy, power, angular field of view, amount of aberration, and all other necessary facts about the instrument. Throughout the book, only elementary mathematics is used, for the benefit of the student and the beginner in the field of optics.The author, an assistant professor at the Imperial College of Science and Technology in London, shows how to set up working models of each of the four types of instruments named above, so that the reader can see for himself the effects of changing the focal length, using different types of lenses, rotating the lens, and other experiments. He also includes a number of experiments to illustrate theoretical principles such as the reflection and refraction of light and focal length measurements of concave and convex lenses.A chapter on the human eye follows, and the author explains how to set up a simple working model of the eye in order to illustrate myopia, astigmatism, hypermetropia, and the visual acuity of the eye. Professor Johnson concludes with an important chapter on the working and testing of optical glass, in which he describes the roughing of lenses, the principles of the grinding and polishing processes, abrasives, edging, angle measurement, and other important steps in the production of optical glass. An appendix is included on the cleaning of glass surfaces, silvering, photographic items, developers, collodion films, and waxes and cements used for various purposes in optical work.This is a valuable work for the student and the amateur hobbyist as well as for many who use optical instruments in science and industry. It is written clearly and economically, with the needs of the practical worker in the field of optics held constantly in mind.X-Ray Diffraction
Par B. E. Warren. 1990
Basic diffraction theory has numerous important applications in solid-state physics and physical metallurgy, and this graduate-level text is the ideal…
introduction to the fundamentals of the discipline. Development is rigorous (throughout the book, the treatment is carried far enough to relate to experimentally observable quantities) and stress is placed on modern applications to nonstructural problems such as temperature vibration effects, order-disorder phenomena, crystal imperfections, the structure of amorphous materials, and the diffraction of x-rays in perfect crystals.Carefully selected problems have been included at the end of each chapter to help the student test his grasp of the material.Geometry, Relativity and the Fourth Dimension
Par Rudolf Rucker. 1977
This is a highly readable, popular exposition of the fourth dimension and the structure of the universe. A remarkable pictorial…
discussion of the curved space-time we call home, it achieves even greater impact through the use of 141 excellent illustrations. This is the first sustained visual account of many important topics in relativity theory that up till now have only been treated separately.Finding a perfect analogy in the situation of the geometrical characters in Flatland, Professor Rucker continues the adventures of the two-dimensional world visited by a three-dimensional being to explain our three-dimensional world in terms of the fourth dimension. Following this adventure into the fourth dimension, the author discusses non-Euclidean geometry, curved space, time as a higher dimension, special relativity, time travel, and the shape of space-time. The mathematics is sound throughout, but the casual reader may skip those few sections that seem too purely mathematical and still follow the line of argument. Readable and interesting in itself, the annotated bibliography is a valuable guide to further study.Professor Rucker teaches mathematics at the State University of New York in Geneseo. Students and laymen will find his discussion to be unusually stimulating. Experienced mathematicians and physicists will find a great deal of original material here and many unexpected novelties. Annotated bibliography. 44 problems.Fourier Series
Par Georgi P. Tolstov. 1962
Richard A. Silverman's series of translations of outstanding Russian textbooks and monographs is well-known to people in the fields of…
mathematics, physics, and engineering. The present book is another excellent text from this series, a valuable addition to the English-language literature on Fourier series.This edition is organized into nine well-defined chapters: Trigonometric Fourier Series, Orthogonal Systems, Convergence of Trigonometric Fourier Series, Trigonometric Series with Decreasing Coefficients, Operations on Fourier Series, Summation of Trigonometric Fourier Series, Double Fourier Series and the Fourier Integral, Bessel Functions and Fourier-Bessel Series, and the Eigenfunction Method and its Applications to Mathematical Physics. Every chapter moves clearly from topic to topic and theorem to theorem, with many theorem proofs given. A total of 107 problems will be found at the ends of the chapters, including many specially added to this English-language edition, and answers are given at the end of the text. Richard Silverman's excellent translation makes this book readily accessible to mathematicians and math students, as well as workers and students in the fields of physics and engineering. He has also added a bibliography, containing suggestions for collateral and supplementary reading. 1962 edition.Nonlinear Mechanics: A Supplement to Theoretical Mechanics of Particles and Continua
Par John Dirk Walecka, Alexander L Fetter. 2006
In their prior Dover book, Theoretical Mechanics of Particles and Continua, Alexander L. Fetter and John Dirk Walecka provided a…
lucid and self-contained account of classical mechanics, together with appropriate mathematical methods. This supplement--an update of that volume--offers a bridge to contemporary mechanics.The original book's focus on continuum mechanics--with chapters on sound waves in fluids, surface waves on fluids, heat conduction, and viscous fluids--forms the basis for this supplement's discussion of nonlinear continuous systems. Topics include linearized stability analysis; a detailed examination of the Rayleigh-Bénard problem, from its formulation to issues of linearized theory of convective instability and expansion in Fourier modes; and the direct derivation of Lorenz equations for simple physical configuration. The first half of the original text deals with particle mechanics, and this supplement returns to the study of systems with a finite number of degrees of freedom. A concluding section presents a series of problems that reinforce the supplement's teachings.From X-rays to Quarks: Modern Physicists and Their Discoveries
Par Emilio Segrè. 1980
A leading figure in twentieth-century physics offers impressions and recollections of the field's development. Nobel Laureate Emilio Segrè (1905-89) knew…
and worked with many of modern physics' preeminent scientists. In this simple but elegant history, he offers compelling views not only of the milestones of scientific discovery but also the personalities involved--their attitudes and politics as well as their trials and triumphs. Highlights include a profile of Albert Einstein, from his unconventional youth to his role as science's elder statesman; the wonder year of 1932, which witnessed the discoveries of the neutron, positron, and deuterium; and the first steps in building particle accelerators.A student and colleague of Enrico Fermi, Segrè made numerous important contributions to nuclear physics, including participation in the Manhattan Project. Segrè is further renowned for his narrative skills as a historian. This book is a companion to the author's From Falling Bodies to Radio Waves: Classical Physicists and Their Discoveries, also available from Dover Publications.Physics of Waves
Par Mark A. Heald, William C. Elmore. 1969
Because of the increasing demands and complexity of undergraduate physics courses (atomic, quantum, solid state, nuclear, etc.), it is often…
impossible to devote separate courses to the classic wave phenomena of optics, acoustics, and electromagnetic radiation. This brief comprehensive text helps alleviate the problem with a unique overview of classical wave theory in one volume.By examining a sequence of concrete and specific examples (emphasizing the physics of wave motion), the authors unify the study of waves, developing abstract and general features common to all wave motion. The fundamental ideas of wave motion are set forth in the first chapter, using the stretched string as a particular model. In Chapter Two, the two-dimensional membrane is used to introduce Bessel functions and the characteristic features of waveguides. In Chapters Three and Four, elementary elasticity theory is developed and applied to find the various classes of waves that can be supported by a rigid rod. The impedance concept is also introduced at this point. Chapter Five discusses acoustic waves in fluids.The remainder of the book offers concise coverage of hydrodynamic waves at a liquid surface, general waves in isotropic elastic solids, electromagnetic waves, the phenomenon of wave diffraction, and other important topics. A special feature of this book is the inclusion of additional material designed to encourage the serious student to investigate topics often not covered in lectures. Throughout, the mathematics is kept relatively simple (mostly differential equations) and is accessible to advanced undergraduates with a year of calculus. In addition, carefully selected problems at the end of each section extend the coverage of the text by asking the student to supply mathematical details for calculations outlined in the section, or to develop the theory for related cases.Impressively broad in scope, Physics of Waves offers a novel approach to the study of classical wave theory -- a wide-ranging but thorough survey of an important discipline that pervades much of contemporary physics. The simplicity, breadth, and brevity of the book make it ideal as a classroom text or as a vehicle for self-study.Electrifying Atmospheres: Charging, Ionisation and Lightning in the Solar System and Beyond
Par Karen L Aplin. 2013
Electrical processes take place in all planetary atmospheres. There is evidence for lightning on Venus, Jupiter, Saturn, Uranus and Neptune,…
it is possible on Mars and Titan, and cosmic rays ionise every atmosphere, leading to charged droplets and particles. Controversy surrounds the role of atmospheric electricity in physical climate processes on Earth; here, a comparative approach is employed to review the role of electrification in the atmospheres of other planets and their moons. This book reviews the theory, and, where available, measurements, of planetary atmospheric electricity, taken to include ion production and ion-aerosol interactions. The conditions necessary for a global atmospheric electric circuit similar to Earth's, and the likelihood of meeting these conditions in other planetary atmospheres, are briefly discussed. Atmospheric electrification is more important at planets receiving little solar radiation, increasing the relative significance of electrical forces. Nucleation onto atmospheric ions has been predicted to affect the evolution and lifetime of haze layers on Titan, Neptune and Triton. For planets closer to Earth, heating from solar radiation dominates atmospheric circulations. Mars may have a global circuit analogous to the terrestrial model, but based on electrical discharges from dust storms, and Titan may have a similar global circuit, based on transfer of charged raindrops. There is an increasing need for direct measurements of planetary atmospheric electrification, in particular on Mars, to assess the risk for future unmanned and manned missions. Theoretical understanding could be increased by cross-disciplinary work to modify and update models and parameterisations initially developed for a specific atmosphere, to make them more broadly applicable to other planetary atmospheres. The possibility of electrical processes in the atmospheres of exoplanets is also discussed.Foundations of Radiation Hydrodynamics
Par Barbara Weibel Mihalas, Dimitri Mihalas. 1984
Radiation hydrodynamics is a broad subject that cuts across many disciplines in physics and astronomy: fluid dynamics, thermodynamics, statistical mechanics,…
kinetic theory, and radiative transfer, among others. The theory developed in this book by two specialists in the field can be applied to the study of such diverse astrophysical phenomena as stellar winds, supernova explosions, and the initial phases of cosmic expansion, as well as the physics of laser fusion and reentry vehicles. As such, it provides students with the basic tools for research on radiating flows.Largely self-contained, the volume is divided into three parts: Chapters 1 to 5 focus on the dynamics of nonradiating fluids and then consider applications of a few astrophysically interesting problems concerning waves, shocks, and stellar winds. The second part of the book -- Chapters 5 to 8 -- deals with the physics of radiation, radiation transport, and the dynamics of radiating fluids, emphasizing the close relationship of radiation hydrodynamics to ordinary fluid dynamics. Part 3 comprises a short appendix on tensor calculus, explaining the use of tensor concepts in writing equations that allow a simple transition from ordinary fluids to relativistic fluids to radiation.Combining relevant material scattered widely among a large number of books, journal papers, and technical reports, this volume will be of immense value to students and researchers in many fields. 1984 edition.Fundamental Formulas of Physics, Volume One
Par Donald H. Menzel. 1960
The republication of this book, unabridged and corrected, fills the need for a comprehensive work on fundamental formulas of mathematical…
physics. It ranges from simple operations to highly sophisticated ones, all presented most lucidly with terms carefully defined and formulas given completely. In addition to basic physics, pertinent areas of chemistry, astronomy, meteorology, biology, and electronics are also included.This is no mere listing of formulas, however. Mathematics is integrated into text, for the most part, so that each chapter stands as a brief summary or even short textbook of the field represented. The book, therefore, fills other needs than the primary function of reference and guide for research. The student will find it a handy review of familiar fields and an aid to gaining rapid insight into the techniques of new ones.The teacher will study it as a useful guide to a broad concept of physics. The chemist, astronomer, meteorologist, biologist, and engineer will not only derive valuable aid from their special chapters, but will understand how their specialty fits into the large scheme of physics.Vol. 1 chapter titles: Basic Mathematical Formulas, Statistics, Nomograms, Physical Constants, Classical Mechanics, Special Theory of Relativity, The General Theory of Relativity, Hydrodynamics and Aerodynamics, Boundary Value Problems in Mathematical Physics, Heat and Thermodynamics, Statistical Mechanics, Kinetic Theory of Gases: Viscosity, Thermal Conduction, and Diffusion, Electromagnetic Theory, Electronics, Sound and Acoustics.Vol. 2 chapter titles: Geometrical Optics, Physical Optics, Electron Optics, Molecular Spectra, Atomic Spectra, Quantum Mechanics, Nuclear Theory, Cosmic Rays and High-Energy Phenomena, Particle Accelerators, Solid State, Theory of Magnetism, Physical Chemistry, Basic Formulas of Astrophysics, Celestial Mechanics, Meteorology, Biophysics.Elementary Statistical Physics
Par Charles Kittel. 1986
Noteworthy for the philosophical subtlety of its foundations and the elegance of its problem-solving methods, statistical mechanics can be employed…
in a broad range of applications -- among them, astrophysics, biology, chemistry, nuclear and solid state physics, communications engineering, metallurgy, and mathematics. Geared toward graduate students in physics, this text covers such important topics as stochastic processes and transport theory in order to provide students with a working knowledge of statistical mechanics.To explain the fundamentals of his subject, the author uses the method of ensembles developed by J. Willard Gibbs. Topics include the properties of the Fermi-Dirac and Bose-Einstein distributions; the interrelated subjects of fluctuations, thermal noise, and Brownian movement; and the thermodynamics of irreversible processes.Negative temperature, magnetic energy, density matrix methods, and the Kramers-Kronig causality relations are treated briefly. Most sections include illustrative problems. Appendix. 28 figures. 1 table.Introduction to the Quantum Theory: Third Edition
Par David Park. 1992
More than a chance to gain new insights into physics, this book offers students the opportunity to look at what…
they already know about the subject in an improved way. Geared toward upper-level undergraduates and graduate students, this self-contained first course in quantum mechanics consists of two parts: the first covers basic theory, and the second part presents selected applications. Numerous problems of varying difficulty examine not only the steps of the proofs but also related ideas.Starting with an introduction that ventures beyond classical physics, the first part examines the physical content of the wave function; general principles; physics in one dimension; hermitian operators, symmetry, and angular momentum; and systems in two and three dimensions. Additional topics include approximate methods of calculation; the theory of scattering; spin and isospin; questions of physical meaning; electromagnetic radiation; systems containing identical particles; and classical dynamics and Feynman's construction. Focusing on applications, the second part explores the theory of alpha decay; electrons in a periodic lattice; the hydrogen spectrum; the helium atom; interatomic forces; the neutron-proton interaction; and the quark model of baryons.Astrophysical Applications of Gravitational Lensing
Par Evencio Mediavilla, José A. Muñoz, Francisco Garzón, Terence J. Mahoney. 2016
Gravitational lenses offer the best, and sometimes the only, means of tackling key problems in many fields of astrophysics and…
cosmology. According to Einstein's theory, the curvature of light-rays increases with mass; gravitational lenses can be used to map the distribution of mass in a Universe in which virtually all matter is dark matter of an unknown nature. Gravitational lensing has significantly improved our knowledge of many astrophysical phenomena, such as exoplanets, galaxies, active galactic nuclei, quasars, clusters, large-scale structure and the Universe itself. All these topics are covered fully in this book, together with two tutorials on lens and microlensing modelling. The future of lensing in relation to large surveys and the anticipated discoveries of thousands more gravitational lenses is also discussed, making this volume an ideal guide for postgraduate students and practising researchers in the use of gravitational lenses as a tool in their investigations.