The problem of surface wave propagation in a reduced Cosserat medium

This article continues a series of publications devoted to the study of waves in the framework of the asymmetric theory of elasticity, where the deformed state of the medium is characterized by independent vectors of translation and rotation. The problem of acoustic Rayleigh wave propagation in half space is considered within a model of the reduced Cosserat medium. A general analytic solution of this problem is obtained. The analysis of this solution is compared with the corresponding solution for a classical elastic medium and full linear Cosserat medium. It is shown that the Rayleigh wave is characterized by a range of forbidden frequencies, where this wave cannot propagate. The dispersion curve consists of two branches. One of them has a cut-off frequency and cut-off wavenumber.     

Influence of ionospheric irregularities on decameter radio wave propagation: Mathematic modeling

Based on numerical simulation and using the Monte Carlo method, an investigation is carried out of the influence of random irregularities in the ionospheric F-region on short-wave propagation along one-hop radio paths.Irkutsk State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 37, No. 11, pp. 1439–1446, November, 1994.     

Stability problem in nonlinear wave propagation

An explicit expression for the excitation spectrum of the stationary solutions of a nonlinear wave equation is obtained. It is found that all branches of many-valued solutions of a nonlinear wave equation between the (2K+1,2K+2) turning points (branch points in the complex plane of the nonlinearity parameter) are unstable. Some parts of branches between the (2K,2K+1) turning points are also unstable. The instability of the latter is related to the possibility that pairs of complex conjugate eigenvalues cross the real axis in the κ plane. Zh. éksp. Teor. Fiz. 114, 1487–1499 (October 1998) Published in English in the original Russian journal. Reproduced here with stylistic changes by the Translation Editor.     

Lamb wave propagation in a plate with a grooved surface with several spatial periodicities

In order to investigate non-destructively the bonding between rough plates, the problem of Lamb waves propagating on a rough plate is addressed in this paper. Numerical analysis is performed on periodical gratings made of identical triangular grooves. If the surface profile is made up of grooves with one periodicity, then a mode conversion is observed. In the wave-number/frequency space, a phonon relation is written between phonons related to the grating and to the incident and reflected-converted modes. If the grooved surface is made up of several spatial periodicities, then the phonon relation is still verified. Signal processing allows us to give an interpretation of the results in the dual space (wave-number/frequency). An experimental study is also performed to corroborate the numerical predictions.     

Beam wave propagation within the second Rytov perturbation approximation

The applicability of the classical Rytov method in statistical wave propagation problems is reconsidered and expanded by demanding results that are of second order in the permittivity fluctuations, rather than limiting them to just the first Rytov perturbation approximation, as is traditionally done. It is shown that one must augment the well-known second order statistics (e.g., log-amplitude variance), as calculated from the first Rytov approximation, with first-order statistics (e.g., the average log-amplitude), as calculated from the second Rytov approximation. Thus, a complete solution is derived for the second Rytov approximation for general beam wave propagation through turbulent media, the permittivity fluctuations of which are described by the Kolmogorov-Obukhov spectrum. This then allows a complete and consistent treatment that yields the fact that the average log-amplitude is, in the general beam wave case, not equal to the additive inverse of the log-amplitude variance. This gives results from the Rytov method that are then in exact agreement with the corresponding limiting case of strong fluctuation theory, as well as a simplified analytical expression for beam wave broadening, and the correct theoretical explanation of the well-known applicability limit for the Rytov method.     

Effects of surface roughness on surface acoustic wave propagation in semiconductor materials

The effect of surface roughness on adhesion and tribological properties of films and interfaces is of key importance. Therefore, it is of utmost importance to be able to measure this quantity and to predict the effects that different roughness levels may cause. Roughness affects the propagation of surface acoustic waves on a material but there is little useful quantitative data on the topic. This work investigates the dispersive effect of roughness on surface acoustic wavepackets (30-200 MHz frequency range) for different degrees of nanometer roughness on silicon (0 0 1) and (1 1 1) surfaces, we show that the roughness-induced frequency dispersion effect is significant, and that although available theories agree qualitatively with the results, the theory is not adequate to predict the real SAW dispersion. These experimental results have considerable implications for design of SAW devices, for accuracy of Brillouin spectroscopy measurements, and for possible applications to non-destructive testing of materials. Previously unknown dispersive effects on anisotropic crystal surfaces are also demonstrated.     

Generation of ionospheric irregularities upon propagation of solitary internal gravity wave during the major magnetic storm of October 29–31, 2003

Using the technique of global detection of ionospheric disturbances, based on processing the data of the global GPS-receiver network, we obtain experimental proof of the existence of a solitary wave (soliton) in the atmosphere during the main phase of the major magnetic storm of October 30, 2003. The soliton with a characteristic duration of about 40 min and a relative amplitude of up to 40%, originated at the moment of the maximum disturbance of the Earth’s magnetic field, traveled without changing its shape at a distance of up to 4500 km with a velocity of 1400 m/s, which exceeded the atmospheric sound velocity at the heights of the main electron-density maximum in the ionosphere (about 300 km) by a factor of 1.5. The intensity of variations in the total electron content in the period range 1–10 min increases by an order of magnitude as the soliton propagates from the North-East to the South-West of the USA in the regions with the maximum amplitude of the large-scale disturbance. This corresponds to enhancement of ionospheric irregularities with scales from 10 to 100 km, and also of small-scale irregularities (SSI) with scales of 100 to 1000 m, since the spectrum of the ionospheric irregularities has a power-law shape. Spatio-temporal characteristics of the density distribution of phase slips of GPS signals are close to the corresponding characteristics of the SSI intensity. This agrees with the existing concept that the phase slips result from scattering of GPS radio signals by SSIs. Both the SSI amplitude and the density of phase slips decrease as the soliton decays in amplitude. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 49, No. 2, pp. 89–104, February 2006.     

The limits of the rotating wave approximation in electromagnetic field propagation in a cavity

We consider three two-level atoms inside a one-dimensional cavity, interacting with the electromagnetic field in the rotating wave approximation (RWA). One of the three atoms is initially excited, and the other two are in their ground state. We numerically calculate the propagation of the field emitted by the excited atom and scattered by the second atom, as well as the excitation probability of the second and third atom. Our numerical results clearly show the limits of the RWA in subtle problems such as relativistic causality in the atom–field interaction.     

Soliton regimes of surface magnetostatic wave propagation in a magnet-semiconductor structure

The nonlinear properties of exchange-free surface magnetostatic spin waves in a layered structure containing films of a ferromagnet and a semiconductor are investigated theoretically. The stability of nonlinear surface magnetostatic waves relative to longitudinal disturbances is investigated using the envelope evolution equation in the weak-nonlinearity approximation. It is shown that, under certain conditions, a surface spin-wave pulse propagates in the form of an envelope soliton. Calculations are performed for the case of an yttrium iron-garnet-indium antimonide structure. Fiz. Tverd. Tela (St. Petersburg) 41, 1272–1275 (July 1999)     

Derivation of a wave equation for pulse propagation beyond a slowly varying envelope approximation

An iterative method is used to derive an accurate weve equation that governs ultrashort pulse propagation in a single mode fibre. In the derivation, the slowly varying evelope approximation (SVEA) is not required. Therefore, the wave equation can be used to describe the propagation of an ultrashort pulse of a few optical cycles. It is found that, compared with the wave equation obtained by making an SVEA, an accurate wave equation has the same coefficients of the linear dispersion terms and different coefficients of the high-order time derivatives of the non-linear terms.     

HF ground wave propagation over a curved rough sea surface

For a vertically polarized line source, in the context of HF (3–30?MHz) ground wave propagation over a curved rough sea surface, this paper presents different asymptotic and rigorous methods to compute the attenuation function. When the Earth's curvature is taken into account, the attenuation function is expressed as a series, in which the roots of a differential equation, depending on the Airy function, must be calculated. In addition, from Taylor series expansions, different closed-form expressions can be obtained. For a smooth sea surface, the purpose of this paper is to compare these different formulations with fast rigorous numerical methods, such as the BMIA-CAG (Banded-Matrix-Iterative Approach CAnonical-Grid) and FB-SA (Forward-Backward Spectral-Acceleration) methods, based on the method of moments and originally developed for rough surfaces. These methods are especially efficient to solve a problem with huge unknowns, which is required to predict the ground wave propagation over a long surface. In addition, from a partial fraction expansion of the attenuation function in the Laplace domain, the Bremmer asymptotic expansion is extended to any order by including the surface roughness.     

Acoustic shock wave propagation in a heterogeneous medium: a numerical simulation beyond the parabolic approximation

Numerical simulation of nonlinear acoustics and shock waves in a weakly heterogeneous and lossless medium is considered. The wave equation is formulated so as to separate homogeneous diffraction, heterogeneous effects, and nonlinearities. A numerical method called heterogeneous one-way approximation for resolution of diffraction (HOWARD) is developed, that solves the homogeneous part of the equation in the spectral domain (both in time and space) through a one-way approximation neglecting backscattering. A second-order parabolic approximation is performed but only on the small, heterogeneous part. So the resulting equation is more precise than the usual standard or wide-angle parabolic approximation. It has the same dispersion equation as the exact wave equation for all forward propagating waves, including evanescent waves. Finally, nonlinear terms are treated through an analytical, shock-fitting method. Several validation tests are performed through comparisons with analytical solutions in the linear case and outputs of the standard or wide-angle parabolic approximation in the nonlinear case. Numerical convergence tests and physical analysis are finally performed in the fully heterogeneous and nonlinear case of shock wave focusing through an acoustical lens.     

Statistical characteristics of a wave propagating through a layer with random irregularities

Statistical characteristics of a wave propagating through a layer with random irregularities are investigated by a simulation procedure. The investigation is carried out within the geometrical optics approximation in its validity range. It is shown that when the irregular layer is a long distance from the source and observer, a significant role in the formation of eikonal (phase path) fluctuations is then played by trajectory fluctuations in regions of the propagation medium, free from irregularities before and after the irregular layer. With these variations taken into account, which are neglected in conventional perturbation theory, we obtained approximate expressions for the dispersion and the correlation function of the eikonal. We investigate the behaviour of the eikonal dispersions, the angles and correlation functions of the eikonal and field for different disturbances of the medium, and for different distances of the receiver and transmitter from the layer boundaries.     

Effect of a sloping bottom on sound propagation

Acoustical Physics - The paper presents the results of field measurements of acoustic fields generated in autumn hydrological conditions of the Sea of Japan shelf by a TON-320Hz autonomous signal...