THE INVARIANT IMBEDDING EQUATIONS FOR THE DISSIPATION FUNCTIONS OF AN INHOMOGENEOUS FINITE SLAB WITH ANISOTROPIC SCATTERING,

Abstract

This report considers the absorption of photons incident to an atmosphere, to the case of an inhomogeneous atmosphere and anisotropic scattering. By use of the invariant imbedding technique, two complete sets of integro-differential equations are derived--the first for the case of monodirectional illumination of the upper boundary, and the second for monodirectional illumination of the lower boundary--using the equations of transfer and taking into account the polarity of the optical properties of the atmosphere. In both sets, the equations and results for scattering and transmission in the homogeneous case reduce to those given by Chandrasekhar.

Document Details

Document Type
Technical Report
Publication Date
Jun 01, 1967
Accession Number
AD0653923

Entities

People

  • Harriet H. Kagiwada
  • Richard E. Bellman
  • Robert E. Kalaba
  • S. Ueno

Organizations

  • RAND Corporation

Tags

DTIC Thesaurus Topics

  • Absorption
  • Atmospheres
  • Boundaries
  • Differential Equations
  • Dissipation
  • Equations
  • Illumination
  • Optical Properties
  • Physical Properties
  • Polarity
  • Scattering

Readers

  • Calculus or Mathematical Analysis
  • Optical Physics and Photonics.
  • Plasma Physics / Magnetohydrodynamics