Multiple Scattering of Waves

Abstract

Multiple scattering effects due to a random array of obstacles are considered. Employing a ``configurational averaging'' procedure, a criterion is obtained for the validity of approximate integral equations describing the various field quantities of interest. The extinction theorem is obtained and shown to give rise to the forward-amplitude theorem of multiple scattering. In the limit of vanishing correlations in position, the complex propagation constant κ of the scattering medium is obtained. Under appropriate restrictions, the expression for κ is shown to include both the square-root law of isotropic scatterers and the additive rule for cross sections valid for sufficiently low densities of anisotropic obstacles. Some specific examples from acoustics and electromagnetic theory then indicate that at least in the simplest cases the results remain valid for physically allowable densities of obstacles.

Electromagnetic interference shielding effectiveness of composite carbon nanotube macro-film at a high frequency range of 40 GHz to 60 GHz

“…According to Waterman-Truell formula, 28 the effective permittivity (ε eff ) of CNT-based materials can be expressed as follows:…”

On the estimation of attenuation from the ambient seismic field: inferences from distributions of isotropic point scatterers

“…At the same time, a wave traveling through an assemblage of isotropic point scatterers can be described by an effective wavenumber whose phase velocity and rate of attenuation depend on (i) the wavenumber of the background medium, (ii) the scatterer density and (iii) the average strength of the scatterers. We note that isotropic point scattering is not essential for the description of a heterogeneous medium by an effective wavenumber (Lax 1951;Waterman & Truell 1961).…”

“…At the same time, a wave traveling through an assemblage of isotropic point scatterers can be described by an effective wavenumber whose phase velocity and rate of attenuation depend on (i) the wavenumber of the background medium, (ii) the scatterer density and (iii) the average strength of the scatterers. We note that isotropic point scattering is not essential for the description of a heterogeneous medium by an effective wavenumber (Lax 1951;Waterman & Truell 1961).The total wavefield at a location r can be described as the sum of the background wavefield 0 and the wavefield due to the scatterers s , that is,Since the medium in which the scatterers are embedded is assumed lossless and homogeneous, propagation in this background medium is described by a real wavenumber k 0 . Similarly, the velocity of the background medium is denoted by c 0 and its wavelength by λ 0 .…”

High Frequency Acoustics in Colloid-Based Meso- and Nanostructures by Spontaneous Brillouin Light Scattering

“…Another EMT method is described by Waterman and Truell. [143] Their approach is in principle a full multiple scattering theory including numerical calculation with n equations for n scatterers. For every scatterer the exact form of the multipole coefficient must be known, and so this method is too complicated to be used for simple calculations of the effective sound velocity.…”