Field Representations and Introduction to Scattering

This is the first volume in the Handbook on Acoustic, Electromagnetic and Elastic Wave Scattering subseries and it serves as an introduction to the remaining volumes. The basic objective of this series is to serve as a major reference source for the uniform treatment of acoustic, electromagnetic and elastodynamic field problems. It provides an indispensable guide for the scientific community and graduate students by acquainting them very quickly with the basic principles of a certain technique as it is applied to any of the three fields, and also provides appropriate references. It was felt that in presenting such a comprehensive collection of treatment methods as they are applied to all three wave fields it would open up a whole range of new ideas to solid mechanists, who would perhaps otherwise not come into contact with such electromagnetic waves literature. These three subseries of volumes will prove a useful aid to researchers in reading and understanding the jargon used in the literature on acoustic, electromagnetic and elastodynamic fields, as well as providing them with the opportunity for the cross-fertilization of ideas.

Table of Contents:
1. Acoustic, Electromagnetic and Elastodynamic Fields (V.V. Varadan, V.K. Varadan). The acoustic field. The electromagnetic field. The elastodynamic field. Infinite-medium time-harmonic Green's functions. 2. Introduction to Integral Representations and Integral Equations for Time-Harmonic Acoustic, Electromagnetic, and Elastodynamic Wave Fields (S. Strouml;m). The differential equations in the linearized theories of acoustic, electromagnetic and elastodynamic wave propagation. The free-space Green's function and dyadic. Green's theorem for scalar and vector fields. Integral representations and integral equations for acoustic waves. Integral representations and integral equations for electromagnetic waves. Integral representations and integral equations for elastodynamic waves. 3. The Scattered Field(S. Strom). The far-field scattering amplitude: the forward amplitude theorem and symmetry properties. The scattering and transition matrices for spherical waves. 4. Transformation Properties of Plane, Spherical and Cylindrical Scalar and Vector Wave Functions (A. Bostrom et al.). Definition of three-dimensional wave functions; expansions of the Green's function. Definition of two-dimensional wave functions; expansions of the Green's function. Transformations between the wave functions. Translations. Rotations. An illustrative problem. Appendices: A. Mathematical comments on the transformations of the outgoing scalar waves. B. Some remarks on the connection to the representation theory for E(B). 5. Scattering of Waves by Spheres and Cylinders(V.V. Varadan et al.). Cylindrical basis functions. Spherical basis functions. Scattering of waves by a circular cylinder-scalar formulation (acoustic waves, electromagnetic TE and TM waves, elastic SH waves). Scattering of P- and SV-waves by a circular cylinder. Scattering of acoustic, electromagnetic and elastic waves by spheres. Vector problems involving fluid/solid interfaces. Conclusion. Appendices: A. Displacement and stress components in cylindrical functions. B. Displacement and stress components in vector spherical functions. C. Fortran computer programs. References. 6. Some Important Mathematical Relations. (V.V. Varadan et al.). Vectors and dyadics. Vector and dyadic calculus. Integral relationships. Special functions. Author index. Subject index.