Wave Propagation In Media Research Articles

Effective interfacial conditions for elastic wave propagation in media separated by thin rough layers

Effective approximate interfacial continuity conditions are derived for the propagation of elastic waves in two media that arc separated by periodically rough‐surfaced layer. The specific model considered is restricted to the situation where both surfaces of the layer have identical one‐dimensional periodicity which are in phase. This is motivated by the desire to obtain results for two rough half‐spaces in full contact (i.e., in the absence of the layer). For small layer thickness and roughness, superimposed effects in the forms of jumps in stresses and displacements across the layer's surfaces are obtained. When examined in conjunction with existing solutions for smooth interfaces these new conditions are found to predict and explain the various effects produced by roughness. These include the predictions of scattering directions, ranges (in frequency of angles of incidence) of surface wave excitations and mode conversions. Results are found to compare favorably with existing experimental data. [Research supported by NSF Grant CME 8021054 and AF Contract F33615‐80‐C‐5015.]

Wave propagation in media with focused gain

Wave propagation in media with focused gain

Effective propagation constants for coherent electromagnetic wave propagation in media embedded with dielectric scatters

In studying the multiple scattering of electromagnetic waves by random distributions of scatterers with appreciable fractional volume, the approach of quasicrystalline approximation together with the hole correction approximation has been a common method. In this paper, it is shown that such an approach will give rise to negative attenuation rate indicating a growth of the coherent wave in space which is a nonphysical solution. The result of the Percus–Yevick equation is a better representation of the pair distribution function for appreciable concentration. We use it together with the quasicrystalline approximation to study multiple scattering of electromagnetic waves by discrete spherical scatters. Waterman’s T matrix formalism is used in formulating the multiple scattering problem. Closed from solutions are obtained for the effective propagation constants in the low frequency limit and agree with Twersky’s results. Effective propagation constants at higher frequencies are calculated by numerical methods.

On the theory of pulse wave propagation in media of discrete random scatterers

The pulse wave propagation is theoretically investigated in a particular case of a medium of discrete random scatterers. As the basic equation the ordinary space‐time transport equation is used under the forward scattering approximation and is solved by means of the eigenfunction method developed in a recent paper. One of the major results is that an explicit expression of pulse intensity is analytically obtained for the realistic scattering amplitude, valid when the size of scatterers is sufficiently large in comparison with the wavelength. The dependence of pulse width broadening on the particle characteristic is also clarified for the case of large optical distances and is compared with that of previous literature. By the same techniques the temporal angular broadening of pulse wave is evaluated in order to find the conditions of applicability of the present method.

Induction probing of magnetostatic delay line fields

Recently, significant advances have been achieved in the development of tunable microwave (1-20GHz) signal processing elements utilizing magnetostatic waves (MSW) propagating in magnetically biased films of Yttrium Iron Garnet (YIG). The devices use transversal filtering techniques similar to those utilized in surface acoustic waves (SAW) technology. Essential to transversal filtering techniques is a detailed knowledge of the field distribution in the wave propagation media. This work reports initial experimental results of induction probing of the spatial distribution of the MSW field in both magnetostatic surface (MSSW) and forward volumn (MSFVW) wave delay lines. The experimental work of this paper indicates a number of conclusions which are of significance to MSW devices; 1. YIG film anisotropy strongly effects MSW propagation and the relative orientation of the bias field, crystal axes and propagation direction are critical to optimum delay line design. 2. Beam spreading and steering effects are significant and strongly dependent on the relative orientation of bias field, crystal axes, and propagation direction.

Nonlinear wave and soliton propagation in media with arbitrary inhomogeneities

Asymptotic solutions of nonlinear wave propagation in media with gentle, but otherwise arbitrary density inhomogeneities, are discussed. In the adiabatic approximation, a nonlinear Schrödinger equation is derived for media with linear, but time-dependent density gradients. The resulting extra term can be eliminated by going to an accelerated reference frame, which makes this modified nonlinear Schrödinger equation completely integrable by the inverse scattering method. Multi-solitons are therefore still the asymptotic states of waves propagating in media with arbitrary inhomogeneities.

Medium-wave propagation in built-up areas

An investigation has taken place into the problems of medium frequency (m.f.) ground-wave propagation in built-up areas. Measurements were made which showed that, in such conditions, the field-strength/distance relationship is often different from that expected on the basis of conventional theories. These conventional theories have been extended and applied to explain the results. A computer prediction method has been devised which uses an integral equation to allow calculations over an inhomogeneous earth, and incorporates a new concept in the value given to surface impedance. Close agreement is shown to exist between the new method and the measured results.

Nonlinear propagation of waves in media with an arbitrary number of chemical reactions: PMM vol. 40, n≗ 4, 1976, pp. 587–598

We consider nonlinear wave motions in chemically active, gaseous mixtures the change in the composition of which is governed by an arbitrary number of reactions taking place. We impose on the equations of state the conditions ensuring that the frozen and the equilibrium speed of sound have similar values. We carry out an asymptotic analysis of the initial system of Euler equations together with the chemical reaction equations. As the result, we obtain an approximate system of equations for the velocity of the medium particles, and for the reaction completeness vector the order of which is equal to the number of the relaxation processes plus one.

Wave propagation in media undergoing uniform linear acceleration

Wave propagation in a homogenous material undergoing uniform linear acceleration is considered. The covariant constitutive equations for a holohedral, nondispersive, dielectric material derived by Lianis are applied. Expressions are found for initially plane waves propagating in the direction of accelerated motion for the case where the material functions are constant. Expressions are also found for the radiation reflected and refracted at the surface of a half−space undergoing uniform linear acceleration. A detailed energy balance across this interface is also presented.

Effect of boundaries on wave propagation in media with microstructure : Part 2, surface waves in a half-space. 3F, 9R. Bull. Seism. Soc. Am. V64, N2, APR. 1974, P387–392 Farshad M., Ahmadi G.

Effect of boundaries on wave propagation in media with microstructure : Part 2, surface waves in a half-space. 3F, 9R. Bull. Seism. Soc. Am. V64, N2, APR. 1974, P387–392 Farshad M., Ahmadi G.

Saturation effects associated with wave propagation in a random medium

A theoretical analysis of the propagation of spherical time-harmonic waves in a random medium is presented. The smoothing method is used to study the incoherent (or randomly fluctuating) component of the wave field. With the aid of the Fresnel approximation, an expression for the second moment of the incoherent wave is obtained which is valid for the case of high-frequency waves propagating in a medium which is statistically homogeneous and isotropic. This expression shows that the rms fluctuations of the wave field increase initially as the square root of the propagation distance, but that at larger distances (and higher frequencies) the fluctuations tend to saturate. These results agree with observations of waves propagating in real media.

Effect of boundaries on wave propagation in media with microstructure: II. Surface waves in a half space : 3F, 9R. Seismol. Soc. Amer. Bull. V64, N2, April, 1974, P387–392

Effect of boundaries on wave propagation in media with microstructure: II. Surface waves in a half space : 3F, 9R. Seismol. Soc. Amer. Bull. V64, N2, April, 1974, P387–392

Propagation of seismic surface waves in media with vertical discontinuities

Propagation of seismic surface waves in media with vertical discontinuities

Effect of boundaries on wave propagation in media with microstructure: II. Surface waves in a half-space

abstract The surface-wave propagation in a half-space according to couple-stress theory is studied herein. Dispersion curves as well as displacement variations with the depth coordinate are obtained for a range of material parameters. Comparison is made with the classical elasticity predictions upon which certain conclusions are reached.

The effect of boundaries on wave propagation in media with microstructure—reflection of plane waves at a free plane boundary

abstract The problem treated here is that of reflection of plane waves from the free plane boundary of a half-space made of a medium with microstructure. It is shown that an incident ray of either dilatational or distortional type, in general, gives rise to four reflected rays, two of each type. Two of these reflected waves are evanescent and the other two propagate into the medium. Each of these reflected waves have their own phase shifts relative to the incident wave.

Propagation of a Gaussian Beam in Planar and Cylindrically Inhomogeneous Media: Comparison of Modal Analysis and Approximate Approaches

This work presents a study on the propagation of electromagnetic waves in media, characterized by k = k0 m k2 y 2 and k = k0 m k2 r2. A vector theory based on Maxwell's equations is used to derive linear homogeneous second-order equations satisfied by the transverse electric and magnetic field components. The various modes of propagation and the corresponding propagation constants have been determined. These are used to study the propagation and focusing of waves which have an intensity distribution along their wavefront. An alternative method for the study of the propagation and focusing of electromagnetic waves has been discussed. This is based on an approximate solution of the wave equation given in previous communications. For parameters of interest, the results obtained from the approximate solution are in excellent agreement with the solution obtained from the modal analysis of the problem. The present study should be of relevance in tropospheric communication and focusing of laser beams in selfoc f...

Blast Waves in Rotating Media

The accumulating evidence for the occurrence of violent events in the nuclei of galaxies1,2 suggests the investigation of the propagation of blast waves in media rotating in a gravitational field. The requirement that the mean free path for the gas in such systems be small (on the scale of kiloparsecs) is easily met; an estimate of λ≡(σn)−1 for the Galaxy suggests a typical value on the order of 10−6 kpc.

Effect of Hammer Length and Nonlinear Paper-ribbon Characteristics on Impact Printing

An analysis of the impact process in a particular type of high-speed printer was undertaken to determine the effect of hammer length on the contact time. The hammer is modeled as a one dimensional wave propagation medium and the paper-ribbon combination as a dissipative, nonlinear medium with hysteresis. The integrated macroscopic viscoelastic parameters for a particular impact geometry and hammer momentum were determined from a combination of the analytical model and the experiments run on an instrumented printer robot. Permanent deformation of the paper-ribbon caused by character penetration was also determined in this manner. The simulated model was then used to predict the change in dynamic behavior of such a system due to variations of the hammer length. The hammer length is shown to have only a tertiary effect on contact time in such a dissipative deformable nonlinear system. This result demonstrates that the widely discussed use of hammer length as a design parameter to control contact time in impact printing is invalid for such a dissipative system.

Wave propagation in time-varying media

This paper examines the propagation of waves in media which are spatially homogeneous but whose properties vary with time abruptly or continuously. Emphasis is placed on the excitation problem and on source-dependent phenomena which are not evident when attention is given only to the source-free case. After a presentation and interpretation of various exact closed-form solutions for simple nondispersive and dispersive media undergoing sudden or gradual temporal changes, attention is given to integral representations required under more general conditions. In the ensuing far-zone asymptotic analysis, dispersion surfaces and space-time rays are used extensively for identification of wave packets and other wave constituents descriptive of the field, and a comparison is made between the asymptotic results and the exact solutions noted above. Asymptotic field solutions are then derived by a direct ray procedure, without intervention of integral representations. The examples considered exhibit a variety of phenomena, among which the most interesting is the focusing of reflected waves when a dispersive medium undergoes a sudden change.

Closed-form solutions to problems of wave propagation in a rigid, workhardening, locking rod

One-dimensional wave propagation in a semi-infinite, rigid, workhardening, locking rod is considered. The general problem is discussed and closed-form solutions are obtained for several special cases. It is anticipated that the latter will provide useful check-cases for numerical programs designed to cope with wave propagation in media with complex constitutive laws. The stipulated mechanical behavior is also interesting in its own right since it is qualitatively typical of soils in uniaxial compressive strain.