Multiple focused-waves production by parametric mixing in a layer with hysteretic quadratic nonlinearity

Nonlinear scattering of a weak probe wave by a strong pump wave in a layer with nonlinearity hysteresis is analysed. It is demonstrated that a spherical probe wave from a point source after nonlinear process of difference frequency excitation is scattered in several foci. Different foci correspond to different frequencies of the transformed wave spectrum. In the case of a plane pump wave and under the condition that nonlinear scattering proceeds without acoustic mode conversion wave front reversal is possible. To achieve wave front reversal in a layer with hysteretic quadratic nonlinearity the pump wave should have a frequency equal to the frequency of the probe wave or to any of its subharmonics.     

The nonlinear propagation of acoustic waves in a viscoelastic medium containing cylindrical micropores

Based on an equivalent medium approach, this paper presents a model describing the nonlinear propagation of acoustic waves in a viscoelastic medium containing cylindrical micropores. The influences of pores' nonlinear oscillations on sound attenuation, sound dispersion and an equivalent acoustic nonlinearity parameter are discussed. The calculated results show that the attenuation increases with an increasing volume fraction of micropores. The peak of sound velocity and attenuation occurs at the resonant frequency of the micropores while the peak of the equivalent acoustic nonlinearity parameter occurs at the half of the resonant frequency of the micropores. Furthermore, multiple scattering has been taken into account, which leads to a modification to the effective wave number in the equivalent medium approach. We find that these linear and nonlinear acoustic parameters need to be corrected when the volume fraction of micropores is larger than 0.1%.     

Calculation of the parameters of spherical inclusions for implementing composite media with negative acoustic refractive index

The parameters of acoustic media appropriate for the appearance of the effect of negative refraction of sound waves, caused by multiple resonant scattering by spherical inclusions, were analyzed. The frequency ranges of transparency windows were calculated, in which effective compressibilities and densities take negative values and the relative level of radiative losses is small. To optimize the parameters, relations were derived for estimating the width of frequency windows corresponding to negative refraction and the value of nonviscous attenuation of the acoustic wave.     

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应用多光子非线性Compton散射模型,研究了Compton散射对等离子体中激光衰减特性的影响.提出了Compton散射是影响激光衰减的一个重要机制,给出了激光能量和功率衰减值的表达式,并进行了数值模拟.结果表明,Compton散射对等离子体中传输的激光能量和功率衰减值有较大影响,理论计算和数值模拟符合得很好.这也为判断等离子体中发生Compton散射提供了依据.     

Dynamic acoustoelastic testing of weakly pre-loaded unconsolidated water-saturated glass beads

Dynamic acoustoelastic testing is applied to weakly pre-loaded unconsolidated water-saturated glass beads. The gravitational acceleration produces, on the probed beads, a static stress of order 130 Pa, thus the granular medium is close to the jamming transition. A low-frequency (LF) acoustic wave gently disturbs the medium, inducing successively slight expansion and compaction of the granular packing expected to modulate the number of contacts between beads. Ultrasound (US) pulses are emitted simultaneously to dynamically detect the induced modification of the granular skeleton. US propagation velocity and attenuation both increase when the LF pressure increases. The quadratic nonlinear elastic parameter β, related to the pressure dependence of US propagation velocity, was measured in the range 60-530 if water-saturated glass beads are considered as an effective medium. A dynamic modification of US scattering induced by beads is proposed to modulate US attenuation. Complex hysteretic behaviors and tension-compression asymmetry are also observed and analyzed by time-domain and spectral analyses. Furthermore acoustic nonlinearities are measured in cases of quasi-static and dynamic variations of the LF wave amplitude, providing quantitatively similar acoustic nonlinearities but qualitatively different.     

Nonlinear unbalanced Bessel beams in the collapse of Gaussian beams arrested by nonlinear losses

Collapse of a Gaussian beam in self-focusing Kerr media arrested by nonlinear losses may lead to the spontaneous formation of a quasi-stationary nonlinear unbalanced Bessel beam with finite energy, which can propagate without significant distortion over tens of diffraction lengths, and without peak intensity attenuation while the beam power is drastically diminishing.     

Wave processes in microinhomogeneous elastic media with hysteretic nonlinearity and relaxation

The nonlinear propagation of an initially harmonic acoustic wave in a microinhomogeneous medium containing defects with quadratic hysteretic nonlinearity and relaxation is studied by the perturbation method. The frequency dependences of the effective nonlinearity parameters are determined for the self-action of the quasi-harmonic acoustic wave and the higher harmonic generation processes.     

材料非线性衰减系数的二次谐波测量方法研究

采用有限幅值法测量材料在基波和非线性引起的二次谐波作用下的衰减系数:利用准线性下的KZK方程推导基波和二次谐波的声压分布,并提取波束修正系数;采用短纯音信号进行非线性实验,对检测得到的基波和二次谐波声压进行衍射修正处理,有效抑制衍射对衰减系数测量的不利影响,继而通过线性拟合的方法计算得到更精确的基波和二次谐波的衰减系数。以水为例进行实验,研究了实验测量所得衰减系数的频率依赖关系,结果表明在非线性条件下水的衰减系数与频率间存在较强的线性关系,而线性条件下衰减系数随频率呈现二次方增长的特性则不适用于非线性条件。该研究提出了准确测量非线性声波衰减系数的方法,为更有效地应用非线性超声检测提供理论依据。      

Stationary and quasi-stationary waves in even-order dissipative systems

A new equation was recently suggested by Rudenko and Robsman [1] for describing the nonlinear wave propagation in scattering media that are characterized by weak sound signal attenuation proportional to the fourth power of frequency. General self-similar properties of the solutions to this equation were studied. It was shown that stationary solutions to this equation in the form of a shock wave exhibit unusual oscillations around the shock front, as distinct from the classical Burgers equation. Here, similar solutions are studied in detail for nonlinear waves in even-order dissipative media; namely, the solutions are compared for the media with absorption proportional to the second, fourth, and sixth powers of frequency. Based on the numerical results and the self-similar properties of the solutions, the fine structure of the shock front of stationary waves is studied for different absorption laws and magnitudes. It is shown that the amplitude and number of oscillations appearing in the stationary wave profile increase with increasing power of the frequency-dependent absorption term. For initial disturbances in the form of a harmonic wave and a pulse, quasi-stationary solutions are obtained at the stage of fully developed discontinuities and the evolution of the profile and width of the shock wave front is studied. It is shown that the smoothening of the shock front in the course of wave propagation is more pronounced when the absorption law is quadratic in frequency.     

多重散射方法研究轴对称空腔覆盖层的声学特性

发展了一种多重散射方法研究声学覆盖层的半数值半解析模型,分析了影响轴对称空腔结构声学性能的主要能量耗散机制。在球坐标条件下推导出轴对称空腔结构的位移和应力场基函数,通过对空腔表面基函数的数值积分,得到散射波和入射波之间的传输矩阵方程,结合分层介质声传播理论计算了周期性空腔结构覆盖层的反射、透射和吸声性能。研究结果表明;空腔共振是低频能量耗散的主要形式,边界条件对材料空腔结构的谐振特性影响很大,利用双空腔耦合共振可以拓宽材料的低频吸声频带;背衬对材料的高频吸声影响较小,材料的高频能量损耗取决于空腔的散射和波型转换特性。      

In vivo biomicroscopy with ultrasound 2

In the first article of this series it was shown that the use of inverse scattering theory to analyse ultrasound reflections could provide high resolution images of the acoustic impedance profile of the retina. Unlike the retina, most tissue structures of interest, like small tumours and arterial plaque deposits, are shielded from view by intervening layers of tissue of appreciable acoustic impedance and attenuation. By analysing a one-dimensional model for a plaque deposit on the wall of a carotid artery embedded in a 5 cm thick layer of tissue, we demonstrate that a relatively high quality image can be recovered when compensation for the attenuation of the intervening tissue is made. We observe that because of the dearth of low frequency power in the recovered signal of ultrasound transducers, it is important that the field of view imaged is not taken to be too large. We compare the exact iterative distorted wave Born approximation inverse scattering method with the approximate but computationally faster plane wave Born approximation method and find that they give images of comparable quality for this model.     

Attenuation and trapping of acoustic energy in composite microwave resonators based on YAG single crystals

The frequency dependence of acoustic wave attenuation in a composite piezoelectric microwave resonator is studied by acoustic resonance spectroscopy. In addition to the attenuation associated with the loss in the lattice, the diffraction loss, and the loss due to the scattering by the roughness of the reflecting faces, an extra attenuation component periodic in frequency is revealed. The appearance of this component is explained by the absence of acoustic energy trapping in the resonator within certain frequency intervals.     

The attenuation of rayleigh surface waves by surface roughness

This paper presents a calculation of the attenuation length of Rayleigh surface waves in the presence of surface roughness. We consider Rayleigh waves on the surface of a semi-infinite isotropic elastic continuum, and the method we use produces the contribution to the attenuation rate proportional to the square of the rms amplitude of the roughness. We obtain explicit expressions for the contribution to the attenuation rate from roughness-induced scattering into bulk transverse and longitudinal acoustic waves, and into Rayleigh waves. Our derivation makes use of a Green's function method. When the wavelength λ of the Rayleigh wave is long compared to the transverse correlation length a that characterizes the surface roughness, all contributions to the attenuation rate are proportional to the fifth power of the frequency. When λ is comparable to or smaller than a, the attenuation constant varies more slowly with frequency. For a model of the surface roughness, we present numerical calculations of the relative magnitude and frequency dependence of the various contributions to the attenuation rate. The Green's functions used here may be applied to a number of calculations. A derivation of their form is provided in an Appendix.     

Finite element analysis of broadband acoustic pulses through inhomogenous media with power law attenuation

Acoustic waves in tissues and weakly attenuative fluids often have an attenuation parameter, alpha(omega), satisfying alpha(omega)= alpha0omegay in which alpha0 is a constant, omega is the frequency, and y is between 1 and 2. This power law attenuation is not predicted by the classical thermoviscous wave equation and researchers have proposed different modified viscous wave equations in which the loss term is a convolution operator or a fractional spatial or temporal derivative. In this paper, acoustic waves undergoing power law attenuation are modeled by a modification to the thermoviscous wave equation in which the time derivative of the viscous term is replaced by a fractional time derivative. An explicit time domain, finite element formulation leads to a stable algorithm capable of simulating axisymmetric, broadband acoustic pulses propagating through attenuative and dispersive media. The algorithm does not depend on the Born approximation, long wavelength limit, or plane wave assumptions. The algorithm is validated for planar and focused transducers and results include radiation patterns from a viscous scatterer in a lossless background and signals reflected from a viscous layer. The program can be used to determine scattering parameters for large, strong, possibly viscous scatterers, in either a lossless or viscous background, for which analytic results are scarce.     

A simple model of ultrasound propagation in a cavitating liquid. Part I: Theory, nonlinear attenuation and traveling wave generation

The bubbles involved in sonochemistry and other applications of cavitation oscillate inertially. A correct estimation of the wave attenuation in such bubbly media requires a realistic estimation of the power dissipated by the oscillation of each bubble, by thermal diffusion in the gas and viscous friction in the liquid. Both quantities and calculated numerically for a single inertial bubble driven at 20 kHz, and are found to be several orders of magnitude larger than the linear prediction. Viscous dissipation is found to be the predominant cause of energy loss for bubbles small enough. Then, the classical nonlinear Caflish equations describing the propagation of acoustic waves in a bubbly liquid are recast and simplified conveniently. The main harmonic part of the sound field is found to fulfill a nonlinear Helmholtz equation, where the imaginary part of the squared wave number is directly correlated with the energy lost by a single bubble. For low acoustic driving, linear theory is recovered, but for larger drivings, namely above the Blake threshold, the attenuation coefficient is found to be more than 3 orders of magnitude larger then the linear prediction. A huge attenuation of the wave is thus expected in regions where inertial bubbles are present, which is confirmed by numerical simulations of the nonlinear Helmholtz equation in a 1D standing wave configuration. The expected strong attenuation is not only observed but furthermore, the examination of the phase between the pressure field and its gradient clearly demonstrates that a traveling wave appears in the medium.     

Experimental study of the Doppler shift generated by a vibrating scatterer

We report an experimental study of the backscattering of a sound wave of frequency f by a surface vibrating harmonically at frequency F (F < f) and amplitude A in the regime where the Doppler effect overcomes bulk nonlinear effects. When the duration to of the analyzed time series of the scattered wave is small compared to the vibration period, the power spectrum of the backscattered wave is proportional to the probability density function of the scatterer velocity, which presents two peaks shifted from f by roughly 2fAomega/c (omega = 2piF). On the contrary, when t0 > F(-1), sidebands at frequencies f +/- nF (n integer) appear in the power spectrum, which are due to the phase modulation of the backscattered wave induced by its reflection on a moving boundary. We use the backscattered power spectrum to validate the phase modulation theory of the Doppler effect in the latter case for 2kA < 1 and 2kA approximately > 1 (k = 2pif/c, where c is the wave velocity) and we test the validity of an acoustic nonintrusive estimator of A as a function of power spectrum bandwidth and of A itself.     

离子通道回旋电子注受激辐射非线性理论

文中对散射波自洽增长的时间响应进行了数值模拟计算,研究了离子密度、电子注入射能量对电磁散射波的功率、频率以及工作效率的非线性影响 关键词： 电磁辐射 非线性 高功率毫米波源 等离子体     

Contrast harmonic imaging

The behavior of ultrasound contrast agents depends highly on the acoustic pressure of the insonified ultrasound wave. For low pressure the expansion and compression is linear to the pressure, for medium acoustic pressure nonlinear behavior starts to occur and for high pressures, but still in the diagnostic range transient scattering can be noticed, resulting in an enhanced scattering followed by a disappearance of the bubble. The nonlinear and transient regime can be utilized for imaging of the contrast agent in or nearby tissue. The magnitude of the nonlinear signal from the contrast has to compete with the nonlinear component of the ultrasound wave, which is generated during propagation. It is shown that contrast is superior to tissue when using low frequencies and imaging the third or fourth harmonic of the transmitted frequency.     

Theory of parametric excitation of acoustic waves

A theory of parametric excitation of acoustic waves is constructed. It is shown that nonlinear attenuation is the main restriction mechanism for a parametrically generated sound wave. The intensity of generated waves is directly proportional to the difference ε between the value of pumping and bare attenuation. The calculated proportionality coefficient depends on the shape of the generated sound wave. Why an ordinary pattern does not form for acoustic waves is explained. The structure of the spectrum of excited waves was studied. It is shown that this structure has exponential asymptotic behavior at the frequency. The width of the intensity distribution depends on the shape of a wave. For different cases it behaves as ε ^α with α=1, 8/7, and 4/3. The results are compared with the experimental data of Ref. 5. Zh. éksp. Teor. Fiz. 112, 1630–1648 (November 1997) Published in English in the original Russian journal. Reproduced here with stylistic changes by the Translation Editor.