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Group Properties Of A One Dimensional System Of Equations For Wave Propagation In Various Media

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Group Properties Of A One Dimensional System Of Equations For Wave Propagation In Various Media

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Author : K. A. Ames
language : en
Publisher:
Release Date : 1988

Group Properties Of A One Dimensional System Of Equations For Wave Propagation In Various Media written by K. A. Ames and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988 with categories.

Wave Propagation In Solids And Fluids

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Author : Julian L. Davis
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Wave Propagation In Solids And Fluids written by Julian L. Davis and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.

The purpose of this volume is to present a clear and systematic account of the mathematical methods of wave phenomena in solids, gases, and water that will be readily accessible to physicists and engineers. The emphasis is on developing the necessary mathematical techniques, and on showing how these mathematical concepts can be effective in unifying the physics of wave propagation in a variety of physical settings: sound and shock waves in gases, water waves, and stress waves in solids. Nonlinear effects and asymptotic phenomena will be discussed. Wave propagation in continuous media (solid, liquid, or gas) has as its foundation the three basic conservation laws of physics: conservation of mass, momentum, and energy, which will be described in various sections of the book in their proper physical setting. These conservation laws are expressed either in the Lagrangian or the Eulerian representation depending on whether the boundaries are relatively fixed or moving. In any case, these laws of physics allow us to derive the "field equations" which are expressed as systems of partial differential equations. For wave propagation phenomena these equations are said to be "hyperbolic" and, in general, nonlinear in the sense of being "quasi linear" . We therefore attempt to determine the properties of a system of "quasi linear hyperbolic" partial differential equations which will allow us to calculate the displacement, velocity fields, etc.

Waves In Continuous Media

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Author : S. L. Gavrilyuk
language : en
Publisher: Springer
Release Date : 2017-01-27

Waves In Continuous Media written by S. L. Gavrilyuk and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-01-27 with Mathematics categories.

Starting with the basic notions and facts of the mathematical theory of waves illustrated by numerous examples, exercises, and methods of solving typical problems Chapters 1 & 2 show e.g. how to recognize the hyperbolicity property, find characteristics, Riemann invariants and conservation laws for quasilinear systems of equations, construct and analyze solutions with weak or strong discontinuities, and how to investigate equations with dispersion and to construct travelling wave solutions for models reducible to nonlinear evolution equations. Chapter 3 deals with surface and internal waves in an incompressible fluid. The efficiency of mathematical methods is demonstrated on a hierarchy of approximate submodels generated from the Euler equations of homogeneous and non-homogeneous fluids. The self-contained presentations of the material is complemented by 200+ problems of different level of difficulty, numerous illustrations, and bibliographical recommendations.

Methods Of Wave Theory In Dispersive Media

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Author : Mikhail Viktorovich Kuzelev
language : en
Publisher: World Scientific
Release Date : 2010

Methods Of Wave Theory In Dispersive Media written by Mikhail Viktorovich Kuzelev and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Science categories.

Ch. 1. Linear harmonic waves in dispersive systems. Initial-value problem and problem with an external source. 1. Harmonic waves in dispersive systems. 2. Initial-value problem. Eigenmode method. 3. Characteristic function of the state vector. Dispersion operator. 4. Laplace transform method -- ch. 2. A case study of linear waves in dispersive media. 5. Transverse electromagnetic waves in an isotropic dielectric. 6. Longitudinal electrostatic waves in a cold isotropic plasma. Collisional dissipation of plasma waves. 7. Transverse electromagnetic waves in a cold isotropic plasma. Dissipation of transverse waves in a plasma. 8. Electromagnetic waves in metals. 9. Electromagnetic waves in a waveguide with an isotropic dielectric. 10. Longitudinal waves in a hot isotropic plasma. Electron diffusion in a plasma. 11. Longitudinal waves in an isotropic degenerate plasma. Waves in a quantum plasma. 12. Ion acoustic waves in a nonisothermal plasma. Ambipolar diffusion. 13. Electromagnetic waves in a waveguide with an anisotropic plasma in a strong external magnetic field. 14. Electromagnetic waves propagating in a magnetized electron plasma along a magnetic field. 15. Electrostatic waves propagating in a magnetized electron plasma at an angle to a magnetic field. 16. Magnetohydrodynamic waves in a conducting fluid. 17. Acoustic waves in crystals. 18. Longitudinal electrostatic waves in a one-dimensional electron beam. 19. Beam instability in a plasma. 20. Instability of a current-carrying plasma -- ch. 3. Linear waves in coupled media. Slow amplitude method. 21. Coupled oscillator representation and slow amplitude method. 22. Beam-plasma system in the coupled oscillator representation. 23. Basic equations of microwave electronics. 24. Resonant Buneman instability in a current-carrying plasma in the coupled oscillator representation. 25. Dispersion function and wave absorption in dissipative systems. 26. Some effects in the interaction between waves in coupled systems. 27. Waves and their interaction in periodic structures -- ch. 4. Nonharmonic waves in dispersive media. 28. General solution to the initial-value problem. 29. Quasi-harmonic approximation. Group velocity. 30. Pulse spreading in equilibrium dispersive media. 31. Stationary-phase method. 32. Some problems for wave equations with a source -- ch. 5. Nonharmonic waves in nonequilibrium media. 33. Pulse propagation in nonequilibrium media. 34. Stationary-phase method for complex frequencies. 35. Quasi-harmonic approximation in the theory of interaction of electron beams with slowing-down media -- ch. 6. Theory of instabilities. 36. Convective and absolute instabilities. First criterion for the type of instability. 37. Saddle-point method. Second criterion for the type of instability. 38. Third Criterion for the type of instability. 39. Type of beam instability in the interaction with a slowed wave of zero group velocity in a medium. 40. Calculation of the Green's functions of unstable systems -- ch. 7. Hamiltonian method in the theory of electromagnetic radiation in dispersive media. 41. Equations for the excitation of transverse electromagnetic field oscillators. 42. Dipole radiation. 43. Radiation from a moving dipole - undulator radiation. 44. Cyclotron radiation. 45. Cherenkov effect. Anomalous and normal doppler effects. 46. Application of the Hamiltonian method to the problem of the excitation of longitudinal waves

Analytical And Numerical Methods For Wave Propagation In Fluid Media

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Author : Krzysztof Murawski
language : en
Publisher: World Scientific
Release Date : 2002-11-06

Analytical And Numerical Methods For Wave Propagation In Fluid Media written by Krzysztof Murawski and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-11-06 with Science categories.

This book surveys analytical and numerical techniques appropriate to the description of fluid motion with an emphasis on the most widely used techniques exhibiting the best performance.Analytical and numerical solutions to hyperbolic systems of wave equations are the primary focus of the book. In addition, many interesting wave phenomena in fluids are considered using examples such as acoustic waves, the emission of air pollutants, magnetohydrodynamic waves in the solar corona, solar wind interaction with the planet venus, and ion-acoustic solitons.

Understanding Acoustics

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Author : Steven L. Garrett
language : en
Publisher: Springer
Release Date : 2017-02-24

Understanding Acoustics written by Steven L. Garrett and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-02-24 with Science categories.

This textbook provides a unified approach to acoustics and vibration suitable for use in advanced undergraduate and first-year graduate courses on vibration and fluids. The book includes thorough treatment of vibration of harmonic oscillators, coupled oscillators, isotropic elasticity, and waves in solids including the use of resonance techniques for determination of elastic moduli. Drawing on 35 years of experience teaching introductory graduate acoustics at the Naval Postgraduate School and Penn State, the author presents a hydrodynamic approach to the acoustics of sound in fluids that provides a uniform methodology for analysis of lumped-element systems and wave propagation that can incorporate attenuation mechanisms and complex media. This view provides a consistent and reliable approach that can be extended with confidence to more complex fluids and future applications. Understanding Acoustics opens with a mathematical introduction that includes graphing and statistical uncertainty, followed by five chapters on vibration and elastic waves that provide important results and highlight modern applications while introducing analytical techniques that are revisited in the study of waves in fluids covered in Part II. A unified approach to waves in fluids (i.e., liquids and gases) is based on a mastery of the hydrodynamic equations. Part III demonstrates extensions of this view to nonlinear acoustics. Engaging and practical, this book is a must-read for graduate students in acoustics and vibration as well as active researchers interested in a novel approach to the material.

Mathematics Of Wave Propagation

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Author : Julian L. Davis
language : en
Publisher: Princeton University Press
Release Date : 2000-05-07

Mathematics Of Wave Propagation written by Julian L. Davis and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-05-07 with Mathematics categories.

Earthquakes, a plucked string, ocean waves crashing on the beach, the sound waves that allow us to recognize known voices. Waves are everywhere, and the propagation and classical properties of these apparently disparate phenomena can be described by the same mathematical methods: variational calculus, characteristics theory, and caustics. Taking a medium-by-medium approach, Julian Davis explains the mathematics needed to understand wave propagation in inviscid and viscous fluids, elastic solids, viscoelastic solids, and thermoelastic media, including hyperbolic partial differential equations and characteristics theory, which makes possible geometric solutions to nonlinear wave problems. The result is a clear and unified treatment of wave propagation that makes a diverse body of mathematics accessible to engineers, physicists, and applied mathematicians engaged in research on elasticity, aerodynamics, and fluid mechanics. This book will particularly appeal to those working across specializations and those who seek the truly interdisciplinary understanding necessary to fully grasp waves and their behavior. By proceeding from concrete phenomena (e.g., the Doppler effect, the motion of sinusoidal waves, energy dissipation in viscous fluids, thermal stress) rather than abstract mathematical principles, Davis also creates a one-stop reference that will be prized by students of continuum mechanics and by mathematicians needing information on the physics of waves.