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Transition operators in acoustic-wave diffraction theory. I - General theory. II - Short-wavelength behavior, dominant singularities of Zk0 and Zk0 exp -1A formal theory of the scattering of time-harmonic acoustic scalar waves from impenetrable, immobile obstacles is established. The time-independent formal scattering theory of nonrelativistic quantum mechanics, in particular the theory of the complete Green's function and the transition (T) operator, provides the model. The quantum-mechanical approach is modified to allow the treatment of acoustic-wave scattering with imposed boundary conditions of impedance type on the surface (delta-Omega) of an impenetrable obstacle. With k0 as the free-space wavenumber of the signal, a simplified expression is obtained for the k0-dependent T operator for a general case of homogeneous impedance boundary conditions for the acoustic wave on delta-Omega. All the nonelementary operators entering the expression for the T operator are formally simple rational algebraic functions of a certain invertible linear radiation impedance operator which maps any sufficiently well-behaved complex-valued function on delta-Omega into another such function on delta-Omega. In the subsequent study, the short-wavelength and the long-wavelength behavior of the radiation impedance operator and its inverse (the 'radiation admittance' operator) as two-point kernels on a smooth delta-Omega are studied for pairs of points that are close together.
Document ID
Document Type
Reprint (Version printed in journal)
External Source(s)
Hahne, G. E. (NASA Ames Research Center Moffett Field, CA, United States)
Date Acquired
August 15, 2013
Publication Date
January 15, 1991
Publication Information
Publication: Physical Review A
Volume: 43
ISSN: 1050-2947
Subject Category
Distribution Limits