Sound-absorbing media with two types of acoustic losses

Sound-absorbing media with two types of acoustic losses, namely, inertial and deformation are considered. Such a medium is described by a complex density and a complex compressibility. It is shown that a certain relation between the latter quantities imparts some specific properties to the medium: a real wave impedance, complete absorption of sound waves at the boundary with the external medium, the properties of a viscous or “superviscous” medium, etc. The results are generalized to the case of a layered inhomogeneous medium with two types of losses.     

Unidirectional saturation spectroscopy,I theory and short dipole lifetime limit

High-intensity multimode laser theory is used to derive the absorption coefficients for 1) a coherent light beam (probe) interacting with a possibly inhomogeneously broadened medium in the presence of an intense second corunning beam, and for 2) the sedibands of a weakly modulated light beam interacting with the medium. The general expressions are specialized to non-saturating probes and the short dipole-lifetime limit, yielding coherent pulsation-dip formulas. These are given for both homogeneous and inhomogeneous broadening and typically consist of simple power-broadened Lorentzians with widths equal to the smaller level-decay constant. The amplitude modulation case features pulsation dips twice as deep as the single-probe case, while the frequency modulation case exhibits no pulsation dip at all. Spectroscopic methods are discussed including the heterodyne advantage obtained with collinear light beams.     

Origin of Starting Earthquakes under Complete Coupling of the Lithosphere Plates and a Base

The boundary problem of rigid coupling of lithospheric plates modeled by Kirchhoff plates with a base represented by a three-dimensional deformable layered medium is considered. The possibility of occurrence of a starting earthquake in such a block structure is investigated. For this purpose, two states of this medium in the static mode are considered. In the first case, the semi-infinite lithospheric plates in the form of half-planes are at a distance so that the distance between the end faces is different from zero. In the second case, the lithospheric plates come together to zero spacing between them. Calculations have shown that in this case more complex movements of the Earth’s surface are possible. Among such movements are the cases described in our previous publications [1, 2].     

Operator of Effective Permittivity of a Statistically Inhomogeneous Medium with Strong Fluctuations

The majority of known works on the theory of multiple scattering of electromagnetic waves in media with strong fluctuations are constrained by the assumption of statistical homogeneity of a medium. In this paper, we consider an isotropic lossy random medium, for which the principle value and multipole moments of the permittivity are invariant with respect to arbitrary rotations about a fixed symmetry axis and translations along the axis and are inhomogeneous in the radial direction. This paper is aimed at calculating the effective permittivity operator (EPO) for such a medium for the case of strong permittivity fluctuations.     

Reflexion und Brechung an optisch einachsigen Medien in Richtung fehlender Doppelbrechung

Reflection and Refraction at Uniaxial Media in Directions of Vanishing Double Refraction The amplitude relations for the reflection and refraction of plane monochromatic waves by uniaxial media in the case of vanishing double refraction of the refracted respectively reflected waves in the uniaxial medium are obtained by a limiting process from generalized Fresnel formulae earlier derived. The incidence both from the isotropic and from the uniaxial medium is considered. The boundary conditions may be fulfilled in the case considered only by addition of refracted respectively reflected waves with amplitudes varying linearly with the distance from the boundary plane in the uniaxial medium. The requirement of vanishing double refraction restricts the possible choice of the common tangential components of all refraction vectors and consequently also of the refraction vectors of incident waves from a primarily twodimensional complex manifold to onedimensional complex manifolds, which are determined in this paper.     

Instability of oscillations in the flow moving through a random medium as the counterpart of the localization of waves in a passive random medium

This paper deals with waves propagating in a one-dimensional flow moving through a randomly layered medium. The flow velocity is assumed to be greater than the group velocity of the waves in the reference system of the flow. As a result, in the laboratory reference system, all the waves propagate in a single direction. Amplitudes of these waves moving through a randomly inhomogeneous medium are growing exponentially. This effect is analogous to the wave localization phenomenon in a randomly inhomogeneous passive medium. The only difference is that the wave propagation in a passive medium is described by the boundary value problem, while all the oscillations in a medium with flow propagate in a single direction and hence the corresponding problem is formulated in the form of the initial value Cauchy problem. In the former case exponentially decreasing solutions are realized in the direction of the wave incidence, while in the latter case (as in the case of parametric resonances) the exponentially increasing solutions are realized.     

Unidirectional saturation spectroscopy, I theory and short dipole lifetime limit

High-intensity multimode laser theory is used to derive the absorption coefficients for 1) a coherent light beam (probe) interacting with a possibly inhomogeneously broadened medium in the presence of an intense second corunning beam, and for 2) the sedibands of a weakly modulated light beam interacting with the medium. The general expressions are specialized to non-saturating probes and the short dipole-lifetime limit, yielding coherent pulsation-dip formulas. These are given for both homogeneous and inhomogeneous broadening and typically consist of simple power-broadened Lorentzians with widths equal to the smaller level-decay constant. The amplitude modulation case features pulsation dips twice as deep as the single-probe case, while the frequency modulation case exhibits no pulsation dip at all. Spectroscopic methods are discussed including the heterodyne advantage obtained with collinear light beams. Work performed as a Humboldt awardee in Germany. Work supported in part by the Space and Missiles Systems Organization, Los Angeles, California. Work supported by the “Deutsche Forschungsgemeinschaft”.     

Interaction of Three Electromagnetic Fields with a Resonance Medium in EPR. The Case of a Small Local Field in Comparison with the Saturating One

A system of Bloch equations modified with allowance for the presence of a dipole–dipole reservoir for the case where the local magnetic field is small in comparison with the saturating one is suggested. The system is used for solving the problem of interaction of three electromagnetic fields: a saturating field, a probe one, and the third - a combination field resulting from the interaction of the first two in a resonance medium. The imaginary and real parts of the system susceptibility at the probe-field frequency have been investigated in detail at both different frequencies of interacting waves and coinciding ones (degenerate case). For the degenerate case, the dependence of the coefficient of the parametric connection of waves on the frequency is considered. The results of the present work are compared with those obtained by us earlier for the case where the local magnetic field is much in excess of the saturating one (Provotorov's case). It is shown that in the problem considered the amplification of weak waves when they pass through the layer of an absorbing resonance medium is inaccessible.     

Emission of radiation by a resonance medium excited with a variable superluminal velocity

Specific properties of the radiation emitted by a spatially modulated resonance medium excited by an ultrashort light pulse propagating through the medium at a variable superluminal velocity are analyzed. In so doing, frequencies different from that of the resonance transition of the medium may appear in the emission spectrum. It is demonstrated that, in contrast to an earlier studied case of medium excitation at constant velocity, variation of the excitation velocity leads to generation of a spectral continuum, the boundaries of which are determined by the range of variation of the medium-excitation velocity.     

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.     

Bremmer级数之推广

本文叙述了在普遍的介质与入射波情况下Bremmer理论之推广,并给予简要证明。对下列三种具体情况导出了Bremmer级数之表达式:1.平面分层介质,平面波斜入射;2.柱状分层介质,直线波源与柱轴重合;3.球状分层介质,点光源位于球心。最后,对于波动过程可以用射线严格描写的条件之数学形式作了探讨,并指出Bellman和Kalaba的一篇文章中的不严格处。     

Resonance-parametric mechanism of optical rectification and high harmonic generation

The generation of zero and high-order harmonics in the spectrum of a laser pulse propagating through a medium containing quantum particles whose constant resonance transition dipole moment is nonzero is studied theoretically. The consideration is performed in the approximation of slowly varying envelopes modified for the case of the medium with the nonzero permanent dipole moment. It is shown that this modification requires consideration of antiresonance terms, in particular, the Bloch-Siegert shift in equations. The conditions are revealed for the efficient optical rectification and excitation of the second harmonic at a quasi-monochromatic signal applied to the medium.     

Large negative Goos-Hanchen shift at metal surfaces

It has been previously established that for p-polarized light incident onto a semi-infinite absorbing medium, large negative Goos-Hanchen (GH) shifts can be expected in the case of weak absorption at incidence close to the Brewster angle. The effect has been demonstrated for certain semiconducting media at optical frequencies. Here we point out that similar phenomenon can take place for strongly reflecting and attenuating medium such as metal at IR frequencies, with large incident angles close to grazing incidence. Moreover, unlike the previously-studied case with semiconductors, the Brewster angle in the present case with metals plays an insignificant role in the possible hindrance of the observation of such large negative shifts.     

Transmission of oscillations through a layer of a nonlinear elastic medium

The transmission of shear one-dimensional periodic perturbations through a layer of a nonlinearly elastic medium under the conditions close to resonance is considered. The layer separates two half-spaces consisting of a medium that is much more rigid, as compared to the medium in the layer. A system of differential equations is obtained for describing the slow variations in the amplitude and waveform of nonlinear strain and stress oscillations at the fixed boundary that occur because of the nonlinear properties of the medium while the other boundary performs arbitrary periodic motions in its plane. The period of these oscillations is close to the period of natural oscillations of the layer. It is shown that, in addition to continuous strain variations at the fixed boundary, strain variations containing strong discontinuities are possible. Relations at the discontinuities are obtained. The analogy between the equations derived for the case under study and the equations describing the propagation of strain waves in a homogeneous anisotropic elastic medium is pointed out.     

Long-range intensity correlations for the multiple scattering of waves in unordered media

The long-range correlations in the reflected and transmitted fluxes in the case of the coherent transport of waves in an unordered medium with discrete inhomogeneities are considered. The correlator and spectrum of the intensity fluctuations are expressed in a general form in terms of the one-center scattering amplitude and the propagators of the mean radiated intensity. The random interference of the waves and the fluctuations of the number of scattering centers in a microvolume of the medium are taken into account simultaneously. Detailed calculations are performed for two limiting radiation propagation regimes, viz., spatial diffusion and small-angle multiple scattering. It is shown that the conservation of the total flux upon elastic scattering leads to the formation of a dip in the spectrum and, accordingly, a negative correlation between the intensities at large distances. In the case of spatial diffusion this feature is displayed upon reflection, and in the case of small-angle multiple scattering it is displayed upon transmission through a slab. The relative roles of the various sources of intensity fluctuations, as well as the sensitivity of the correlations to factors that influence the wave propagation regime, viz., the finite size of the scattering sample, absorption in the medium, and the presence of a frequency shift in the incident waves, are analyzed. We find that fluctuations in the distribution of the scatterers show up most strongly in a medium with strong, i.e., “non-Born,” centers, especially if they exhibit absorption. Zh. éksp. Teor. Fiz. 111, 1674–1716 (May 1997)     

Mie scattering efficiency of a large spherical particle embedded in an absorbing medium

The Mie scattering calculations are usually performed for non-absorbing spherical particles embedded in a non-absorbing medium. We consider a case of an absorbing sphere placed in an absorbing medium. We find, by numerical calculation for large size parameter of the order of 10⁴, that the scattering efficiency of a spherical particle in an absorbing medium approaches the reflectance of a plane surface at perpendicular incidence.     

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.     

Ac susceptibility response of bulk YBCO superconductors in the presence of a temperature gradient

Low-frequency ac susceptibility measurements on ceramic YBCO superconductors carried out at the presence of a quasi-one-dimensional temperature gradient are compared with those made without the temperature gradient. The values of the different characteristic temperatures measured on samples without and with a temperature gradient are identical but in the second case itch characteristic temperature is a medium value. When the temperature gradient is constant on the sample the arithmetic medium value of the local temperatures is the effective characteristic temperature different phenomena.     

Two analytic methods applied to radiative transfer in the linear-anisotropic scattering medium with graded index and diffuse gray boundaries

The curved ray-tracing method is extended to radiative transfer in the graded index medium with diffuse gray boundary conditions instead of black boundary conditions and the pseudo-source adding method is extended to the case of the linear-anisotropic scattering medium with graded index from non-scattering medium. Furthermore, the equivalence of the two methods is verified by formulation derivation. As exact analytical solutions, both the methods have high accuracy and fast computational speed. The predicted temperature distributions and dimensionless radiative heat flux at radiative equilibrium are determined by the proposed methods, and the numerical results are compared with the data in references. The results show that the present methods have a good accuracy. Influences of various combinations of refractive index and boundary emissivities on the temperature distributions and dimensionless radiative heat flux are also investigated.