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Long Distance Energy Correlations in Random Media


Zwillinger, Daniel Ian (1983) Long Distance Energy Correlations in Random Media. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/G3DN-MZ83.


This thesis considers the long distance motion of waves in a random medium. Using the geometrical optics approximation and a stochastic limit theorem, we find evolution equations for rays and for energy correlations, in two and three dimensions.

Our equations are valid on a long distance scale, well after the focusing of rays has become significant. We construct asymptotic expansions of the two point energy correlation function in two and three dimensions.

In two dimensions we numerically solve the partial differential equation that determines the two point energy correlation function. We also perform Monte-Carlo simulations to calculate the same quantity. There is good agreement between the two solutions.

We present the solution for the two point energy correlation function obtained by regular perturbation techniques. This solution agrees with our solution until focusing becomes significant. Then our solution is valid (as shown by the Monte-Carlo simulations), while the regular perturbation solution becomes invalid.

Also presented are the equations that describe energy correlations after a wave has gone through a weakly stochastic plane layered medium.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:Applied Mathematics
Degree Grantor:California Institute of Technology
Division:Physics, Mathematics and Astronomy
Major Option:Applied Mathematics
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Keller, Herbert Bishop
Thesis Committee:
  • Keller, Herbert Bishop (chair)
  • Franklin, Joel N.
  • Caughey, Thomas Kirk
  • Cohen, Donald S.
  • White, Ben
Defense Date:27 October 1982
Record Number:CaltechETD:etd-11032005-093758
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:4388
Deposited By: Imported from ETD-db
Deposited On:03 Nov 2005
Last Modified:20 Dec 2019 19:30

Thesis Files

PDF (Zwillinger_di_1983.pdf) - Final Version
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