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The third part considers advanced topics, including the Burger equation, diffraction and scattering, solitons, and the inverse scattering transform. Waves are a ubiquitous and important feature of the physical world, and throughout history it has been a major challenge to understand them. They can propagate on the surfaces of solids and of fluids; chemical waves control the beating of your heart; traffic jams move in waves down lanes crowded with vehicles.

This introduction to the mathematics of wave phenomena is aimed at advanced undergraduate courses on waves for mathematicians, physicists or engineers. Some more advanced material on both linear and nonlinear waves is also included, thus making the book suitable for beginning graduate courses. The authors assume some familiarity with partial differential equations, integral transforms and asymptotic expansions as well as an acquaintance with fluid mechanics, elasticity and electromagnetism. The context and physics that underlie the mathematics is clearly explained at the beginning of each chapter.

Worked examples and exercises are supplied throughout, with solutions available to teachers. Read more Read less. Review "This introduction to the mathematics of wave phenomena is aimed at advanced undergraduate courses on waves for mathematicians, physicists, or engineers. No customer reviews.

Linear Elastic Waves (Cambridge Texts in Applied Mathematics #26) (Hardcover)

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The authors assume some familiarity with partial differential equations, integral transforms and asymptotic expansions as well as with fluid mechanics, elasticity, and electromagnetism. The context and physics that underlie the mathematics is clearly explained at the beginning of each chapter. Worked examples and exercises are supplied throughout, with solutions available to teachers. Customer Reviews.

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Linear Elastic Waves : John G. Harris :

Customer Service. In The Spotlight. From a didactic point of view, the readership, in this case the students, would surely prefer the other, the more obvious way. However, for people working in the area it is nice to obtain an additional view. Chapter 3, entitled Reflection, Refraction and Interfacial Waves , deals with waves at an interface between two materials having different densities and wave velocities.

Wave Motion (Cambridge Texts in Applied Mathematics)

Furthermore, the chapter describes waves that propagate along an interface, while decaying perpendicularly away from it. In this chapter, it becomes obvious that the author does not cover the subject in a complete manner. By considering the reflection, he deals only with an incident longitudinal plane wave, and the refraction is treated only for an incident shear SV plane wave. For a textbook as well as for a reference book, it would be advantageous to deal with the missing cases as well.

Obviously, this chapter does not incorporate all possible cases, since the reader is expected to solve the reflection coefficients himself the solution is given, but the derivation is left to the reader. However, the explanation of the phase matching condition is excellent. As a consequence of dealing with reflections, the Rayleigh wave is introduced in this chapter as well. Again some plots presenting the decaying vertical and horizontal amplitudes with depth of the Rayleigh wave, as well as the orientation of the Rayleigh wave particle orbit would be helpful.


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  8. The chapter closes with an example that uses the introduced ideas to derive an integral representation for the scattering of an acoustic wave by an elastic inclusion. According to its title, Radiation and Diffraction , Chapter 5 deals with the basic propagation processes that are encountered when studying radiation or edge diffraction.

    The first problem under consideration consists of calculating the transient, antiplane radiation excited by a line source at the surface of a half-space using the Cagniard-deHoop method to invert the integral transformations. The second one consists of calculating the time-harmonic, inplane radiation from a two-dimensional center of compression buried in a half-space by using plane wave spectral techniques and the method of steepest descent.

    Finally, the last one treats the calculation of the diffraction of a time harmonic plane antiplane shear wave by a semi-infinite crack using the Wiener-Hopf method and by using matched asymptotic expansions. An appendix describing the relation between the diffraction integral and the Fresnel integral closes the chapter. The last chapter, Guided Waves and Dispersion , treats antiplane shear problems. The guided waves are constructed by using partial waves, and their dispersions are calculated by using the transverse resonance principle.

    Both harmonic and transient excitations of a closed waveguide are examined by using a mode expansion.


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    The harmonic excitation of an open waveguide by a line source is also studied by using both ray and mode representations. The last problem under consideration deals with the propagation in a closed waveguide with a slowly varying thickness using an asymptotic expansion that combines features of both rays and modes. The chapter ends by examining the propagation of information and energy with the group velocity.

    All derivations are carefully developed, however, more illustrations would enhance the mathematical development and understanding. Plenty of textual explanation is provided to clarify the topic under consideration.