ENERGY-DEPENDENT NEUTRON TRANSPORT THEORY IN PLANE GEOMETRY. II. EIGENFUNCTIONS AND FULL-RANGE COMPLETENESS,

Abstract

An earlier treatment of the energy-dependent transport equation is extended to include the case in which cross sections are functions of energy. The technique again consists of finding solutions to the homogeneous transport equation after expanding in terms of a complete set of functions in the energy variable. The full-range completeness theorem for these eigenfunctions requires the solution of a coupled set of singular integral equations. This solution is effected by a generalization of a trick used by Case and is applied to the problem for the infinite medium Green's function. Numerical results are given for a heavy gas model. The half-range completeness theorem, which may be applied to half-space and finite slab problems, is proven in a companion paper. (Author)

Document Details

Document Type
Technical Report
Publication Date
Jun 01, 1965
Accession Number
AD0617880

Entities

People

  • A. Léonard
  • Joel H. Ferziger

Organizations

  • RAND Corporation

Tags

Communities of Interest

  • Air Platforms

DTIC Thesaurus Topics

  • Boltzmann Equation
  • Cooperation
  • Differential Equations
  • Eigenvectors
  • Equations
  • Geometry
  • Integral Equations
  • Integrals
  • Mathematical Analysis
  • Mathematics
  • Neutron Transport Theory
  • Plane Geometry
  • Sizes (Dimensions)
  • Theorems
  • Transport Ships

Fields of Study

  • Mathematics

Readers

  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Linear Algebra
  • Solar Physics

Technology Areas

  • Space