Wave anisotropy of shear viscosity and elasticity

The paper presents the theory of shear wave propagation in a “soft solid” material possessing anisotropy of elastic and dissipative properties. The theory is developed mainly for understanding the nature of the low-frequency acoustic characteristics of skeletal muscles, which carry important diagnostic information on the functional state of muscles and their pathologies. It is shown that the shear elasticity of muscles is determined by two independent moduli. The dissipative properties are determined by the fourth-rank viscosity tensor, which also has two independent components. The propagation velocity and attenuation of shear waves in muscle depend on the relative orientation of three vectors: the wave vector, the polarization vector, and the direction of muscle fiber. For one of the many experiments where attention was distinctly focused on the vector character of the wave process, it was possible to make a comparison with the theory, estimate the elasticity moduli, and obtain agreement with the angular dependence of the wave propagation velocity predicted by the theory.     

Influence of the slow wave on the relation between the angular resonances and the leaky guided modes properties for a poroelastic plate embedded in water

A numerical study of the guided modes in a water-saturated poroelastic plate that obeys the Biot theory is presented. In the first part, we study the leaky guided modes and the angular resonances when the slow wave does not propagate. Two types of guided modes exist. The first ones occur from coupling of the fast longitudinal wave with the shear wave; most of them propagate whatever the frequency is, provided that it is not close to their cut-off frequencies. The leaky guided modes of the second type occur from coupling of the two longitudinal waves and the shear wave. These modes do not propagate (they are highly damped) as long as the slow wave remains diffusive. We show that the characteristics of the angular resonances can be linked to the leaky guided waves of the first type in the same way as for an elastic plate. The guided modes of the second type may not be associated to angular resonances. In the second part, we consider a thinner plate in a higher frequency range so that the slow wave can propagate. Once again its influence is studied both on the leaky guided modes and on the angular resonances.     

Generalization of Biot’s equations with allowance for shear relaxation of a fluid

On the basis of the generalized variational principle for dissipative continuum mechanics, a system of generalized Biot’s equations is derived to describe the wave propagation in a two-phase porous permeable medium in the presence of shear relaxation in the pore-filling fluid. It was shown that the inclusion of shear viscoelasticity of the fluid leads to the appearance of two transverse modes in addition to two longitudinal modes described by the Biot theory. One of the transverse modes is an acoustic mode, whereas the other is a diffusion mode characterized by the linear frequency dependence of phase velocity and attenuation coefficient in the low-frequency region.     

Temperature dependence of elastic constants in δ-Pu

It is shown that the variation of the bulk and shear moduli in δ-Pu in a temperature range of 300–500 K is due to the phonon redistribution between different vibrational modes caused by the dispersion of the Grüneisen coefficients (phonon viscosity). The constants of interaction of the high-frequency acoustic modes with a long-wavelength deformation induced by an ultrasonic wave are estimated.     

Modeling of magnetoelastic shear waves due to point source in a viscoelastic crustal layer over an inhomogeneous viscoelastic half space

In the present study, propagation of magnetoelastic shear wave due to a momentary point source in a viscoelastic crustal layer over inhomogeneous viscoelastic half space has been discussed. Green’s function technique and Fourier transform along with method of successive approximation are used to find the closed-form solutions for displacement and generalized shear wave period equation. Attenuation of the resultant shear wave is computed and effects of magnetic field, width of the layer, complex wave number, viscosity, and inhomogeneity parameters are distinctly marked on dissipation curves using two-dimensional and surface plots. It is found that effect of layer’s magnetoelastic coupling parameter on attenuation pattern of shear wave is just the reverse of half space magnetoelastic coupling parameter. Similarly, internal friction of layer has somewhat different effect on shear wave angular frequency than lower half space viscosity. Certain published results are also derived as special cases to the present study.     

Non-universal shear viscosity from Einstein gravity

A very famous result of gauge/gravity duality is the universality of the ratio of shear viscosity to entropy density in every field theory holographically dual to classical, two-derivative (Einstein) gravity. We present a way to obtain deviation from this universality by breaking the rotational symmetry spontaneously. In anisotropic fluids additional shear modes exist and their corresponding shear viscosities may be non-universal. We confirm this by explicitly calculating the shear viscosities in a transversely isotropic background, a p-wave superfluid, and study its critical behavior. This is a first decisive step towards further applications of gauge/gravity duality to physical systems.     

Guided waves in a stratified half-space

The dispersion and excitation mechanisms and the energy distribution of guided waves in a stratified half-space are studied. All possible guided waves excited by a symmetric point source in two or three-layer medium models and their relation to the medium parameters are analyzed in detail. The excitation and propagation characteristics, as well as the energy distribution along the depth direction, of all modes of the surface waves and trapped waves are numerically investigated and analyzed thoroughly not only in the case when the shear wave velocity increases from up to down layers but also when a low-velocity layer is contained in halfspace, especially when the shear wave velocity decreases from up to down layers. It is found that there exist many guided wave modes in the case where the shear wave velocity of each layer increases from up to down layers. However, there is less than one guided wave mode in the case where the shear wave velocity of each layer decreases from up to down layers. The trapped waves exist and propagate along the low-velocity structure in the stratified half-space. It is also found that the characteristic of a mode is related to the source frequency. It is possible that a surface wave at one value of frequency is like a trapped wave at another value of frequency. Finally, the relation of the characteristics of all guided waves (surface waves and trapped waves) to the parameters of media is studied.     

Twisted shear Alfvén waves with orbital angular momentum

It is shown that a dispersive shear Alfvén wave (DSAW) in a magnetized plasma can propagate as a twisted Alfvén vortex beam carrying orbital angular momentum (OAM). We obtain a wave equation from the generalized ion vorticity equation and the magnetic field-aligned electron momentum equation that couple the scalar and vector potentials of the DSAW. A twisted shear Alfvén vortex beam can trap and transport plasma particles and energy in magnetoplasmas, such as those in the Earth?s auroral zone, in the solar atmosphere, and in Large Plasma Device (LAPD) at University of California, Los Angeles.     

对称平板漏波导中的非线性导波

本文从平面波理论出发,研究了薄膜为非线性介质的对称平板漏波导的TE_0模传输特性.计算结果表明,膜厚大于一临界值时,不存在稳定的TE_0模,膜厚小于临界值时,最多能存在两种峰值场强的TE_0模.膜厚越小,两种峰值场强相差越大.     

On the acoustic modes in a duct containing a parabolic shear flow

The exact solution of the acoustic wave equation in an unidirectional shear flow with a parabolic velocity profile is obtained, representing sound propagation in a plane, parallel walled duct, with two boundary layers over rigid or impedance walls. It is shown that there are four cases, depending on the critical level(s) where the Doppler shifted frequency vanishes: (i) for propagation upstream the critical levels are outside the duct (case II); (ii) for propagation downstream there may be two (case IV), one (case I) or no (case III) critical level inside the duct. The acoustic wave equation is transformed in each of the four cases to particular forms of the extended hypergeometric equation, which has power series solutions, some involving logarithmic singularities. In the cases where critical levels occur, at real or ‘imaginary’ distance, matching of two or three pairs of solutions, valid over regions each overlapping the next, is needed. The particular case of the parabolic velocity profile is used to address general properties of sound in unidirectional shear flows. For example, it is shown that for ducted shear flows, there exist a pair of even and odd eigenfunctions, in the absence of critical levels. It is also proved, in more than one instance, that there is no single set of eigenvalues and eigenfunctions valid across one or two shear layers. This leads to the general conjecture, considering the acoustics of shear flows in ducts, that critical levels separate regions with distinct sets of eigenvalues and eigenfunctions.     

Decay of solitons in an isotropic collisionless quasineutral plasma with isothermal pressure

Soliton-type solutions of the complete unreduced system of transport equations describing the plane-parallel motions of an isotropic collisionless quasineutral plasma in a magnetic field with constant ion and electron temperatures are studied. The regions of the physical parameters for fast and slow magnetosonic branches, where solitons and generalized solitary waves—nonlocal soliton structures in the form of a soliton “core” with asymptotic behavior at infinity in the form of a periodic low-amplitude wave—exist, are determined. In the range of parameters where solitons are replaced by generalized solitary waves, soliton-like disturbances are subjected to decay whose mechanisms are qualitatively different for slow and fast magnetosonic waves. A specific feature of the decay of such disturbances for fast magnetosonic waves is that the energy of the disturbance decreases primarily as a result of the quasistationary emission of a resonant periodic wave of the same nature. Similar disturbances in the form of a soliton core of a slow magnetosonic generalized solitary wave essentially do not emit resonant modes on the Alfvén branch but they lose energy quite rapidly because of continuous emission of a slow magnetosonic wave. Possible types of shocks which are formed by two types of existing soliton solutions (solitons and generalized solitary waves) are examined in the context of such solutions.     

Resonance modes in optical fibres

The weakly nonlinear boundary value problem of wave propagation in an optical fibere(for the transverse electric mode,for example)is formulated and a modified linear solution is obained.It is shown that a self-consistent theory of fibre optics should be weakly nonlinear,The mode of critical refraction that does not exist in the linear theory is obtained,showing that it is a mode consisting of resonance modes,It is shown that the signal carriers in a long fibre are of resonance modes,not normal modes,Some experimental data are given for comparison with the theoretical predictions and the agreement seems satisfactory.     

PBG-PCF基模特性全矢量平面波多极方法联合数值研究

用全矢量平面波方法与多极方法联合数值研究六重对称带隙型光子晶体光纤的基模特性.通过全矢量平面波方法可确定组成PBG-PCF的二维光子晶体的带隙,基模(束缚模)存在其频率要落在带隙内且须在k0a=βa的直线附近上部区域,在带隙外形成辐射(泄漏模).把频率作为输入变量用多极方法计算,数据导出用MATLAB数学软件作出模场分布图,结果发现,不是所有基模可能存在的区域都有基模存在,为带隙型光子晶体光纤的基模寻找提供一种可行的方法.     

On the dielectric response function and dispersion relation in strongly coupled magnetized dusty plasmas

Using the generalized viscoelastic fluid model, we derive the dielectric response function in a strongly coupled dusty magnetoplasma which reveals two different dust acoustic(DA) wave modes in the hydrodynamic and kinetic limits. The effects of the strong interaction of dust grains and the external magnetic on these DA modes, as well as on the shear wave are examined. It is found that both the real and imaginary parts of DA waves are significantly modified in strongly coupled dusty magnetoplasmas. The implications of our results to space and laboratory dusty plasmas are briefly discussed.     

Application of surface and normal ultrasonic waves for measuring the parameters of technical fluids: I. Shear viscosity measurements

The effect of the viscosity of a fluid on the propagation of the zero mode of a horizontally polarized normal wave in a thin (compared to the wavelength) waveguide immersed in the fluid is studied. It is shown that, to a first approximation in the ratio of the shear impedance of the fluid to the shear impedance of the waveguide, the wave amplitude decays exponentially as a function of the distance at a damping coefficient proportional to the square root of the shear viscosity of the fluid. The decrease in the wave amplitude induced by the shear viscosity of the fluid is numerically estimated, and the results obtained point to the possibility of developing a method for its measurement at a high accuracy. This method was developed and tested on a waveguide in the form of an aluminum ribbon 0.3 mm thick and 14 cm long at a frequency of 2 MHz. The decrease in the signal amplitude when the waveguide is immersed in distilled water (tabulated shear viscosity is 1.05 × 10^?3 Pa s) is found to be 0.42 dB as compared to the amplitude in the unloaded waveguide, which can be considered as the sensitivity of the experimental setup. A method for calibrating the sensor is described. The shear viscosities of solutions of saccharose in distilled water are measured, and the experimental results agree well with the theoretical estimates.     

Shear instability in fluids with a density-dependent viscosity

We present a shear instability, which can be triggered in compressible fluids with density-dependent viscosity at shear rates above critical. The instability mechanism is generic: It is based on density-dependent viscosity, compressibility, as well as flow two-(three-)dimensionality that provides coupling between streamwise and transversal velocity components and density variations. The only factor stabilizing the instability is fluid elasticity. The corresponding eigenvalue problem for a plane Couette flow is solved analytically in the limiting cases of large and small wave numbers.     

Exchange mechanism for localization of phonons near the surface of a magnetically ordered crystal

It is shown that first-principles inclusion of nonuniform exchange interaction leads to the creation of a new type of generalized shear acoustic wave propagating near the mechanically free surface of a magnet. Criteria are formulated that can be used to specify conditions under which an “exchange” type of surface acoustic wave can exist at the boundary between a magnetic and a nonmagnetic medium once the spectrum of magnetoelastic oscillations of the unbounded magnetic crystal is known. Fiz. Tverd. Tela (St. Petersburg) 40, 299–304 (February 1998)     

Vector soliton of self-induced transparency of a generalized love wave

A theory of acoustic self-induced transparency of a two-component vector soliton for a generalized Love wave is constructed. The three-layer system contains a resonance transition layer with paramagnetic impurity atoms or quantum dots. It is shown that, under these conditions, a vector soliton of the generalized Love wave can be formed. It oscillates at the sum and difference frequencies in the vicinity of the carrier wave frequency. Explicit analytical expressions for the parameters of a nonlinear surface acoustic wave are presented. The parameters depend on the elastic properties of the contacting media, the resonance transition layer, and the transverse structure of the wave. Numerical calculations are carried out for the three-layer Al₂O₃/ZnO/SiO₂ system. The significant difference between the two-component vector soliton and singlecomponent soliton is shown.     

非对称型Kerr类介质膜漏波导中的非线性导波

本文研究了特定边界条件下非对称型Kerr类介质膜漏波导中TE₀光波的传播特性。计算结果表明,介质膜厚存在一临界值。临界值之上没有导波存在,临界值之下能同时存在强场TE₀模和弱场TE₀模,它们具有不同的传播波数。这两个模的膜内传播功率、场强峰值位置随膜厚和光场频率的变化各不相同,色散关系也有极大差别。在对称极限之下,弱场TE₀模的色散为零。 关键词：     

The shear diffusion coefficient for generalized theories of gravity

Near the horizon of a black brane in Anti-de Sitter (AdS) space and near the AdS boundary, the long-wavelength fluctuations of the metric exhibit hydrodynamic behaviour. The gauge–gravity duality then relates the boundary hydrodynamics for generalized gravity to that of gauge theories with large finite values of 't Hooft coupling. We discuss, for this framework, the hydrodynamics of the shear mode in generalized theories of gravity in d+1$d+1$ dimensions. It is shown that the shear diffusion coefficients of the near-horizon and boundary hydrodynamics are equal and can be expressed in a form that is purely local to the horizon. We find that the Einstein-theory relation between the shear diffusion coefficient and the shear viscosity to entropy ratio is modified for generalized gravity theories: Both can be explicitly written as the ratio of a pair of polarization-specific gravitational couplings but implicate differently polarized gravitons. Our analysis is restricted to the shear-mode fluctuations for simplicity and clarity; however, our methods can be applied to the hydrodynamics of all gravitational and matter fluctuation modes.