Scalar Wave Theory: Green's Functions and Applications

Scalar Wave Theory: Green's Functions and Applications

by John DeSanto

Paperback(Softcover reprint of the original 1st ed. 1992)

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Product Details

ISBN-13: 9783642847400
Publisher: Springer Berlin Heidelberg
Publication date: 02/12/2012
Series: Springer Series on Wave Phenomena , #12
Edition description: Softcover reprint of the original 1st ed. 1992
Pages: 193
Product dimensions: 6.10(w) x 9.25(h) x 0.02(d)

Table of Contents

1. Scalar Wave Theory.- 1.1 Fluid Equations.- 1.2 Sound.- 1.3 Wave Equations.- 1.4 Spatially Variable Density.- 1.5 Helmholtz Equation and Separable Solutions.- 1.6 One-Dimensional Problems and Sturm-Liouville Theory.- 1.7 Calculation of Eigenvalues from Eigenfunctions.- 1.8 Interface Boundary Conditions.- 1.9 Energy and Momentum.- Appendices.- 1.A Wave Equation Derivation for Spatially Varying Density.- 1 B Wave Equation Derivation for Spatially and Temporally Variable Density with Quadratic Velocity Terms.- 2. Green’s Functions.- 2.1 Basic Definition.- 2.2 Eigenfunction Expansion.- 2.3 One-Dimensional Examples.- 2.4 Elementary Source.- 2.5 Green’s Functions for the Wave Equation.- 2.6 Green’s Functions for the Wave Equation in Two Dimensions.- 2.7 Green’s Functions for the Wave Equation in One Dimension.- 2.8 Green’s Functions for the Helmholtz Equation.- 2.8.1 Three Dimensions.- 2.8.2 Two Dimensions.- 2.8.3 One Dimension.- 2.9 Integral Representations: Helmholtz Green’s Functions.- 2.9.1 Weyl Representation.- 2.9.2 Sommerfeld Representation.- 2.9.3 Explicit Evaluation of G(3).- 2.9.4 Weyrich Representation.- 2.9.5 Plane-Wave Decomposition of G(2).- 2.9.6 Explicit Evaluation of G(2).- 2.9.7 Explicit Relation Between G(3) and G(2).- 2.10 Delta Functions in Different Coordinate Systems.- 2.10.1 Cylindrical Coordinates.- 2.10.2 Spherical Coordinates.- 2.11 Other Examples of Green’s Functions.- 2.A Dirac-Plemelj Relations.- 3. Scalar Plane Wave Scattering.- 3.1 Scattering from a Plane Interface.- 3.2 Examples.- 3.3 Interface Values and Impedances.- 3.4 Impedance Boundary Condition.- 3.5 Wave Fronts and Ray Parameter.- 3.6 Total Transmission.- 3.7 Total Internal Reflection.- 3.8 Effect of Surface Roughness.- 4. Spherical Waves Scattering from Planar c2.- 4.6 Case 2: c1 < c2.- 4.7 Transmitted Field.- 4.A Steepest Descent Method.- 5. Two-Layered Liquid Half-Space (Pekeris Waveguide).- 5.1 Geometry and Notation.- 5.2 Green’s Function.- 5.3 Analytic Properties of G2.- 5.4 Normal Mode (NM) Representation.- 5.5 Fourier-Bessel Representation.- 5.6 Pseudo-proper Modes.- 5.7 Leaky Waves.- 5.8 Branch Line Integral (BLI).- 5.9 Virtual Modes.- 5.10 Modal Attenuation.- 5.A Proof of the Contour Representation.- References.

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