A Simple Discrete Model Of Scattering In A Fluctuating Inhomogeneous Medium

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Simulation of the propagation of an acoustic wave through a

turbulent medium is introduced. The technique involves two elements: the generation of 3-D, random, hypothetical, isotropic velocity fields in terms of a collection of discrete Fourier

Author Manuscript NIH Public Access echo ultrasound

and scattering strength of particles are estimated from an analysis of the radio frequency (rf) echo signal power spectrum. Simple correlation functions and the accurate scattering theory of Faran [J.

Spin waves in a randomly inhomogeneous anisotropic medium

of the spin waves in a medium with spatially fluctuating magnetic anisotropy. So far as we know, this question has not been investigated before, either in a microscop- ic model or phenomenologically. We can mention only the following papers. For a discrete model of an amor- phous magnet, Harris, Plischke and ~uckermann''~'

Preliminary comparisons of the typical polarized radiative

scattering media. Compared with other methods, the scattering-absorbtion process can be calculated easily and is physically clear. The SOS method can trace the photons for each scattering event, the inhomogeneous structure of the medium, as well as take into account gaseous absorption processes. In other words, the SOS

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tion of the medium to a positive average temperature. Such a result would be natural in a finite domain with homogeneous Neumann condition. Here it is derived for a Cauchy problem. It is of course drastically different from diffusion in a homogeneous medium or any infinite inhomogeneous mass medium, where the average temperature is zero. In a

Finite-difference time-domain simulation of scattering from

its ability to model complex geometries with relative ease. In these studies, the treatment of the background soil (host medium) has been evolving in complexity, from the simple homogeneous dielectric slabs [13] to lossy, dispersive media with discrete particles [17], [18] and random rough surfaces [19].

Simulation of the Propagation of an Acoustic Wave Through a

fluctuating temperature fields. In this paper we offer a third approach- explicit nu- merical simulation of the motion of an acoustic ray propa- gating through a hypothetical, inhomogeneous velocity field. The hypothetical field consists of a small number of randomly oriented, discrete, Fourier velocity wave vectors


radiation data. According to Lighthill's model [1], the jet noise is generated by the fluctuating part of the fluid velocities in the jet. In this case, the pressure field is governed by an inhomogeneous wave equation, where the source term is given by the second order divergence of the Reynolds stress tensor. A great majority of works [2]

Attenuation measurement uncertainties caused by speckle

tainty. 8- The theory is developed from a simple model of weak scattering from randomly positioned inhomogeneities, and results are compared with measurements of speckle sta- tistics and attenuation results from human livers. 4 An important practical question to be addressed is the minimum volume of tissue required to obtain accurate esti-

The Two&Dimensional Gaussian Beam Synthetic Method: Testing

velocity model must be parameterized. The velocities are input as discrete points and then interpolated using cubic splines. This results in continuous velocities as well as first and second derivatives. For velocities given on a mesh in two or three dimensions, this involves a tensor product of one-dimensional splines [De Boor, 1980].


components. Then a scattering model is constructed by sum-ming up the contributions from forest components believed to be important [10]-[12]. The physical models are based upon the interaction of electromagnetic waves with the forest canopy. A canopy can be modeled either as a discrete or a continuous inhomogeneous medium. As a discrete medium


roughness scattering in layered media described in [1,2]. Consider an inhomogeneous medium with parameters, mass density, ρ~( r ) , and compressibility, κ~( r ) , fluctuating

Describing Small-scale Structure in Random Media Using Pulse

frequency (rf) echo signal power spectrum. Simple correlation functions and the accurate scattering theory of Faran [J. J. Faran, J. Acoust. Soc. Am. 23, 405-418 ( 1951 ) ], which includes the effects of shear waves, were used separately to model backscatter from spherical particles and thereby describe the structures of the medium.