Wave Propagation. Scattering Theory

1993 ◽  
Keyword(s):  
Wave Propagation ◽  
Scattering Theory

On the kinetic theory of wave propagation in random media

1973 ◽  
Vol 274 (1242) ◽  
pp. 523-549 ◽  
Keyword(s):  
Wave Propagation ◽  
Energy Transfer ◽  
Scattering Theory ◽  
Random Media ◽  
Order Approximation ◽  
Random Medium ◽  
Second Law Of Thermodynamics ◽  
Second Law ◽  
Conservation Of Energy ◽  
Transfer Processes

This paper considers the theory of the multiple scattering of waves in extensive random media. The classical theory of wave propagation in random media is discussed with reference to its practical limitations, and in particular to the inability of the lowest order approximation to the Bethe-Salpeter equation, which describes the propagation of correlations, to account for conservation of energy. An alternative kinetic theory is formulated, based on the theory of energy transfer processes in random media. The proposed theory satisfies conservation of energy and the Second Law of Thermodynamics. It is illustrated by a consideration of three problems each of which is difficult or impossible to treat by classical scattering theory. These involve the transmission of energy through a slab of random medium; the scattering theory of geometrical optics; and scattering by a randomly inhomogeneous half-space.

Spectral representation and scattering theory for the wave equation with two unbounded media

1993 ◽  
Vol 113 (2) ◽  
pp. 423-447 ◽  
Author(s):  
G. F. Roach ◽  
Bo Zhang
Keyword(s):  
Wave Propagation ◽  
Wave Equation ◽  
Stationary Phase ◽  
Scattering Theory ◽  
Spectral Representation ◽  
Fourier Transforms ◽  
Eigenfunction Expansions ◽  
Wave Operators ◽  
Unbounded Media ◽  
Generalized Eigenfunction

AbstractIn this paper, we establish the generalized eigenfunction expansions for wave propagation in inhomogeneous, penetrable media in ℝn(n ≥ 2) with an unbounded interface. We then use them together with the method of stationary phase to prove the existence of the wave operators and to obtain the representations of the wave operators in terms of the generalized Fourier transforms.

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