Evaluation of a wave-vector-frequency-domain method for nonlinear wave propagation

A wave-vector-frequency-domain method is presented to describe one-directional forward or backward acoustic wave propagation in a nonlinear homogeneous medium. Starting from a frequency-domain representation of the second-order nonlinear acoustic wave equation, an implicit solution for the nonlinear term is proposed by employing the Green's function. Its approximation, which is more suitable for numerical implementation, is used. An error study is carried out to test the efficiency of the model by comparing the results with the Fubini solution. It is shown that the error grows as the propagation distance and step-size increase. However, for the specific case tested, even at a step size as large as one wavelength, sufficient accuracy for plane-wave propagation is observed. A two-dimensional steered transducer problem is explored to verify the nonlinear acoustic field directional independence of the model. A three-dimensional single-element transducer problem is solved to verify the forward model by comparing it with an existing nonlinear wave propagation code. Finally, backward-projection behavior is examined. The sound field over a plane in an absorptive medium is backward projected to the source and compared with the initial field, where good agreement is observed.     

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%.     

Nonlinear wave interactions in porous media filled with a quantum fluid

The problem of the nonlinear interaction between the fourth sound and an acoustic wave propagating in a porous medium filled with superfluid helium is solved. Based on the Landau equations of quantum fluid dynamics and on the Biot theory of mechanical waves in a porous medium, nonlinear wave equations are derived for studying the aforementioned interaction. An expression is obtained for the vertex that determines the excitation of an acoustic wave by two waves of the fourth sound. The possibility of an experimental observation of this process is estimated.     

Acoustic phonon emission from a weakly coupled superlattice under vertical electron transport: observation of phonon resonance

We report measurements of acoustic phonon emission from a weakly coupled AlAs/GaAs superlattice (SL) under vertical electron transport. The phonons were detected using superconducting bolometers. A peak (resonance) was observed in emission parallel to the SL growth axis when the electrical energy drop per SL period matched the energy of the first SL mini-Brillouin zone-center phonon mode. This peak was mirrored by an increase of the differential conductance of the SL. These results are evidence for stimulated emission of terahertz phonons as previously predicted theoretically and suggest that such a SL may form the basis of a SASER (sound amplification by stimulated emission of radiation) device.     

Anomalous delay of phonons reflected from the surface of a superlattice

We study theoretically the propagation of acoustic phonons in a superlattice (SL) with a free surface. A phonon incident normally on the SL from a substrate is perfectly reflected, but it comes back to the substrate either with a time delay or with a time advance. Specifically the time delay is enhanced considerably if the frequency of the incident phonon coincides with an eigenfrequency of the vibrational modes localized at the surface of the SL. This suggests the observability of the surface vibrational modes by a time-resolved phonon reflection experiment.     

The use of a hybrid model to compute the nonlinear acoustic performance of silencers for the finite amplitude acoustic wave

In the present study, a hybrid method is proposed for predicting the acoustic performance of a silencer for a nonlinear wave. This method is developed by combining two models: (i) a frequency-domain model for the computation of sound attenuation due to a silencer in a linear regime and (ii) a wavenumber space model for the prediction of the nonlinear time-evolution of finite amplitudes of the acoustic wave in a uniform duct of the same length as the silencer. The present method is proposed under the observation that the physical process of the nonlinear sound attenuation phenomenon of a silencer may be decoupled into two distinct mechanisms: (a) a linear acoustic energy loss that owes to the mismatch in the acoustic impedance between reactive elements and/or the sound absorption of acoustic liners in a silencer; (b) a nonlinear acoustic energy loss that is due to the energy-cascade phenomenon that arises from the nonlinear interaction between components of different frequencies. To establish the validity of the present model for predicting the acoustic performance of silencers, two model problems are considered. First, the performance of simple expansion mufflers with nonlinear incident waves has been predicted. Second, proposed method is applied for computing nonlinear acoustic wave propagation in the NASA Langley impedance duct configuration with ceramic tubular liner (CT57). Both results obtained from the hybrid models are compared with those from computational aero-acoustic techniques in a time-space domain that utilize a high-order finite-difference method. Through these comparisons, it is shown that there are good agreements between the two predictions. The main advantage of the present method is that it can effectively compute the nonlinear acoustic performance of silencers in nonlinear regimes without time-space domain calculations that generally entail a greater computational burden.     

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.     

Propagation of acoustic wave in viscoelastic medium permeated with air bubbles

Based on the modification of the radial pulsation equation of an individual bubble, an effective medium method (EMM) is presented for studying propagation of linear and nonlinear longitudinal acoustic waves in viscoelastic medium permeated with air bubbles. A classical theory developed previously by Gaunaurd (Gaunaurd GC and \"{U}berall H, {\em J. Acoust. Soc. Am}., 1978; 63: 1699--1711) is employed to verify the EMM under linear approximation by comparing the dynamic (i.e. frequency-dependent) effective parameters, and an excellent agreement is obtained. The propagation of longitudinal waves is hereby studied in detail. The results illustrate that the nonlinear pulsation of bubbles serves as the source of second harmonic wave and the sound energy has the tendency to be transferred to second harmonic wave. Therefore the sound attenuation and acoustic nonlinearity of the viscoelastic matrix are remarkably enhanced due to the system's resonance induced by the existence of bubbles.     

Numerical simulation of the nonlinear ultrasonic pressure wave propagation in a cavitating bubbly liquid inside a sonochemical reactor

We investigate the acoustic wave propagation in bubbly liquid inside a pilot sonochemical reactor which aims to produce antibacterial medical textile fabrics by coating the textile with ZnO or CuO nanoparticles. Computational models on acoustic propagation are developed in order to aid the design procedures. The acoustic pressure wave propagation in the sonoreactor is simulated by solving the Helmholtz equation using a meshless numerical method. The paper implements both the state-of-the-art linear model and a nonlinear wave propagation model recently introduced by Louisnard (2012), and presents a novel iterative solution procedure for the nonlinear propagation model which can be implemented using any numerical method and/or programming tool. Comparative results regarding both the linear and the nonlinear wave propagation are shown. Effects of bubble size distribution and bubble volume fraction on the acoustic wave propagation are discussed in detail. The simulations demonstrate that the nonlinear model successfully captures the realistic spatial distribution of the cavitation zones and the associated acoustic pressure amplitudes.     

Characterization of high intensity focused ultrasound transducers using acoustic streaming

A new approach for characterizing high intensity focused ultrasound (HIFU) transducers is presented. The technique is based upon the acoustic streaming field generated by absorption of the HIFU beam in a liquid medium. The streaming field is quantified using digital particle image velocimetry, and a numerical algorithm is employed to compute the acoustic intensity field giving rise to the observed streaming field. The method as presented here is applicable to moderate intensity regimes, above the intensities which may be damaging to conventional hydrophones, but below the levels where nonlinear propagation effects are appreciable. Intensity fields and acoustic powers predicted using the streaming method were found to agree within 10% with measurements obtained using hydrophones and radiation force balances. Besides acoustic intensity fields, the streaming technique may be used to determine other important HIFU parameters, such as beam tilt angle or absorption of the propagation medium.     

Turbulent diffusion in a compressible medium

This paper examines the diffusion of impurity particles in a compressible turbulent medium and compares it to diffusion in an incompressible medium. The turbulent diffusion coefficients are calculated using exact formulas expressed in terms of the Green’s function describing impurity transport in an infinite homogeneous, isotropic, stationary turbulent medium. To obtain an approximate expression for the Green’s function, numerical solutions of the nonlinear DIA (direct interaction approximation) equation (which in this paper are obtained for the first time for the case of compressible turbulence) are employed. Two types of turbulence are examined, acoustic and a mixture of shock waves. These are described by different generalized spectra. Finally, it is shown that compressibility significantly enhances the diffusion coefficient in the case of acoustic turbulence and reduces it in the second case. Zh. éksp. Teor. Fiz. 114, 930–945 (September 1998)     

Comparison of sonochemiluminescence images using image analysis techniques and identification of acoustic pressure fields via simulation

One common method to determine the existence of cavitational activity in power ultrasonics systems is by capturing images of sonoluminescence (SL) or sonochemiluminescence (SCL) in a dark environment. Conventionally, the light emitted from SL or SCL was detected based on the number of photons. Though this method is effective, it could not identify the sonochemical zones of an ultrasonic systems. SL/SCL images, on the other hand, enable identification of ‘active’ sonochemical zones. However, these images often provide just qualitative data as the harvesting of light intensity data from the images is tedious and require high resolution images. In this work, we propose a new image analysis technique using pseudo-colouring images to quantify the SCL zones based on the intensities of the SCL images and followed by comparison of the active SCL zones with COMSOL simulated acoustic pressure zones.     

Simulation of the acoustic field emitted from medical linear transducer in a heterogeneous tissue

A numerical model is developed to simulate the acoustic field in heterogeneous tissue from a medical linear transducer.The coupled full-wave equation for nonlinear ultrasound is solved using a staggered-grid finite difference time domain method.The distribution of acoustic pressure and power in human abdominal wall with heterogeneities in sound speed,density,and nonlinear parameter are obtained.Compared with homogeneous medium,when sound speed in tissue is uniform and density unchanged,the acoustic energy decreases only1.8 dB in the focal region;when density in tissue is uniform and sound speed unchanged,the energy decreases 3.8 dB in the focal region,which is almost the same as heterogeneous tissue.Thus,the primary factor of the aberration of focused beam is the heterogeneous distribution of the tissue sound speed.     

Generation of acoustic solitons by a single-mode electromagnetic field

Mechanisms of acoustic pulse generation by a single-mode electromagnetic field propagating in a photoelastic material are analyzed. The anisotropy induced by acoustic excitations in an isotropic medium leads to nonlinear coupling between the polarization components of a single-mode electromagnetic field. For different conditions, it is shown that the acoustic-electromagnetic wave interaction due to mixing of the polarization components of light and acoustic waves can give rise to soliton-like coherent acoustic excitations in a thin crystal plate. When spatial dispersion is ignored, the governing system of equations for unidirectional acoustic solitons can be reduced to an integrable model. It is shown that qualitatively different scenarios of formation of acoustic solitons are possible, depending on the directions of deformation and field polarization.     

单向声传播结构研究

受到电子二极管整流效应的启发,对单向声传播结构展开了一系列的理论与实验研究：将超晶格结构与非线性声学材料组合构成了可实现声整流效应的声二极管结构;通过将反对称弹性结构引入到复合结构板来产生Lamb波的不对称模式转化,设计了可实现Lamb波单向传播的线性声学结构;基于声子晶体的部分禁带特性,在有限尺度声学系统中设计并实现了单向声学波导结构;设计并实现了由纯板与声栅构成的声单向传播结构,具有小尺寸与高效率的特点,且声波出射角度可调;基于声学梯度材料设计了可在极宽频带内实现不对称声传播的声学结构。     

Trapping an intensely bright, stable sonoluminescing bubble

Previous works on single bubble sonoluminescence in sulfuric acid solutions have stressed the fact that the sonoluminescence (SL) emissions are the highest ever found, but at the same time the bubble moves in orbits. We have fixed the SL bubble spatially and at the same time we have reached higher SL emissions using another harmonic acoustic signal to produce the acoustic excitation. Multiple harmonic excitation produces up to a fourfold increase in SL emissions, reaching the peak value of about 40 microW for a moving bubble and 15 microW for a nonmoving bubble. The ability to have a bright stationary bubble also opens new research opportunities. In particular, we develop a new method to measure the absolute radius evolution of the bubble that exploits this stability.     

Sound field of thermoacoustic tomography based on a modified finite-difference time-domain method

A modified finite-difference time-domain （FDTD） method is proposed for the sound field simulation of the thermoacoustic tomography （TAT） in the acoustic speed inhomogeneous medium. First, the basic equations of the TAT are discretized to difference ones by the FDTD. Then the electromagnetic pulse, the excitation source of the TAT, is modified twice to eliminate the error introduced by high frequency electromagnetic waves. Computer simulations are carried out to validate this method. It is shown that the FDTD method has a better accuracy than the commonly used time-of-flight （TOF） method in the TAT with the inhomogeneous acoustic speed. The error of the FDTD is ten times smaller than that of the TOF in the simulation for the acoustic speed difference larger than 50%. So this FDTD method is an efficient one for the sound field simulation of the TAT and can provide the theoretical basis for the study of reconstruction algorithms of the TAT in the acoustic heterogeneous medium.     

Sonoluminescence and sonochemiluminescence from a microreactor

Micromachined pits on a substrate can be used to nucleate and stabilize microbubbles in a liquid exposed to an ultrasonic field. Under suitable conditions, the collapse of these bubbles can result in light emission (sonoluminescence, SL). Hydroxyl radicals (OH()) generated during bubble collapse can react with luminol to produce light (sonochemiluminescence, SCL). SL and SCL intensities were recorded for several regimes related to the pressure amplitude (low and high acoustic power levels) at a given ultrasonic frequency (200kHz) for pure water, and aqueous luminol and propanol solutions. Various arrangements of pits were studied, with the number of pits ranging from no pits (comparable to a classic ultrasound reactor), to three-pits. Where there was more than one pit present, in the high pressure regime the ejected microbubbles combined into linear (two-pits) or triangular (three-pits) bubble clouds (streamers). In all situations where a pit was present on the substrate, the SL was intensified and increased with the number of pits at both low and high power levels. For imaging SL emitting regions, Argon (Ar) saturated water was used under similar conditions. SL emission from aqueous propanol solution (50mM) provided evidence of transient bubble cavitation. Solutions containing 0.1mM luminol were also used to demonstrate the radical production by attaining the SCL emission regions.     

非均匀组织医学超声发射声场仿真

为了分析医学超声在非均匀组织中的分布特性,建立了超声发射声场的计算模型。采用交错网格有限差分法对耦合超声非线性方程进行数值求解,获得了声速、密度及非线性参数非均匀分布情况下人体腹壁组织内的超声声场分布数据。同均匀介质相比:当声速均匀而密度非均匀时,声束仍聚焦良好,焦点处声能下降了1.8 dB;当密度均匀而声速非均匀时,声束发散严重,焦点处声能下降了3.8 dB,下降程度与非均匀组织接近。组织声速在空间分布的非均匀性是导致聚焦声束能量分布畸变的主要原因。      

Nonlinear wave processes in porous waterlike media containing a system of capillaries partially filled with a viscous liquid

A nonlinear dynamic state equation of waterlike porous material that contains a system of cylindrical capillaries partially filled with viscous liquid was received. It is shown that an acoustic nonlinearity of such media contains the relaxation elastic and inelastic components due to the nonlinear dependence of the capillary and viscous pressure in fluid on the capillary diameter. For the medium, theoretical study of such nonlinear phenomena as generation of the second harmonic and a difference frequency wave, self-demodulation of high-frequency pulses as well as the change in the propagation velocity and absorption coefficient of a test wave being under an action of static loading have been carried out. The frequency dependences of medium nonlinearity parameters for these processes were determined.