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  • 1
    ISSN: 1420-9039
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract Reciprocity and scattering theorems for the normalized spherical scattering amplitude for elastic waves are obtained for the case of a rigid scatterer, a cavity and a penetrable scattering region. Depending on the polarization of the two incident waves reciprocity relations of the radial-radial, radial-angular, and angular-angular type are established. Radial and angular scattering theorems, expressing the corresponding scattering amplitudes via integrals of the amplitudes over all directions of observation, as well as their special forms for scatterers with inversion symmetry are also provided. As a consequence of the stated scattering theorems the scattering cross-section for either a longitudinal, or a transverse incident wave is expressed through the forward value of the radial, or the angular amplitude, correspondingly. All the known relative theorems for acoustic scattering are trivially recovered from their elastic counterparts.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Chichester, West Sussex : Wiley-Blackwell
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this paper a necessary and sufficient condition for a pair of vector functions to be radiation patterns is presented. More precisely, it is proved that two vector functions, the first in the radial direction and the second in the tangential one, are radiation patterns if and only if there are two entire harmonic vector functions whose radial and tangential projections, respectively, are identical with the previous functions on the unit sphere and whose L2-norm over a sphere of radius R is a function of exponential type in the variable R.
    Type of Medium: Electronic Resource
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  • 3
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In the present work, the problem of electromagnetic wave propagation in three-dimensional stratified media is studied. The method of decoupling the electric and magnetic fields is implemented, and the spectral approach is adopted, componentwise, to the vector equation involving the electric field. Operational calculus of self-adjoint, positive operators in suitable Hilbert spaces is used to solve the corresponding initial value problems. The spectral families of these operators for the cases of the whole space and of a finite layer are constructed. A discussion on the applicability of the obtained results to physical problems is also included. © 1998 B.G. Teubner Stuttgart-John Wiley & Sons Ltd.
    Type of Medium: Electronic Resource
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  • 4
    ISSN: 1573-2703
    Keywords: Scattering theory ; linear elasticity ; low-frequency expansions ; coated materials
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Technology
    Notes: Abstract This work deals with the scattering of a plane harmonic elastic wave by a penetrable spherical scatterer with a concentric spherical penetrable inclusion. We evaluate the zeroth and first-order approximations of the Rayleigh expansion of the displacement fields. The major line of applications belongs to the science of the particulate composite material. So, as an application of the method, a typical particulate composite material is examined and the behaviour of the scattering cross section with respect to the elastic properties of the medium is presented.
    Type of Medium: Electronic Resource
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