Statistics of waves propagating in a random medium

We present a review of part of the results obtained by the authors for the statistics of coherent radiation propagating in a random medium both in the framework of diagrammatic techniques and random matrix theory. Distribution functions for the total transmission coefficient and the angular transmission coefficient for the diffusive transport and the crossover between the diffusive and ballistic regimes are obtained.The authors acknowledge the financial support of the Israeli Academy of Sciences and of the Schottenstein Center.     

On the properties of electromagnetic waves propagating inside moving dielectric media

The properties of electromagnetic waves propagating inside isotropic or uniaxial dielectric media moving in an arbitrary direction are analysed. The scalar products of electromagnetic field vectors inside these moving media are investigated in the kEB system from Maxwell's equations and Lorentz-covariant constitutive relations. Several important equations are derived. They are useful in discussing problems such as the energy density and radiation pressure, which are of interest in theoretical studies and many application subjects.     

Inwards propagating waves in a limit cycle medium

The existence of a novel inwards propagating wave motion is demonstrated in a limit-cycle medium both for the FitzHugh-Nagumo and for modified Chernyak-Starobin-Cohen reaction-diffusion systems. The waves (pulses) are seen to be moving "backwards," that is, towards the point where the triggering pulse was initiated, instead of the regular propagation away from the origin. The feasibility of the phenomenon and some of its features are analyzed.     

On the stability of periodic waves in a resonant medium

We study the stability of two periodic waves existing in two-level systems. It is shown that one periodic wave is unstable, while the other is stable up to one-dimensional perturbations. The results are obtained using the formalism of supersymmetric quantum mechanics for one-dimensional periodic potentials.     

On the stability of capillary waves on the surface of a space-charged dielectric liquid jet moving in a material medium

We have derived and analyzed the dispersion equation for capillary waves with an arbitrary symmetry (with arbitrary azimuthal numbers) on the surface of a space-charged cylindrical jet of an ideal incompressible dielectric liquid moving relative to an ideal incompressible dielectric medium. It has been proved that the existence of a tangential jump of the velocity field on the jet surface leads to a periodic Kelvin–Helmholtz- type instability at the interface between the media and plays a destabilizing role. The wavenumber ranges of unstable waves and the instability increments depend on the squared velocity of the relative motion and increase with the velocity. With increasing volume charge density, the critical value of the velocity for the emergence of instability decreases. The reduction of the permittivity of the liquid in the jet or an increase in the permittivity of the medium narrows the regions of instability and leads to an increase in the increments. The wavenumber of the most unstable wave increases in accordance with a power law upon an increase in the volume charge density and velocity of the jet. The variations in the permittivities of the jet and the medium produce opposite effects on the wavenumber of the most unstable wave.     

Patch nearfield acoustic holography in a moving medium

To realize the accurate reconstruction of sound field in a moving medium under the condition of limited holographic aperture, a patch nearfield acoustic holography (NAH) in a moving medium is proposed. The proposed method not only reduces the influence caused by the limited aperture effects through sound field extrapolation, but also perfectly suits for sound field reconstruction in a moving medium by improving the shape of the modified Tikhonov regularization filter and the noise estimation method in accordance with flow effects. In the method, two cases that the flow direction is parallel to and perpendicular to the hologram surface are considered. Especially in the perpendicular case, the expression of the wavenumber component in the z direction is improved to make the proposed method suitable for the moving medium at a high Mach number. Simulations are investigated to examine the performance of the proposed method and show its advantages by comparing with NAH in a moving medium and the conventional patch NAH. It is found that, the proposed method is effective and robust at different flow velocities of the medium and different frequencies of the sound source.     

Nonlinear spherically divergent shock waves propagating in a relaxing medium

The propagation of nonlinear spherically diverging N-waves in atmosphere was studied experimentally and theoretically. The relative effects of nonlinear, dissipation, and relaxation phenomena on the N-wave duration and amplitude were investigated based on the numerical solutions of the modified Burgers equation. It is shown that, under the experimental conditions, the duration of a pulse increases mainly due to nonlinear propagation, whereas the amplitude depends on the combined effects of nonlinearity, dissipation, and relaxation. The frequency response of the measuring system is obtained. The calibration of the amplitude and duration of the experimental waveforms is performed based on the nonlinear lengthening of the propagating pulse. The results of numerical modeling show good agreement with experimental data. Published in Russian in Akusticheskiĭ Zhurnal, 2008, Vol. 54, No. 1, pp. 40–50. The article was translated by the author (V.A. Khokhlova).     

Dispersion process of electromagnetic waves in a moving medium

The propagation of electromagnetic waves in a moving isotropic plasma and in a moving magnetoactive plasma is considered using the invariant methods of tensor analysis. Expressions are obtained for the dielectric permittivity tensor, the dispersion equations, and the refractive indexes of electromagnetic waves in these media. Using these results it is possible to establish corrections to the angular displacement which occurs when radiation passes through a moving electron plasma.Published from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 39, No. 1, pp. 121–129, January, 1996.     

Finite-amplitude standing acoustic waves in a cubically nonlinear medium

The acoustic field in a resonator filled with a cubically nonlinear medium is investigated. The field is represented as a linear superposition of two strongly distorted counterpropagating waves. Unlike the case of a quadratically nonlinear medium, the counterpropagating waves in a cubically nonlinear medium are coupled through their mean (over a period) intensities. Free and forced standing waves are considered. Profiles of discontinuous oscillations containing compression and expansion shock fronts are constructed. Resonance curves, which represent the dependences of the mean field intensity on the difference between the boundary oscillation frequency and the frequency of one of the resonator modes, are calculated. The structure of the profiles of strongly distorted “forced” waves is analyzed. It is shown that discontinuities are formed only when the difference between the mean intensity and the detuning takes certain negative values. The discontinuities correspond to the jumps between different solutions to a nonlinear integro-differential equation, which, in the case of small dissipation, degenerates into a third-degree algebraic equation with an undetermined coefficient. The dependence of the intensity of discontinuous standing waves on the frequency of oscillations of the resonator boundary is determined. A nonlinear saturation is revealed: at a very large amplitude of the resonator wall oscillations, the field intensity in the resonator ceases depending on the amplitude and cannot exceed a certain limiting value, which is determined by the nonlinear attenuation at the shock fronts. This intensity maximum is reached when the frequency smoothly increases above the linear resonance. A hysteresis arises, and a bistability takes place, as in the case of a concentrated system at a nonlinear resonance.     

Coherence of acoustic modes propagating through shallow water internal waves

The 1995 Shallow Water Acoustics in a Random Medium (SWARM) experiment [Apel et al., IEEE J. Ocean. Eng. 22, 445-464 (1997)] was conducted off the New Jersey coast. The experiment featured two well-populated vertical receiving arrays, which permitted the measured acoustic field to be decomposed into its normal modes. The decomposition was repeated for successive transmissions allowing the amplitude of each mode to be tracked. The modal amplitudes were observed to decorrelate with time scales on the order of 100 s [Headrick et al., J. Acoust. Soc. Am. 107(1), 201-220 (2000)]. In the present work, a theoretical model is proposed to explain the observed decorrelation. Packets of intense internal waves are modeled as coherent structures moving along the acoustic propagation path without changing shape. The packets cause mode coupling and their motion results in a changing acoustic interference pattern. The model is consistent with the rapid decorrelation observed in SWARM. The model also predicts the observed partial recorrelation of the field at longer time scales. The model is first tested in simple continuous-wave simulations using canonical representations for the internal waves. More detailed time-domain simulations are presented mimicking the situation in SWARM. Modeling results are compared to experimental data.     

On the stability of a cylindrical jet moving in a material medium along an external electrostatic field

A dispersion relation is derived for capillary waves with arbitrary symmetry (with arbitrary azimuthal numbers) on the surface of a jet of an ideal incompressible dielectric liquid moving in an ideal incompressible dielectric medium along an external uniform electrostatic field. A tangential discontinuity in the velocity field on the jet surface is shown to cause Kelvin-Helmholtz periodical instability at the interface and destabilize axisymmetric, flexural, and flexural-deformational waves. Both the flexural and flexural-deformational instabilities have a threshold and are observed not at an arbitrarily small velocity of the jet but starting from a certain finite value. It is shown that the instability of waves generated by the tangential discontinuity of the velocity field is periodic only formally (from the pure mathematical point of view). Actually, the jet disintegrates within the time of instability development, which is shorter than the half-cycle of the wave.     

Interaction of waves with a birefringent medium moving with acceleration

Recent experiments demonstrated that the energy of a neutron traversing an accelerated sample of a refractive medium changes. Later, it was realized that such an accelerated-medium effect (AME) is quite a general phenomenon characteristic of waves and particles of different nature. This paper discusses some special features of the effect for a birefringent medium. In this case, AME shows quite new features. In neutron optics, where birefringence is due to the spin dependence of the refractive index, AME results in a nonstationary state with a precessing spin. In the case of the propagation of a two-flavor neutrino through an accelerated layer of matter, AME affects substantially the ensuing evolution of a neutrino flavor state as it propagates through a free space.     

Fundamental limits of waves propagating in an inhomogeneous multilayer metal-dielectric medium

The dispersion equations have been derived for various types of orthogonally polarized waves in a five-layer dielectric medium shielded by metal screens. The dispersion characteristics of electromagnetically coupled waves propagating in two waveguide dielectric layers, isolated from each other and from the metal screens by separating and intermediate dielectric layers, have been investigated. The fundamental limits of the spectrum of fundamental, higher-order, waveguide, and reactive types of waves are determined by the relative retardation and reduced-frequency range.