Coherent waves in a multiply scattering poro-elastic medium obeying Biot's theory

Twersky's theory is generalized to multiple scattering by a uniform random distribution of cylinders in a poro-elastic medium. The high-frequency regime only, where no dispersion effects occur in the absence of scatterers, is investigated in the frame of Biot's theory. The scatterers lie within a slab of the host medium, and an incident wave gives rise to a fast longitudinal coherent wave, a slow longitudinal one, as well as a shear one in the slab. The dispersion equations of those three coherent waves are derived. The shear coherent wave propagates independently of the other two, while the longitudinal coherent waves obey a coupled dispersion equation involving conversion terms. Numerically speaking, coupling effects are significant only when forward scattering by a single cylinder of the fast wave into the slow one (or the slow wave into the fast) is larger than forward scattering with no conversion.     

Fast compressional wave attenuation and dispersion due to conversion scattering into slow shear waves in randomly heterogeneous porous media

Within the viscosity-extended Biot framework of wave propagation in porous media, the existence of a slow shear wave mode with non-vanishing velocity is predicted. It is a highly diffusive shear mode wherein the two constituent phases essentially undergo out-of-phase shear motions (slow shear wave). In order to elucidate the interaction of this wave mode with propagating wave fields in an inhomogeneous medium the process of conversion scattering from fast compressional waves into slow shear waves is analyzed using the method of statistical smoothing in randomly heterogeneous poroelastic media. The result is a complex wave number of a coherent plane compressional wave propagating in a dynamic-equivalent homogeneous medium. Analysis of the results shows that the conversion scattering process draws energy from the propagating wave and therefore leads to attenuation and phase velocity dispersion. Attenuation and dispersion characteristics are typical for a relaxation process, in this case shear stress relaxation. The mechanism of conversion scattering into the slow shear wave is associated with the development of viscous boundary layers in the transition from the viscosity-dominated to inertial regime in a macroscopically homogeneous poroelastic solid.     

Theory of sound propagation in superfluid-filled porous media

The theory of sound propagation in macroscopically isotropic and homogeneous porous media saturated with superfluid ⁴He has been developed neglecting all damping processes. The case when the normal fluid component is locked inside a porous medium by viscous forces is investigated in detail. It is shown that in this case one shear wave and two longitudinal, fast and slow, waves exist. Fast wave as well as slow wave is accompanied with temperature oscillations. The velocities of these waves are obtained.     

Coherent backscattering of light by complex random media of spherical scatterers: numerical solution

Novel Monte Carlo techniques are described for the computation of reflection coefficient matrices for multiple scattering of light in plane-parallel random media of spherical scatterers. The present multiple scattering theory is composed of coherent backscattering and radiative transfer. In the radiative transfer part, the Stokes parameters of light escaping from the medium are updated at each scattering process in predefined angles of emergence. The scattering directions at each process are randomized using probability densities for the polar and azimuthal scattering angles: the former angle is generated using the single-scattering phase function, whereafter the latter follows from Kepler's equation. For spherical scatterers in the Rayleigh regime, randomization proceeds semi-analytically whereas, beyond that regime, cubic spline presentation of the scattering matrix is used for numerical computations. In the coherent backscattering part, the reciprocity of electromagnetic waves in the backscattering direction allows the renormalization of the reversely propagating waves, whereafter the scattering characteristics are computed in other directions. High orders of scattering (~10 000) can be treated because of the peculiar polarization characteristics of the reverse wave: after a number of scatterings, the polarization state of the reverse wave becomes independent of that of the incident wave, that is, it becomes fully dictated by the scatterings at the end of the reverse path. The coherent backscattering part depends on the single-scattering albedo in a non-monotonous way, the most pronounced signatures showing up for absorbing scatterers. The numerical results compare favourably to the literature results for nonabsorbing spherical scatterers both in and beyond the Rayleigh regime.     

Scattering of longitudinal waves (sound) by defects in fluids. Rough surface

The classical theory of scattering of longitudinal waves (sound) by small inhomogeneities (scatterers) in an ideal fluid is generalized to a distribution of scatterers and such as to include the effect of the inhomogeneities on the elastic properties of the fluid. The results are obtained by a new method of solving the wave equation with spatial restrictions (caused by the presence of the scatterers), which can also be applied to other types of inhomogeneities (like surface roughness, for instance). A coherent forward scattering is identified for a uniform distribution of scatterers (practically equivalent with a mean-field approach), which is due to the fact that our treatment does not include multiple scattering. The reflected wave is obtained for a half-space (semi-infinite fluid) of uniformly distributed scatterers, as well as the field diffracted by a perfect lattice of scatterers. The same method is applied to a (inhomogeneous) rough surface of a semi-infinite ideal fluid. A perturbation-theoretical scheme is devised, with the roughness function as a perturbation parameter, for computing the waves scattered by the surface roughness. The waves scattered by the rough surface are both waves localized (and propagating only) on the surface (two-dimensional waves) and waves reflected back in the fluid. They exhibit directional effects, slowness, attenuation or resonance phenomena, depending on the spatial characteristics of the roughness function. The reflection coefficients and the energy carried on by these waves are calculated both for fixed and free surfaces. In some cases, the surface roughness may generate waves confined to the surface (damped, rough-surface waves).     

Coherent opposition effects for semi-infinite discrete random medium in the double-scattering approximation

The rigorous equations of the theory of multiple scattering of light by a layer of disordered medium have been used in the double-scattering approximation for semi-infinite medium to determine the influence of the particle properties on the coherent opposition effects. The effects were found to be strongly dependent on the concentration of scatterers in the medium. The polarization opposition effect is more sensitive to the properties of the scatterers than the photometric opposition effect. The interference of waves could result in the negative polarization at the backscattering direction as well as in the positive polarization.     

Measurements of ultrasound velocity and attenuation in numerical anisotropic porous media compared to Biot’s and multiple scattering models

This article quantitatively investigates ultrasound propagation in numerical anisotropic porous media with finite-difference simulations in 3D. The propagation media consist of clusters of ellipsoidal scatterers randomly distributed in water, mimicking the anisotropic structure of cancellous bone. Velocities and attenuation coefficients of the ensemble-averaged transmitted wave (also known as the coherent wave) are measured in various configurations. As in real cancellous bone, one or two longitudinal modes emerge, depending on the micro-structure. The results are confronted with two standard theoretical approaches: Biot’s theory, usually invoked in porous media, and the Independent Scattering Approximation (ISA), a classical first-order approach of multiple scattering theory. On the one hand, when only one longitudinal wave is observed, it is found that at porosities higher than 90% the ISA successfully predicts the attenuation coefficient (unlike Biot’s theory), as well as the existence of negative dispersion. On the other hand, the ISA is not well suited to study two-wave propagation, unlike Biot’s model, at least as far as wave speeds are concerned. No free fitting parameters were used for the application of Biot’s theory. Finally we investigate the phase-shift between waves in the fluid and the solid structure, and compare them to Biot’s predictions of in-phase and out-of-phase motions.     

一阶速度-应力Biot双相各向同性介质弹性波

提出一种等价的一阶双曲型速度一应力Biot双相各向同性介质弹性波波动方程,以实现双相介质混合波场中纯快慢纵波和纯横波波场分离的问题.应用散度和旋度理论证明双相介质等价方程波场分离的可行性,采用高阶交错网格有限差分法构建高精度正演算子,推导其PML吸收边界条件和稳定性条件,并对均匀双相介质和层状非均匀双相介质模型进行数值...     

Propagation of magnetoacoustic surface waves along static plasma slab surrounded by moving plasma and neutral gas

The existence and propagation of fast and slow magnetoacoustic surface waves (MASW) is investigated in our work by taking a theoretical model of a static plasma slab as the middle layer with a moving plasma region at the top and neutral gas medium as the bottom layer. Applying linear MHD, the dispersion relation is obtained and the propagation of magnetoacoustic surface waves, in the compressional limit for steady flow and for different values of dimensionless wave numbers, is analyzed. Steady flow of plasma along a structured atmosphere may cause enhancement of existing surface modes, disappearance of some modes and generation of new surface wave modes. The possible regions for the propagation of fast and slow surface and body waves for different mass density ratios and magnetic field ratios and with a small flow velocity are studied. Our discussion may help in analyzing more complicated cases.     

Propagation of light through a monolayer of particles: Analysis of phase and coherent transmittance

Phase variations of a wave transmitted through a monolayer of spherical scatterers are studied as functions of size, optical constants, and particle concentration for light incident normally to the surface of the layer. The analysis is performed in the quasi-crystal approximation of the theory of multiple scattering of waves and in the single scattering approximation. The results obtained allow one to estimate the limits of applicability of the single scattering approximation to layers with partial ordering of scatterers in analysis of the transmitted wave phase. The variations of the phase of the wave in the range of the parameters where the coherent component of the transmitted beam exhibits quenching are studied. It is shown that small variations in the refractive index of the particles may give rise to strong variations of the phase. This effect can be used for phase modulation of light beams, e.g., in liquid crystal films controlled by an electric (or magnetic) field.     

含少量气泡流体饱和孔隙介质中的弹性波

考虑孔隙流体中含有少量气泡,且气泡在声波作用下线性振动,研究声波在这种孔隙介质中的传播特性.本文先由流体质量守恒方程和孔隙度微分与流体压力微分的关系推导出了含有气泡形式的渗流连续性方程;在处理渗流连续性方程中的气体体积分数时间导数时,应用Commander气泡线性振动理论导出气体体积分数时间导数与流体压强时间导数的关系,进而得到了修正的Biot形式的渗流连续性方程;最后结合Biot动力学方程求得了含气泡形式的位移场方程,便可得到两类纵波及一类横波的声学特性.通过对快、慢纵波的频散、衰减及两类波引起的流体位移与固体位移关系的考察,发现少量气泡的存在对快纵波和慢纵波的传播特性影响较大.     

Acoustic properties of wood in tridimensional representation of slowness surfaces

Mechanical behaviour of wood considered as an orthotropic solid can be determined with ultrasonic technique. The propagation phenomena in wood are complex and theoretically are regulated by Christoffel's equation. Three type of waves can propagate in wood. During the propagation phenomena three slowness sheets are observed, corresponding to a fast longitudinal wave (inner sheet) and two shear waves, one fast and one slow (outer sheet). These waves are submitted continuously to mode conversion phenomena. The polarization angle changes when the propagation direction is out of the principal directions of symmetry of the material. In this article an analysis of the propagation phenomena in tridimensional representation is performed for different wood species. This approach contributes to the understanding of dynamic aspects of particle displacement associated with the wave fronts propagation. Globally, the anisotropy of each species, expressed by their acoustical behaviour is well represented.     

Breakdown of wave diffusion in 2D due to loops

The validity of the diffusion approximation for the intensity of multiply scattered waves is tested with numerical simulations in a strongly scattering 2D medium of finite extent. We show that the diffusion equation underestimates the intensity and attribute this to both the neglect of recurrent scattering paths and interference within diffusion theory. We present a theory to quantify this discrepancy based on counting all possible scattering paths between point scatterers. Interference phenomena, due to loop paths, are incorporated in a way similar to coherent backscattering.     

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)     

Influence of Coating Layer on Acoustic Wave Propagation in a Random Complex Medium with Resonant Scatterers

We investigate the influence of coating layer on acoustic wave propagation in a dispersed random medium consisting of coa.ted fibers.In the strong-scattering regime, the characteristics of wave scattering resonances are found to evolve regularly with the properties of the coating layer.By theoretical calculation,frequency gaps are found in acoustic excitation spectra in a random medium.The scattering cross section results present the evolution of scattering resonances with the properties of the coating layer,which offers a good explanation for the change of the frequency gaps.The velocity of the propagation quasi-mode is also shown to depend on the filling fraction of the coating layer.We use the generalized coherent potential-approximation approach to solve acoustic wave dispersion relations in a complicated random medium consisting of coating-structure scatterers.It is shown that our model reveals subtle changes in the behavior of the acoustic wave propagating quasi-modes.     

充水有限长圆柱薄壳声散射:Ⅰ.理论

研究水中充水有限长圆柱薄壳的声散射。采用弹性薄壳理论结合边界条件导出了有限长圆柱薄壳倾斜入射时散射声场的解析解,内部充水的作用反映在系统总阻抗中增加了内部流体阻抗。数值计算表明,在反向散射声场中,刚性散射部分仅在正横附近有比较大的贡献,而斜入射时起主要作用的是弹性散射部分。散射波相速度频散曲线的计算表明,与内部真空的情况相比内部充水后除正横附近的纵波和剪切波以外,增加了一组内部流体引起的附加波,其对散射声场贡献非常重要。在计算的频率-角度谱图中,内部流体附加波呈现"碗"形共振曲线。      

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.     

Compton散射下激光等离子体纵波色散特性

应用电子与多光子集团非线性Compton散射模型,研究了Compton散射下激光等离子体纵波色散特性.结果表明:长波支纵色散曲线由解析上的长波、数值计算结果和短波组成,长波支和短波支纵色散均随相对论正负电子对特征温度的增大而增大,随Compton散射引起的频率的增量的增大而降低,且单温激光等离子体的色散曲线与散射前的双温等离子体的色散曲线相似.     

Multiple scattering in a trabecular bone: influence of the marrow viscosity on the effective properties

The Foldy and the Waterman and Truell approximations are used to determine the effective properties of the coherent wave that emerges after multiple scattering of a plane longitudinal fast wave by the largest pores in a trabecular bone. The unit scattering cell considered is either a single pore or two close cylindrical pores (cluster), at a fixed overall bone porosity. In the cluster case, the effective attenuation is about twice that obtained with one single pore per scatterer. It is shown that taking into account the marrow viscosity leads only to minor differences on the effective dispersion and attenuation.     

Effective wave numbers for thermo-viscoelastic media containing random configurations of spherical scatterers

The dispersion relation is derived for the coherent waves in fluid or elastic media supporting viscous and thermal effects and containing randomly distributed spherical scatterers. The formula obtained is the generalization of Lloyd and Berry's [Proc. Phys. Soc. London 91, 678-688 (1967)], the latter being limited to fluid host media, and it is the three-dimensional counterpart of that derived by Conoir and Norris [Wave Motion 47, 183-197 (2010)] for cylindrical scatterers in an elastic host medium.