A variational principle for waves in discrete random media
type: Item
instance of: scholarly article
title: A variational principle for waves in discrete random media
zbMATH Open document ID: 0553.73008
DOI: 10.1016/0165-2125(85)90039-3
author: Richard L. Weaver
published in: Wave Motion
publication date: 1985-01-01T00:00:00Z
full work available at URL: http://hdl.handle.net/2142/112202
review text: A new variational principle is derived for the Green function of the linear haramonic 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.
Mathematics Subject Classification ID: 74A40
Mathematics Subject Classification ID: 74S30
Mathematics Subject Classification ID: 74J99
Mathematics Subject Classification ID: 49S05
Mathematics Subject Classification ID: 74E05
Mathematics Subject Classification ID: 35P25
zbMATH DE Number: 3881937
zbMATH Keywords: Green function
zbMATH Keywords: linear haramonic response
zbMATH Keywords: scalar wave field
zbMATH Keywords: discretely heterogeneous medium
zbMATH Keywords: exact multiple scattering integral equations
zbMATH Keywords: functional of trial configuration dependent fields
zbMATH Keywords: stationary with respect to small variations
zbMATH Keywords: trial dependence in the fields
zbMATH Keywords: Lax quasicrystalline multiple scattering equations
zbMATH Keywords: these equations are optimal
MaRDI profile type: Publication
OpenAlex ID: W1969517154
cites work: The Multiple Scattering of Waves. I. General Theory of Isotropic Scattering by Randomly Distributed Scatterers
cites work: Multiple Scattering of Waves. II. The Effective Field in Dense Systems
cites work: Multiple Scattering of Waves
cites work: From global scaling, à la Kolmogorov, to local multifractal scaling in fully developed turbulence
cites work: A variational approach to the theory of the elastic behaviour of multiphase materials
cites work: Variational principles for dynamic problems for inhomogeneous elastic media
cites work: Elastic waves in a fiber-reinforced composite
cites work: Q4068221
cites work: Elastic wave propagation in a discrete random medium
cites work: Multiple scattering of elastic waves by cylinders of arbitrary cross section. I. SH waves
cites work: Multiple Scattering of Waves in Irregularly Laminated Composites
cites work: Waves in random media
cites work: Q5821083
cites work: Q5600005
description: scientific article; zbMATH DE number 3881937