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Problems in classical scattering, the Dirichlet, Neumann, and transmission problems for the Helmholtz equation, and the problem of a perfect reflector for Maxwell's equations are formulated as problems in integral equations. The spectrum of the integral operators is shown to vary in each case. However, a result from func tional analysis on the perturbation of spectra is used not only to establish...
What classical and quantum physics have in common is that they deal with material objects, be they elastic bodies imbedded in a medium, atomic nuclei, or even elementary particles. Each of these target objects, when hit by an incident signal (a propagating wave, or a beam of particles), will be excited into eigenvibrations, and in its vibrating state will reemit waves or particles which will carry...
A number of problems, conjectures, and results in radar scattering theory and related fields are reported. Some experiments useful for suggesting theoretical problems or confirming theoretical results are also sketched.
The earth's environment contains propagation channels wherein waves can be guided because of the presence of transverse boundaries or transverse refractive index gradients. By a new approach, high-frequency guiding by a single concave surface or by the boundary of an inhomogeneous surface duct has recently been analyzed in terms of a judiciously chosen combination of rays and modes. In essence, the...
The scattering of waves by random surfaces and media has long been of considerable interest from both theoretical and experimental viewpoints. This paper briefly reviews the work of our group toward developing variational principles which are applicable to the scattering of scalar and vector waves from stochastic systems. These principles have the general form 4π<T> = <N1><...
By means of the Resonance Theory of viscoelastic wave-scattering from cavities in solids, we examine several multipole contributions to the sonar cross sections of fluid-filled cavities in solid rubbers. The analysis is done first ignoring, and then accounting for mode-conversion in the solid rubber matrix. The results are analytically particularized to the simpler cases of a) the nth multipole of...
The recently proposed mixed representation in quantum mechanics is discussed and applied to the scattering of a particle by a potential in three dimensions. Such scattering becomes equivalent to a one-dimensional reflection problem with a nonlocal potential. [/p]
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