Book Revims in use. These simple models would then provide a convenient tool for understanding and extrapolation in the area of fast reactor physics, comparable to the models used successfully in thermal reactors. Here again the work reported along these lines is based on weighted residuals, or modal techniques.
The present monograph, which is essentially a compilation of three papers published by the author in Nuclear Science and E?qpbering during 1967 addresses itself to problems in both of the aress mentioned. The major emphasis in the book is given to the develop ment of simple modal approximations using few trial functions with more or less immediate physical meaning. Several examples of the application of these ideas to relatively simply physioal situations and ingenious ways to derive spectrum and importance trial functions for fast reactors are developed in detail. The flexibility of the approach is illustrated and its predictions found reasonably accurate.
The first chapter gives a new unified derivation of several modal approximation methods. It uses an operator weighted integration of the differential equation to obtain the results usually derived by the simpler weighted residuals procedure. Some new approximation schemes are suggested but not applied. It is surprising that one of the most widely ap- plied modal approximations, the Galerkin method, is only implied here, and even though it is later used in examples it is never explicitly mentioned.
Leaving aside the fact that multigroup methods, P, approximations and S. approximations can be considered as modal teohniques, the most successful of the "properly" modal methods are those developed as an answer to the first problem mentioned.
These techniques have been developed within the context of the multigroup approach. The number of trial functions used can be quite large and has lately been extended to include discontinuous functions. This is achieved by the consideration of special variational principles and careful analysis of boundary conditions. The fact that this whole area of modal approximations is not mentioned in the book, reduces its usefulness as a codification of the modal expansion method, which is one of its main purposes.