Excerpt from Multiple Scattering of Waves by Planar Random Distributions of Parallel Cylinders and Bosses We derive closed-form representations which are valid at least when the minimum separation of cylinders is large com pared to radius and wavelength; these apparently suffice to take into account the largest effects of multiple scattering. We show that these representations hold either when there is a high degree of order in the distribution of neighbors, or for all distributions near grazing incidence. Other representations are also discussed. The most interesting result we obtain concerns the be havior near grazing incidence. Whereas the single-scattered wave may become infinite as grazing incidence is approached, the multiple scattered wave approaches the negative of the incident wave. Thus the results reduce to those for a dielectric plane near grazing incidence, the incident wave being perfectly reflected with the appropriate sign change. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.

Excerpt from Multiple Scattering of Waves by a Volume Distribution of Parallel Cylinders Whr the case of isotropic scatterers our wave function is essentially of the form obtained previously by Reiche2 and Foldy3; for non-isotropic scatter ers our wave function differs from that of'laxy in that the propagation constant depends on the angle of incidence. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.

Excerpt from Multiple Scattering of Radiation, Vol. 2: The Grating This report is section b of a series of papers on multiple scattering of radiation. The first three sections, dealing respectively with an arbit rary configuration of parallel cylinders, a planar configuration, and two cylinders will be found in Research Report EM - bn. Formal solutions satis fying any of the usually prescribed boundary conditions at the surface of each cylinder were obtained for the previous scattering problems by explicit ly taking into account all contributions to the excitation of each cylinder by the radiation the remaining cylinders scattered. The solution was ex pressed as the incident wave plus a sum of an infinite number of orders of scattering. The first order, the usual single scattering approximation, resulted from the excitation of each cylinder by only the incident plane wave; the second order arose from the excitation of each element by the first order of scattering from the remaining elements, etc. In the present report we will consider the multiple scattering of radiation by a finite grating of parallel cylinders. To obviate repetition the results of the. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.

The multiple scattering is treated of plane waves by two identical infinite, widely spaced, parallel elliptic cylinders in the case where the major axes are parallel and the minor axes collinear and vic -versa. The results obtained provide some idea of the nature of the interaction terms in the fields scattered by combinations of cylinders. They show how the Mathieu function solutions of the individual cylinders are modified when the individual solutions for the two cylinders are combined. They also indicate the possible application of a combination of elliptic cylinders as a wave filter since the cylinders select different kinds of Mathieu functions to be multiply scattered according to the relative orientations of the major axes. (Author).