[PDF] High Frequency Scattering By An Impenetrable Sphere eBook

Author : Herch Moyses Nussenzveig
Publisher :
Page : 131 pages
File Size : 49,98 MB
Release : 1965
Category : Scattering (Mathematics)
ISBN :

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The scattering of a scalar plane wave by a totally reflecting sphere (hard-core potential) at high frequencies is treated by a modified Watson transformation. The behavior of the solution both in the near and far regions of space is discussed, as well as the accuracy and domain of applicability of the WKB approximation and classical diffraction theory. It is shown that different transformations are required in the forward and backward half-spaces, and corresponding integral representations for the primary wave are derived. The transformations are rigorously proved and the convergence of the residue series is discussed. In the shadow region, the physical interpretation of the complex angular momentum poles in terms of surface waves is in agreement with Keller's geometrical theory of diffraction. In the lit region, sufficiently far from the shadow boundary, the WKB expansion for the wave function is confirmed up to the second order. On the surface of the sphere, Kirchhoff's approximation is accurate, except in the penumbra region, where the behavior is described by Fock's function. The diffraction effects in the neighborhood of the shadow boundary are investigated and the corrections to classical diffraction theory are obtained.

Author : H M Nussenzveig
Publisher : Palala Press
Page : 136 pages
File Size : 32,53 MB
Release : 2018-03-02
Category :
ISBN : 9781378952528

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This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.

Author : H. M. Nussenzveig
Publisher : Forgotten Books
Page : 138 pages
File Size : 22,10 MB
Release : 2017-10-22
Category : Mathematics
ISBN : 9780265606766

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Excerpt from High-Frequency Scattering by an Impenetrable Sphere As will be shown in Section VI, this treatment is also incomplete, for it does not apply to the backward half-space. A certain amount of confusion seems to exist in the literature concerning the application of Watson's transformation in the lit region. 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.

Author : S. I. Rubinow
Publisher : Forgotten Books
Page : 56 pages
File Size : 29,33 MB
Release : 2017-12-23
Category : Mathematics
ISBN : 9780484503464

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Excerpt from Scattering From a Penetrable Sphere at High Frequencies We consider a scalar plane wave incident on a penetrable sphere in the limit of high frequencies for which the wave length of the incident wave is small compared to the radius of the Sphere. Quantum mechanically, the prob lem represents the scattering of a highly energetic particle by an attractive square well. It is also closely related to the corresponding electromagnetic problem which occurs in the scattering of light by water droplets. As such, it has engaged the attention of very many scientists whom we can not hope to enumerate here. A.more or less complete historical record of the contributors to the raindrop prdblem.may be found in van de Hulst's book [i]. The justifi cation of the present work lies in the new representation of the scattering amplitude which is particularly appropriate to the study of it in the high frequency or short wave length limit. By means of it, it is possible to dis tinguish the contributions of the geometric optics field and of the diffracted field. 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.

Author : Allan D. Pierce
Publisher : Academic Press
Page : 340 pages
File Size : 23,88 MB
Release : 2013-10-22
Category : Science
ISBN : 1483257703

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High Frequency and Pulse Scattering investigates high frequency and pulse scattering, with emphasis on the phenomenon of echoes from objects. Geometrical and catastrophe optics methods in scattering are discussed, along with the scattering of sound pulses and the ringing of target resonances. Caustics and associated diffraction catastrophes are also examined. Comprised of two chapters, this volume begins with a detailed account of geometrically based approximation methods in scattering theory, focusing on waves transmitted through fluid and elastic scatterers and glory scattering; surface ray representations of scattering by shells and other smooth objects; and caustics and associated diffraction catastrophes. The second chapter deals with the relation between sound pulses and the vibrational spectra of elastic submerged objects. The theory of the scattering of sound pulses from elastic and impenetrable objects is described, together with the theory of surface wave pulses. Target resonances and the singularity expansion method are also analyzed. This book will be of interest to physicists.

Author : Andrey V. Osipov
Publisher : John Wiley & Sons
Page : 824 pages
File Size : 11,27 MB
Release : 2017-04-17
Category : Technology & Engineering
ISBN : 0470512385

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This self-contained book gives fundamental knowledge about scattering and diffraction of electromagnetic waves and fills the gap between general electromagnetic theory courses and collections of engineering formulas. The book is a tutorial for advanced students learning the mathematics and physics of electromagnetic scattering and curious to know how engineering concepts and techniques relate to the foundations of electromagnetics

Author : Tom Rother
Publisher : Springer Nature
Page : 265 pages
File Size : 15,54 MB
Release : 2020-02-13
Category : Science
ISBN : 3030364488

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This book introduces readers to scattering from a practical/numerical point of view. The focus is on basic aspects like single scattering, multiple scattering, and whether inhomogeneous boundary conditions or inhomogeneous scatterers have to be taken into account. The powerful T-matrix approach is explained in detail and used throughout the book, and iterative solution methods are discussed. In addition, the book addresses appropriate criteria for estimating the accuracy of numerical results, as well as their importance for practical applications. Python code is provided with each chapter, and can be freely used and modified by readers. Moreover, numerous scattering results for different configurations are provided for benchmarking purposes. The book will be particularly valuable for those readers who plan to develop their own scattering code, and wish to test the correct numerical implementation of the underlying mathematics.