Scattering and Nonscattering Obstacles
Abstract
Two problems of Helmholtz's equation for a wave incident on an obstacle are considered. For the first, the scattering problem, the obstacle's response satisfies Sommerfeld's outgoing wave radiation condition, and the net radiative response is positive; for the second, the response satisfies a standing wave condition (an appropriate combination of outgoing and incoming waves) such that the net radiative response is zero. The essential features of the solutions are exhibited in terms of amplitude functions g (the usual scattering amplitude) and g', and the interrelation of the functions are stressed in the derivation of integral equations g(g') (introduced earlier in multiple scattering contexts). The scattering amplitude g is always complex, but the simpler function g' is shown to be imaginary for nonabsorbing obstacles having inversion symmetry. Long-wavelength approximations for g' may be obtained from potential theory and perturbation procedures, and corresponding approximations for g then follow from g(g'). (jhd)
Document Details
- Document Type
- Technical Report
- Publication Date
- Aug 01, 1983
- Accession Number
- ADA222757
Entities
People
- Victor Twersky
Organizations
- University of Illinois at Chicago