## Low and high frequency asymptoticsThis volume focuses on asymptotic methods in the low and high frequency limits for the solution of scattering and propagation problems. Each chapter is pedagogical in nature, starting with the basic foundations and ending with practical applications. For example, using the Geometrical Theory of Diffraction, the canonical problem of edge diffraction is first solved and then used in solving the problem of diffraction by a finite crack. In recent times, the crack problem has been of much interest for its applications to Non-Destructive Evaluation (NDE) of flaws in structural materials. |

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### Contents

Rayleigh Scattering | 1 |

Matched Asymptotic Expansions Applied to Diffraction of Elastic Waves | 71 |

A Uniform GTD Approach to EM Scattering and Radiation | 265 |

Copyright | |

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### Common terms and phrases

Achenbach acoustic amplitude angle applied approximation asymptotic expansions boundary conditions caustic circular complex ray components constant convex surface coordinates cosh crack creeping wave curvature cylinder Datta defined denotes diffracted field diffracted ray diffraction coefficient displacement edge diffraction Elastic Waves elastodynamic electromagnetic evanescent expressions far-field Felsen geometrical optics given Green's function incident field incident ray incident wave inner expansion Keller Kouyoumjian line source lit region low frequency magnetic matching modal field motion normal obtained outer expansion P-wave Pathak perfectly conducting phase fronts phase path plane wave propagation quasi-caustic radiation radius ray congruences ray fields ray path ray system Rayleigh Rayleigh scattering reflection coefficient resonances respectively satisfy SB transition scalar scattered field scattering problem Section shadow boundary shadow region shown in Fig sin2 sinh solution spheroid surface ray surface wave symmetric tensor tensor elements Theory of Diffraction unit vector wavefront wavenumber whispering gallery modes