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Author: Robert Hermann
Publisher: Math-Sci Press
ISBN: 9780915692033
Category : Mathematics
Languages : en
Pages : 132
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Book Description
Author: Robert Hermann
Publisher: Math-Sci Press
ISBN: 9780915692033
Category : Mathematics
Languages : en
Pages : 132
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Book Description
Author: Somnath Datta
Publisher: World Scientific
ISBN: 9811228132
Category : Science
Languages : en
Pages : 384
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Book Description
This book takes the reader from the preliminary ideas of the Special Theory of Relativity (STR) to the doorsteps of the General Theory of Relativity (GTR).The first part explains the main concepts in a layman's language, including STR, the Lorentz transformation, relativistic mechanics. Thereafter the concept of tensors is built up in detail, especially Maxwell's stress tensor with illustrative examples, culminating in the energy-momentum conservation in electromagnetic fields. Mathematical structure of Minkowski's space-time is constructed and explained graphically. The equation of motion is formulated and then illustrated by the example of relativistic rocket. The principle of covariance is explained with the covariant equations of classical electrodynamics. Finally, the book constructs the energy tensor which constitutes the source term in Einstein's field equation, which clears the passage to the GTR.In the book, the concepts of tensors are developed carefully and a large number of numerical examples taken from atomic and nuclear physics. The graphs of important equations are included. This is suitable for studies in classical electrodynamics, modern physics, and relativity.
Author: Robert Hermann
Publisher:
ISBN:
Category : Calculus of tensors
Languages : en
Pages : 120
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Book Description
Author: Daniel A. Fleisch
Publisher: Cambridge University Press
ISBN: 9780521171908
Category : Science
Languages : en
Pages : 206
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Book Description
Vectors and tensors are among the most powerful problem-solving tools available, with applications ranging from mechanics and electromagnetics to general relativity. Understanding the nature and application of vectors and tensors is critically important to students of physics and engineering. Adopting the same approach used in his highly popular A Student's Guide to Maxwell's Equations, Fleisch explains vectors and tensors in plain language. Written for undergraduate and beginning graduate students, the book provides a thorough grounding in vectors and vector calculus before transitioning through contra and covariant components to tensors and their applications. Matrices and their algebra are reviewed on the book's supporting website, which also features interactive solutions to every problem in the text where students can work through a series of hints or choose to see the entire solution at once. Audio podcasts give students the opportunity to hear important concepts in the book explained by the author.
Author: John M. Ball
Publisher: Springer Science & Business Media
ISBN: 3642599389
Category : Science
Languages : en
Pages : 477
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Book Description
A traditional way to honor distinguished scientists is to combine collections of papers solicited from friendly colleagues into dedicatory volumes. To honor our friend and colleague Mort Gurtin on the occasion of his sixty-fifth birthday, we followed a surer path to produce a work of intrinsic and lasting scientific value: We collected pa pers that we deemed seminal in the field of evolving phase interfaces in solids, a field to which Mort Gurtin himself has made fundamental contributions. Our failure for lack of space to include in this volume every paper of major significance is mitigated by the ma gisterial introduction prepared by Eliot Fried, which assesses the contributions of nu merous works. We hope that this collection will prove useful and stimulating to both researchers and students in this exciting field. August 1998 JohnM. Ball David Kinderlehrer Paulo Podio-Guidugli Marshall Slemrod Contents Introduction: Fifty Years of Research on Evolving Phase Interfaces By Eliot Fried. 0 •••••••••••••••••••••••••••••••••••••••••••••••• 0 ••••• 1 I. Papers on Materials Science Surface Tension as a Motivation for Sintering By C. Herring 33 Two-Dimensional Motion of Idealized Grain Boundaries By W. W. Mullins 0 ••••••••••• 0 ••••••••••••••••••• 70 Morphological. Stability of a Particle Growing by Diffusion or Heat Flow By w. w. Mullins and R. F. Sekerka 75 Energy Relations and the Energy-Momentum Tensor in Continuum Mechanics By J. D. Eshelby 82 The Interactions of Composition and Stress in Crystalline Solids By F. e. Larche and 1. W. Cahn 120 II.
Author: Dwight E. Neuenschwander
Publisher: JHU Press
ISBN: 142141564X
Category : Mathematics
Languages : en
Pages : 244
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Book Description
It is an ideal companion for courses such as mathematical methods of physics, classical mechanics, electricity and magnetism, and relativity.--Gary White, editor of The Physics Teacher "American Journal of Physics"
Author: Ryosuke Yanagihara
Publisher: Springer Nature
ISBN: 9811662347
Category : Science
Languages : en
Pages : 170
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Book Description
The energy momentum tensor (EMT) is one of the most fundamental observables in physics. Recently, a novel method to define EMT on the basis of the gradient-flow formalism has been proposed. It turned out that the EMT operator can be constructed even on the lattice with the method, which enables non-perturbative computations. This approach has been successfully applied to the analyses on thermodynamic quantities. This book presents the study on spatial EMT distributions around static charges via the gradient flow in lattice simulations based on SU(3) Yang-Mills theory. Static charges are employed as probes to explore complex quantum systems, and EMT then characterizes the response of vacuum as well as hot medium under the existence of the charges, which significantly provides profound and novel insights into the non-perturbative phenomena, such as the confinement of quarks. In addition, the book treats the study on the EMT distribution around a magnetic vortex in the Abelian-Higgs model, which is compared with the lattice result. These achievements open up various future studies for revealing non-trivial aspects of the strong interaction. The book also includes well-organized reviews on general properties of EMT, lattice gauge theory and the gradient-flow formalism with its application to the definition of EMT. They are useful for students and young researchers as a brief introduction to this field.
Author: Mirjana Dalarsson
Publisher: Academic Press
ISBN: 0128034017
Category : Science
Languages : en
Pages : 276
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Book Description
Tensors, Relativity, and Cosmology, Second Edition, combines relativity, astrophysics, and cosmology in a single volume, providing a simplified introduction to each subject that is followed by detailed mathematical derivations. The book includes a section on general relativity that gives the case for a curved space-time, presents the mathematical background (tensor calculus, Riemannian geometry), discusses the Einstein equation and its solutions (including black holes and Penrose processes), and considers the energy-momentum tensor for various solutions. In addition, a section on relativistic astrophysics discusses stellar contraction and collapse, neutron stars and their equations of state, black holes, and accretion onto collapsed objects, with a final section on cosmology discussing cosmological models, observational tests, and scenarios for the early universe. This fully revised and updated second edition includes new material on relativistic effects, such as the behavior of clocks and measuring rods in motion, relativistic addition of velocities, and the twin paradox, as well as new material on gravitational waves, amongst other topics. Clearly combines relativity, astrophysics, and cosmology in a single volume Extensive introductions to each section are followed by relevant examples and numerous exercises Presents topics of interest to those researching and studying tensor calculus, the theory of relativity, gravitation, cosmology, quantum cosmology, Robertson-Walker Metrics, curvature tensors, kinematics, black holes, and more Fully revised and updated with 80 pages of new material on relativistic effects, such as relativity of simultaneity and relativity of the concept of distance, amongst other topics Provides an easy-to-understand approach to this advanced field of mathematics and modern physics by providing highly detailed derivations of all equations and results
Author: Akitomo Tachibana
Publisher: Springer
ISBN: 9811031320
Category : Science
Languages : en
Pages : 189
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Book Description
This book presents new aspects of quantum electrodynamics (QED), a quantum theory of photons with electrons, from basic physics to physical chemistry with mathematical rigor. Topics covered include spin dynamics, chemical reactivity, the dual Cauchy problem, and more. Readers interested in modern applications of quantum field theory in nano-, bio-, and open systems will enjoy learning how the up-to-date quantum theory of radiation with matter works in the world of QED. In particular, chemical ideas restricted now to nonrelativistic quantum theory are shown to be unified and extended to relativistic quantum field theory that is basic to particle physics and cosmology: realization of the new-generation quantum theory. Readers are assumed to have a background equivalent to an undergraduate student's elementary knowledge in electromagnetism, quantum mechanics, chemistry, and mathematics.
Author: Yvette Kosmann-Schwarzbach
Publisher: Springer Science & Business Media
ISBN: 0387878688
Category : Mathematics
Languages : en
Pages : 205
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Book Description
In 1915 and 1916 Emmy Noether was asked by Felix Klein and David Hilbert to assist them in understanding issues involved in any attempt to formulate a general theory of relativity, in particular the new ideas of Einstein. She was consulted particularly over the difficult issue of the form a law of conservation of energy could take in the new theory, and she succeeded brilliantly, finding two deep theorems. But between 1916 and 1950, the theorem was poorly understood and Noether's name disappeared almost entirely. People like Klein and Einstein did little more then mention her name in the various popular or historical accounts they wrote. Worse, earlier attempts which had been eclipsed by Noether's achievements were remembered, and sometimes figure in quick historical accounts of the time. This book carries a translation of Noether's original paper into English, and then describes the strange history of its reception and the responses to her work. Ultimately the theorems became decisive in a shift from basing fundamental physics on conservations laws to basing it on symmetries, or at the very least, in thoroughly explaining the connection between these two families of ideas. The real significance of this book is that it shows very clearly how long it took before mathematicians and physicists began to recognize the seminal importance of Noether's results. This book is thoroughly researched and provides careful documentation of the textbook literature. Kosmann-Schwarzbach has thus thrown considerable light on this slow dance in which the mathematical tools necessary to study symmetry properties and conservation laws were apparently provided long before the orchestra arrives and the party begins.
