University of Illinois Urbana-Champaign

Variational principle for waves in discrete random media

Weaver, Richard L.

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https://hdl.handle.net/2142/112202

Description

Title
Variational principle for waves in discrete random media
Author(s)
Weaver, Richard L.
Issue Date
1984-02
Keyword(s)
  • Variational Principle
  • Waves
  • Discrete Random Media
Abstract
A new variational princple is derived for the Green's function of the linear harmonic response of a scalar wave field in a discretely heterogeneous medium. The variational principle is derived directly from exact multiple scattering integral equations and is stated in terms of a certain functional of trial configuration dependent fields. The functional is found to be stationary with respect to small variations in the fields when those fields have their correct configuration dependence. A certain trial dependence in the fields is shown to generate the Lax quasicrystalline multiple scattering equations. It is furthermore clear that these equations are optimal in the sense that any more realistic form for the trial fields unavoidably generates approximate equations entailing the generally unknown high order correlation functions. At its stationary point the proposed functional takes on a physically significant value. It becomes the change in the medium admittance due to the introduction of the scatterers. In a nonlossy medium this is related to the spectral density of modes. As errors in the trial fields cancel to first order, the final evaluation of the functional at its stationary point is especially accurate. Other related functionals are proposed and discussed as well.
Publisher
Department of Theoretical and Applied Mechanics. College of Engineering. University of Illinois at Urbana-Champaign
Series/Report Name or Number
  • TAM R 463
  • 1984-6001
ISSN
0073-5264
Type of Resource
text
Language
eng
Permalink
http://hdl.handle.net/2142/112202
Sponsor(s)/Grant Number(s)
National Science Foundation 84/02 NSF MEA 81 22124 84/02
Copyright and License Information
Copyright 1984 Board of Trustees of the University of Illinois

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Technical Reports - Theoretical and Applied Mechanics (TAM) PRIMARY
TAM technical reports include manuscripts intended for publication, theses judged to have general interest, notes prepared for short courses, symposia compiled from outstanding undergraduate projects, and reports prepared for research-sponsoring agencies.