Approximate Solutions of Steady-State Neutron Transport Problems for Slabs (Classic Reprint) PDF Download
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Author: Herbert B. Keller Publisher: Forgotten Books ISBN: 9780266954316 Category : Mathematics Languages : en Pages : 68
Book Description
Excerpt from Approximate Solutions of Steady-State Neutron Transport Problems for Slabs In Part I (sections 2-5) we consider the elastic scatter ing transport equation for an infinite plane slab of finite thickness and arbitrary composition. The convergence of the approximate solution, which is obtained explicitly, to the exact solution in the appropriate limit is demonstrated. It is also shown that the approximate solution is stable with respect to the growth of small errors introduced by approximation or inaccurate knowledge of the inhomogeneous source terms. The method and solution are easily modified to solve the spherically symmetric case. 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: Herbert B. Keller Publisher: Forgotten Books ISBN: 9780266954316 Category : Mathematics Languages : en Pages : 68
Book Description
Excerpt from Approximate Solutions of Steady-State Neutron Transport Problems for Slabs In Part I (sections 2-5) we consider the elastic scatter ing transport equation for an infinite plane slab of finite thickness and arbitrary composition. The convergence of the approximate solution, which is obtained explicitly, to the exact solution in the appropriate limit is demonstrated. It is also shown that the approximate solution is stable with respect to the growth of small errors introduced by approximation or inaccurate knowledge of the inhomogeneous source terms. The method and solution are easily modified to solve the spherically symmetric case. 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: Perry A. Newman Publisher: ISBN: Category : Case method Languages : en Pages : 122
Book Description
The solution of an initial-value problem in linear transport theory is obtained by using the normal-mode expansion technique of Case. The problem is that of monoenergetic neutrons migrating in a thin slab surrounded by infinitely thick reflectors and the scattering is taken to be isotropic. The results obtained indicate that the reflector may give rise to a branch-cut integral term typical of a semi-infinite medium whereas the central slab may contribute a summation over discrete residue terms. Exact expressions are obtained for these discrete time eigenvalues, and numerical results showing the behavior of real time eigenvalues as a function of the material properties of the slab and reflector are presented. These eigenvalues are finite in number and may disappear into the branch cut or continuum as the material properties are varied; such disappearing eigenvalues correspond to exponentially time-decaying modes. The two largest eigenvalues can be compared with critical dimensions of slabs and spheres, and the numerical values are shown to agree with the critically results of others. In the limit of purely absorbing reflectors or a bare slab, the present solution has the same properties as have been previously reported by others who used the approach of Lehner and Wing.
Author: Herbert B. Keller
Author: Herbert B. Keller
Author: Herbert Keller
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