INVARIANT IMBEDDING AND WAVE PROPAGATION IN STOCHASTIC MEDIA

Abstract

The principle of invariant imbedding leads to the formulation of various functional equations describing plane wave propagation in stochastic media. The approach involves first the derivation of stochastic functional equations for reflection and transmission coefficients, followed by the taking of expected values of appropriate functions of the random state variables. This makes possible the determination of their characteristic functions and distribution functions, by means of still other functional equations, or by computational schemes of the Monte Carlo type. The particular example in which a plane wave is incident on a stratified slab which is characterized by stochastic wave numbers in each stratum is discussed. The distribution functions for the amplitude of the random reflected and transmitted waves are then determined as functions of the thickness of the slab. The effects of multiple scattering are taken into account.

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Document Details

Document Type
Technical Report
Publication Date
Aug 29, 1958
Accession Number
AD0607017

Entities

People

  • Richard E. Bellman
  • Robert E. Kalaba

Organizations

  • RAND Corporation

Tags

Communities of Interest

  • Air Platforms

DTIC Thesaurus Topics

  • Boundary Value Problems
  • Differential Equations
  • Diffuse Reflection
  • Distribution Functions
  • Electromagnetic Wave Propagation
  • Equations
  • Nonlinear Differential Equations
  • Plane Waves
  • Probability Distributions
  • Radiative Transfer
  • Radio Waves
  • Random Variables
  • Random Walk
  • Real Variables
  • Reflection
  • Scattering
  • Wave Propagation

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Electromagnetic Wave Scattering and Antenna Radiation Engineering
  • Regression Analysis.