IEEE T4anaction.6 on Pt&4ma Science, VoZ,.PS-3, No.4, DecembeA 1975

VARIATIONAL METHODS IN NUCLEAR REACTOR PHYSICS

by W. M Stacey, Jr.

Academic Press, New York and London, 1974, 181 pp., diagrams, 6x9 in., price, $18. 50

The utilization of variational methods for the solution ofproblems of physical systems dates back to the early days ofthe Bernoullis. The author brings, in an effective way, tothe attention and appreciation of practising engineers andscientists the philosophy of recent mathematical methods ofvaried origin, while not yet minimizing the classicalapproaches in the calculus of variations. The book thus con-tains a comprehensive treatment of the theory of variationalmethods applied to reactor physics, with applications in al-lied engineering and scientific disciplines.

Chapter I and II consider conventional approaches to theapplication of variational methods for the solution of avail-able mathematical formulations of physical systems: withhints for development of a generalized perturbation theoryapplicable to the study of the effects of parameter changes ona system model.

Chapter III deals in a comprehensive way with methodsof mathematical formulation to achieve a satisfactory modelfor simulation and for studying the dynamic performance ofthe system. This is well-developed for a generalized phys-ical process, especially applicable to neutron kinetics andneutron transport theory.

Chapter IV advances the theory of synthesis methods

based on variational formulation for deriving systematicallythe approximate mathematical equations which describe thephysical system. The method of approach is "more classi-cal": in the sense that it avoids direct derivations from thephysical systems and utilizes methods stemming from thecalculus of variations. The methods include especial em-phasis on spectral and spatial approximations in neutron dif-fusion theory and angular approximations in neutron trans-port theory.

Chapter V considers different methods of approach forthe representation of physical systems by using functionalequations obtained by transformation of dependent variables.Emphasis is on certain major variational procedures: theHamilton-Jacobi differential equation, Pontryagin's maxi-mum principle, Bellman's dynamic programming, and vari-ational field theory. Use of variational field theory to obtaina new formulation of neutron diffusion theory suggests a non-standard but powerful solution technique for the solution ofsystems.

In the opinion of the reviewer, the author has given ac-count of the various mathematical formulations and the vari-ational field theory approach in a very effective way. Thebook is a valuable reference for both graduate students andin-practice professionals.

M. K. S. MoorthyBurns and Roe, Inc.700 Kinderkamack RoadOradell, New Jersey

22g