One of my graduate students decided to use a popular commercial software in order to investigate scattering by three-dimensional (3-D) objects. Within a few weeks, he came up with very nice plots of scattering patterns as well as colorful spatial profiles of scattered fields. As the 3-D objects were of complicated shapes and my brain is still wired to analytical treatments of scattering, I asked him to repeat his calculations for a sphere made of an isotropic material. After looking at the diagrams he supplied, I decided that something had gone wrong.

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Editorial: Vanishing methods

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.

Field representations and introduction to scattering

From crime figures to health scares, election polls to stock market forecasts, numbers make the news all the time. But are they accurate? John Allen Paulos, travels through the pages of an average newspaper, revealing how mathematics is at the heart of the articles we read everyday - even horoscopes and the sports pages - and how often they mislead us. By understanding simple concepts such as probability, chaos theory and game theory, you'll be able to see through faulty statistics, stock market forecasters and conspiracy theorists - and make the figures truly add up.

A Mathematician Reads the Newspaper

: The book represents an exhaustive study of the scattering properties of acoustically soft and hard bodies and of perfect conductors, presented for 15 geometrically-simple shapes Such shapes are important in their own right and as a basis for synthesizing the radiation and scattering properties of more complex configurations Each shape is treated in a separate chapter whose contents are presented in stylized format for easy reference Emphasis is placed on results in the form of formulae and diagrams Although no detailed derivation are included, an outline of methods in scattering theory is given in the Introduction

Electromagnetic and acoustic scattering by simple shapes

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Editorial: Vanishing methods

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Field representations and introduction to scattering

A Mathematician Reads the Newspaper

Electromagnetic and acoustic scattering by simple shapes