The Equivalence of the Isotropic and Monodirectional Source Problems.

by H. H. Natsuyama, Robert E. Kalaba

Purchase

Purchase Print Copy

 FormatList Price Price
Add to Cart Paperback-245 pages $20.00 $16.00 20% Web Discount

A demonstration that the solution of the problem of multiple scattering in a slab that is illuminated by parallel rays of radiation can be expressed in terms of the solution of the problem in which there are isotropic sources of radiation. The quantities of interest for the monodirectional case (the X, Y, I, S, J, and T functions) are given algebraically in terms of the b and h functions that express the internal intensities for the isotropic source problem. For I, this avoids a matrix inversion, thus overcoming a difficulty associated with the direct application of Chandrasekhar's invariance principles. This study is an extension of RM-4906-PR; the formulas given can be used with the tables of RM-4958-PR and a desk calculator to compute the standard functions for the monodirectional case. 13 pp. Refs.

This report is part of the RAND Corporation Research memorandum series. The Research Memorandum was a product of the RAND Corporation from 1948 to 1973 that represented working papers meant to report current results of RAND research to appropriate audiences.

Our mission to help improve policy and decisionmaking through research and analysis is enabled through our core values of quality and objectivity and our unwavering commitment to the highest level of integrity and ethical behavior. To help ensure our research and analysis are rigorous, objective, and nonpartisan, we subject our research publications to a robust and exacting quality-assurance process; avoid both the appearance and reality of financial and other conflicts of interest through staff training, project screening, and a policy of mandatory disclosure; and pursue transparency in our research engagements through our commitment to the open publication of our research findings and recommendations, disclosure of the source of funding of published research, and policies to ensure intellectual independence. For more information, visit www.rand.org/about/research-integrity.

The RAND Corporation is a nonprofit institution that helps improve policy and decisionmaking through research and analysis. RAND's publications do not necessarily reflect the opinions of its research clients and sponsors.