Variational Methods in Nuclear Reactor Physics

Variational Methods in Nuclear Reactor Physics

1st Edition - January 1, 1974

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  • Editor: Weston M. Jr. Stacey
  • eBook ISBN: 9780323160438

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Nuclear Science and Technology, Volume 10: Variational Methods in Nuclear Reactor Physics presents the mathematical methods of a variational origin that are useful in obtaining approximate solutions to science and engineering problems. This book is composed of five chapters and begins with a discussion on the variation principles for physical systems described by both inhomogeneous and homogeneous equations to develop a generalized perturbation theory. Chapter 2 deals with the applications of variational estimates and generalized perturbation theory to neutron transport problems. Chapter 3 covers the variation principles of the Lagrangian form that are constructed for a general, linear- time-dependent process and for the specific case of the P1 neutron kinetics equations. Chapter 4 presents the general procedure for the variational derivation of synthesis approximations and their applications to problems in reactor physics. This chapter also examines the relationship of the spatial synthesis and finite-element method and a hybrid method that combines features of both methods. Chapter 5 describes the relationship of variation theory with the Hamilton-Jacobi theory and with the optimization theories of the maximum principle and dynamic programming. Nuclear physicists and researchers will find this text invaluable.

Table of Contents

  • Preface


    1. Variational Estimates and Perturbation Theory

    1.1. Source Problems

    1.2. Eigenvalue Problems

    1.3. Generalized Perturbation Theory

    1.4. Higher-Order Variational Principles


    2. Applications of Variational Estimates and Generalized Perturbation Theory

    2.1. Self-Shielding Factor for an Isolated Slab in a Diffusing Medium

    2.2. Resonance Absorption of Neutrons

    2.3. Reactivity Worths and Reaction Rate Ratios in Critical Nuclear Reactors

    2.4. Nuclear Reactor Kinetics

    2.5. Controlled Thermonuclear Reactor Blankets

    2.6. Radiation Shielding

    2.7. Heterogeneity Reactivity Effects in Nuclear Reactors


    3. Variational Formulations

    3.1. Linear, Time-Dependent Processes

    3.2. P1 Multigroup Neutron Kinetics

    3.3. Monoenergetic Neutron Transport Theory

    3.4. Least Squares


    4. Synthesis

    4.1. Synthesis Approximations—General

    4.2. Spatial Synthesis in Multigroup Neutron P1 Theory

    4.3. Spectral Synthesis in Multigroup Neutron P1 Theory

    4.4. Angular Synthesis in Monoenergetic Neutron Transport Theory


    5. Variational Theory

    5.1. Canonical and Involutory Transformations of Variational Principles

    5.2. Transformations of the Variational Principles of Reactor Physics

    5.3. Variational Field Theory


    Appendix. Linear Function Spaces and Functionals



Product details

  • No. of pages: 192
  • Language: English
  • Copyright: © Academic Press 1974
  • Published: January 1, 1974
  • Imprint: Academic Press
  • eBook ISBN: 9780323160438

About the Editor

Weston M. Jr. Stacey

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