The Mathematical Development of the End-Point Method

Abstract

The end-point method is mathematically developed and its application to the Milne kernel studied in detail. The general solution of the Wiener-Hopf integral equation is first obtained. The Mime kernel appears in applying this method to the integral equation describing the diffusion and multiplication of neutrons in multiplying and scattering media. The neutrons are treated as monochromatic, isotropically scattered and of the same total mean free path in all materials involved. Only problems with spherical symmetry are treated, these being reducible to equivalent infinite slab problems. Solutions are obtained for tamped and untamped spheres; in the former case both growing and decaying exponential asymptotic solutions in the tamper are treated in detail. Appendix I treats the effects of the approximations inherent in the end-point method (cf. LADC - 79). Appendix II gives the solution of the inhomogeneous Wiener-Hopf equation. (AN)

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Document Details

Document Type
Technical Report
Publication Date
Apr 10, 1945
Accession Number
ADA301212

Entities

People

  • S. Frankel
  • Sarah Goldberg

Organizations

  • Oak Ridge National Laboratory

Tags

Communities of Interest

  • Air Platforms

DTIC Thesaurus Topics

  • Attenuation
  • Boundaries
  • Cartesian Coordinates
  • Collisions
  • Contour Integrals
  • Elastic Scattering
  • Equations
  • Geometry
  • Integral Equations
  • Integrals
  • Materials
  • Mean Free Path
  • Notation
  • Scattering
  • Spatial Distribution
  • Three Dimensional
  • United States

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Nuclear and Radiation Engineering.