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Excerpt from Multiple Scattering in One Dimension
It may be mentioned that our results apply to certain natural one dimensional problems that occur in practice. These problems have to do with the construction of artificial dielectrics in wave guides and transmission lines (electrical and acoustical). In the language of transmission line theory, the scattering elements are small lumped impedances or admittances placed along the transmission line. Our results provide a basis for deciding to what degree collections of such elements may be regarded as forming an artificial (continuous) dielectric. As they stand, the results apply either to scattering by impedances arranged in series or to admittances arranged in parallel. It is an easy matter.
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Multiple Scattering in One Dimension (Classic Reprint)
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Paperback. Zustand: New. Print on Demand. This book is a rigorous mathematical treatment of the scattering of radiation by a finite collection of elementary scatterers. It provides a justification for two formal procedures now in wide use for treating such problems. The scattering elements are assumed to be identical non-dissipative point scatterers which are completely characterized by an impedance function and which are microscopic in the sense that the ratio of the scatterer impedance to the free space wave impedance is much less, in absolute value, than unity. The author begins by formulating both the single configuration problem and the corresponding statistical problem. The solutions of these problems are approximated by solutions of related continuum problems and general estimates are given for the errors of approximation. By expressing these errors solely in terms of the basic parameters, he establishes sufficient conditions which ensure that the errors are small. Certain natural sufficient conditions are given which ensure a close approximation to the continuum problems, and estimates of the error of approximation are developed. These conditions and estimates are expressed solely in terms of the basic physical parameters of the scattering process. For example, the author shows that, in the special case in which the scatterers are distributed uniformly, the continuum solution approaches the exact solution as the number of scatterers approaches infinity. This book is a reproduction of an important historical work, digitally reconstructed using state-of-the-art technology to preserve the original format. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in the book. print-on-demand item. Bestandsnummer des Verkäufers 9781333001728_0
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Multiple Scattering in One Dimension (Classic Reprint)
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Multiple Scattering in One Dimension (Classic Reprint)
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