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Variational methods in nuclear reactor physics
Book Reviews
VARIATIONAL METHODS IN NUCLEAR REACXOR PHYSICS, by W. M. Stacey. 181 pages, diagrams, 6 x 9 in. New York, Academic Press Inc., 1974. Price, $18.50. In Volume 10 of Academic Press series of monographs on Nuclear Science and Technology, the author’s Preface says “it is possible to read the book with no prior knowledge of the subject”. However, this is definitely a specialist’s book and it would be difficult for anyone unversed in the field to appreciate the issues raised. After a brief chapter which quotes only the essence of the mathematical procedures, with no concession to the reader except an extensive reference list, there are four chapters on applications of variational estimates, on variational formulations of specific problems such as nuclear kinetics and transform theory, and on the use of variational procedures to obtain approximate solutions to elaborate problems such as arise in describing the spatial and spectral variations of neutron flux. The final brief chapter on variational theory indicates some links between the methods used in the text and with the Hamilton-Jacobi theory and the optimization techniques of conventional modern control theorists. As elsewhere in the monograph the derivations here are sparse and the conclusions, though presented authoritatively, are not always clearly justified by the material presented. The author in his published papers has contributed in this area, and this monograph can be viewed more as a commentary than a full presentation. This reviewel sees it as a literature survey (there are 200 references), and collecting and correlating this material should be useful for those who may wish to evaluate variational methods.
The text comes alive in Chap. 2 when dealing with actual applications, but slips back to a rather dull style of presentation in the theoretical sections. No new ideas seem to have come from the exercise and no conclusions are stressed. The book should not be considered as an introduction to the concepts of variational methods. Because of space limitations much of the mathematics is too concentrated for the novice and this brevity means it is not easy to read. The specialist will appreciate the guided tour of the relevant literature and the author’s assessments of various contributions; he will want to go to the original papers for full details and these are well referenced. C. A. STAPLETON Department of Systems and Control University of New South Wales Kensington, Australia
SIGNAL PROCESSING: DISCRETE SPECTRAL ANALYSIS,DETECTION, AND ESTIMATION, by Mischa Schwartz and Leonard Shaw. 396 pages, diagrams, 6:X 91 in., New York, McGraw-Hill, Inc., 1975. Price, $18.50. Careful attention was obviously given to pedagogy in the preparation of this senior level text. It was written primarily for electrical engineering and computer science students, but the many examples drawn from diverse fields make the material’s broader application evident. Prerequisites are elementary courses in signal analysis and probability, and some knowledge of programming if the computer exercises provided are to be assigned. Chapter 1 describes the signal processing facets of air traffic control radar systems, an example used illustratively and as a source of problems throughout. Chapter
219
VARIATIONAL METHODS IN NUCLEAR REACXOR PHYSICS, by W. M. Stacey. 181 pages, diagrams, 6 x 9 in. New York, Academic Press Inc., 1974. Price, $18.50. In Volume 10 of Academic Press series of monographs on Nuclear Science and Technology, the author’s Preface says “it is possible to read the book with no prior knowledge of the subject”. However, this is definitely a specialist’s book and it would be difficult for anyone unversed in the field to appreciate the issues raised. After a brief chapter which quotes only the essence of the mathematical procedures, with no concession to the reader except an extensive reference list, there are four chapters on applications of variational estimates, on variational formulations of specific problems such as nuclear kinetics and transform theory, and on the use of variational procedures to obtain approximate solutions to elaborate problems such as arise in describing the spatial and spectral variations of neutron flux. The final brief chapter on variational theory indicates some links between the methods used in the text and with the Hamilton-Jacobi theory and the optimization techniques of conventional modern control theorists. As elsewhere in the monograph the derivations here are sparse and the conclusions, though presented authoritatively, are not always clearly justified by the material presented. The author in his published papers has contributed in this area, and this monograph can be viewed more as a commentary than a full presentation. This reviewel sees it as a literature survey (there are 200 references), and collecting and correlating this material should be useful for those who may wish to evaluate variational methods.
The text comes alive in Chap. 2 when dealing with actual applications, but slips back to a rather dull style of presentation in the theoretical sections. No new ideas seem to have come from the exercise and no conclusions are stressed. The book should not be considered as an introduction to the concepts of variational methods. Because of space limitations much of the mathematics is too concentrated for the novice and this brevity means it is not easy to read. The specialist will appreciate the guided tour of the relevant literature and the author’s assessments of various contributions; he will want to go to the original papers for full details and these are well referenced. C. A. STAPLETON Department of Systems and Control University of New South Wales Kensington, Australia
SIGNAL PROCESSING: DISCRETE SPECTRAL ANALYSIS,DETECTION, AND ESTIMATION, by Mischa Schwartz and Leonard Shaw. 396 pages, diagrams, 6:X 91 in., New York, McGraw-Hill, Inc., 1975. Price, $18.50. Careful attention was obviously given to pedagogy in the preparation of this senior level text. It was written primarily for electrical engineering and computer science students, but the many examples drawn from diverse fields make the material’s broader application evident. Prerequisites are elementary courses in signal analysis and probability, and some knowledge of programming if the computer exercises provided are to be assigned. Chapter 1 describes the signal processing facets of air traffic control radar systems, an example used illustratively and as a source of problems throughout. Chapter
219