Invariant Imbedding and a Resolvent of the Photon-Diffusion Equation

Abstract

In the study of radiative transfer, the classical Boltzmann-type approach focuses attention on the statistical behavior of the particles within the medium. There are, however, analytical and computational advantages in the invariant-imbedding approach, which leads to the determination of the diffusely reflected and transmitted intensities in slab geometry. In the present paper it is shown that the invariant-imbedding technique is also extremely useful for the study of the internal intensity of radiation in a finite, homogeneous, flat layer. In other words, the technique provides us directly with a complete solution of scattering problems of light in a finite plane-parallel atmosphere.

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Document Details

Document Type
Technical Report
Publication Date
Mar 01, 1964
Accession Number
AD0437813

Entities

People

  • Richard E. Bellman
  • Robert E. Kalaba
  • Sueo Ueno

Organizations

  • RAND Corporation

Tags

Communities of Interest

  • Air Platforms

DTIC Thesaurus Topics

  • Boltzmann Equation
  • Couette Flow
  • Differential Equations
  • Diffuse Reflection
  • Diffusion
  • Equations
  • Geometry
  • High Temperature
  • Integral Equations
  • Integrals
  • Intensity
  • Partial Differential Equations
  • Probability
  • Radiation
  • Radiative Transfer
  • Scattering
  • Thickness

Fields of Study

  • Physics

Readers

  • Calculus or Mathematical Analysis
  • Theoretical Analysis.