Yushieh Ma

A multiple scattering theory for elastic wave propagation in discrete random media

A multiple scattering theory for elastic wave propagation in a discrete random medium is presented. A self‐consistent multiple scattering formalism using the T matrix of a single scatterer in conjunction with the quasicrystalline approximation (QCA) and a self‐consistent pair correlation function is employed to study the phase velocity and coherent attenuation of elastic waves by a random distribution of cavities and elastic inclusions embedded in an elastic matrix. Both uniform and Gaussian size distributions are assumed. The theoretical results obtained in this study are shown to be in excellent agreement with experimental observations.

Multiple scattering of compressional and shear waves by fiber‐reinforced composite materials

A multiple scattering formalism using a T matrix to characterize the response of a single fiber to an incident wave is presented to describe P‐ and SV‐wave propagation in a fiber‐reinforced composite. A convenient numerical procedure is then developed to compute the effective elastic moduli, attenuation, and phase velocity as a function of frequency and fiber concentration.

Scattering and attenuation of elastic waves in random media

In seismic exploration, elastic waves are sent to investigate subsurface geology. However, the transmission and interpretation of the elastic wave propagation is complicated by various factors. One major reason is that the earth can be a very complex medium. Nevertheless, in this paper, we model some terrestrial material as an elastic medium consisting of randomly distributed inclusions with a considerable concentration. The waves incident on such an inhomogeneous medium undergo multiple scattering due to the presence of inclusions. Consequently, the wave energy is redistributed thereby reducing the amplitude of the coherent wave.The coherent or average wave is assumed to be propagating in a homogeneous continuum characterized by a bulk complex wavenumber. This wavenumber depends on the frequency of the probing waves; and on the physical properties and the concentration of discrete scatterers, causing the effective medium to be dispersive. With the help of multiple scattering theory, we are able to analytically predict the attenuation of the transmitted wave intensity as well as the dispersion of the phase velocity. These two sets of data are valuable to the study of the inverse scattering problems in seismology. Some numerical results are presented and also compared, if possible, with experimental measurements.

Comments on ultrasonic propagation in suspensions

In determining the velocity and attenuation of suspensions of spherical particles, results obtained from the computationally simpler multiple scattering approach of Waterman and Truell (WTF) and from a multiple scattering formalism (MSF), which considers the pair correlation function, have been compared in order to justify the range and applicability of the former method. Although the difference between the results increases as the concentration of suspensions increases, the frequency‐dependent attenuation computed from the two approaches can be quite different particularly in the low‐frequency range even at lower concentrations. Due to the unavailability of experimental data for ultrasonic propagation, data from analogous optical experiments on suspensions of latex spheres are compared. The MSF shows excellent agreement, whereas the WTF shows large discrepancies from the experimental data.

Microwave Sintering of Ceramics

Theoretical considerations regarding microwave sintering of ceramics are discussed. It is shown how the rigorous application of multiple scattering theory may permit a better understanding of this interesting process. The possibility of thermal runaway being chaotic is discussed. Experimental results, and a possible connection to percolation theory, are also given.

Scattered intensity of a wave propagating in a discrete random medium.

The present paper aims at a computational scheme to obtain numerical results for the second moment (average intensity) of a wave field propagating in a medium consisting of randomly distributed scatterers, not necessarily simple in shape. A formalism is presented that parallels the diagram method and shows the approximations made in the intensity computation of anisotropic scattering whenever finite size scatterers with a considerable concentration are considered. The back and forth scattering between a pair of scatterers, which has been neglected in the ladder approximation, automatically appears in our formalism taking into account all the multiple scattering between two particles through the pair statistics. Sample numerical results for average intensity scattered by particles are presented and compared to some microwave and optical measurements.

Multiple scattering of elastic waves by cylinders of arbitrary cross section. II. Pair‐correlated cylinders

Multiple scattering of elastic waves by randomly distributed cylinders of arbitrary cross section has been considered. Because the pair‐correlation function, as well as the quasicrystalline approximation, has been incorporated in the presented formalism, the effective phase velocity, as well as the coherent attenuation in dense systems, has been investigated. A more efficient scattering formalism (SF) has been employed rather than the exciting field formalism (EF) used earlier by the authors. Closed form expressions for the phase velocity and the attenuation are given in the Rayleigh limit, and numerical results are presented for a wide range of frequencies and concentrations.

Anisotropic dielectric properties of media containing aligned nonspherical scatterers

Electromagnetic wave propagation in a medium containing a random distribution of aligned, pair-correlated nonspherical scatterers is studied using the T -matrix to characterize the single scatterer response, the quasicrystalline approximation (QCA) and the correlation function. The resulting dispersion equation for the average medium is numerically solved as a function of frequency and the direction of propagation. Numerical results are presented for the attenuation of electromagnetic waves versus frequency, concentration, and direction of propagation.

A propagator model for scattering of acoustic waves by bubbles in water

A propagator model is presented for acoustic wave propagation through a bubble swarm. Both phase velocity and coherent attenuation are studied as a function of frequency and compared with experimental measurements of Silberman [J. Acoust. Soc. Am. 29, 925 (1957)].

Multifrequency remote acoustic sensing of suspended materials in water

A multifrequency acoustic technique is employed as an oceanographic tool to infer the characteristic information, e.g., concentration, size distribution, and mean size, about suspended materials in the deep ocean environment. The technique employs the single scattering theory which is valid for a sparse distribution of scatterers in water. Theoretical results are presented as the acoustic response versus frequencies for different size distributions.