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In Non-Destructive Testing and Evaluation (NDT&E), an ultrasonic method called Nonlinear Coda Wave Interferometry (NCWI) has recently been developed to detect cracks in heterogeneous materials such as concrete. The underlying principle of NCWI is that a pump wave is used to activate the crack breathing which interact with the source probe signal. The resulting signal is then measured at receiver probes. In this work, a static finite element model (FEM) is used to simulate the pump wave/crack interaction in order to quantifies the average effect of the pump waves on a crack. By considering both crack opening and closure phases during the dynamic pump wave excitation, this static model aims to determine the pump stress amplitude for a given relative crack length variation due to the dynamic pump wave excitation at different amplitudes. Numerical results show, after reaching certain stress amplitude, a linear relationship between the relative crack length variation and the equivalent static load when considering a partially closed crack at its tips. Then, numerical NCWI outputs, e.g., the relative velocity change θ and the decorrelation coefficient Kd, have been calculated using a spectral element model (SEM). These results agree with previously published experimental NCWI results derived for a slightly damaged 2D glass plate.

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Recent advances in electronics miniaturization have led to the development of low-power, low-cost, point-of-care ultrasound scanners. Low-cost systems employing simple bi-level pulse generation devices need only utilize binary phase modulated coded excitations to significantly improve sensitivity; however the performance of complementary codes in the presence of nonlinear harmonic distortion has not been thoroughly investigated. Through simulation, it was found that nonlinear propagation media with little attenuative properties can significantly deteriorate the Peak Sidelobe Level (PSL) performance of complementary Golay coded pulse compression, resulting in PSL levels of -62 dB using nonlinear acoustics theory contrasted with -198 dB in the linear case. Simulations of 96 complementary pairs revealed that some pairs are more robust to sidelobe degradation from nonlinear harmonic distortion than others, up to a maximum PSL difference of 17 dB between the best and worst performing codes. It is recommended that users consider the effects of nonlinear harmonic distortion when implementing binary phase modulated complementary Golay coded excitations.

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In this work, we characterize acoustic resonance phenomena occurring between gas bubbles in a segmented gas-liquid flow in a microchannel irradiated with a frequency around 500 kHz. A large acoustic amplitude can be reached, leading to gas-liquid interface deformation, atomization of micrometer sized droplets, and cavitation. A numerical approach combining an acoustic frequency-domain solver and a Lagrangian Surface-Evolver solver is introduced to predict the acoustic deformation of gas-liquid interfaces and the dynamic acoustic magnitude. The numerical approach and its assumptions were validated with experiments, for which a good agreement was observed. Therefore, this numerical approach allows to provide a description and an understanding of the acoustic nature of these phenomena. The acoustic pressure magnitude can reach hundreds of kPa to tens of MPa, and these values are consistent with the observation of atomization and cavitation in the experiments. Furthermore, volume of fluid simulations were performed to predict the atomization threshold, which was then related to acoustic resonance. It is found that dynamic acoustic resonance gives rise to atomization bursts at the gas bubble surface. The presented approach can be applied to more complex acoustic fields involving more complex channel geometries, vibration patterns, or two-phase flow patterns.

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Gas bubbles present in liquids underpin many natural phenomena and human-developed technologies that improve the quality of life. Since all living organisms are predominantly made of water, they may also contain bubbles-introduced both naturally and artificially-that can serve as biomechanical sensors operating in hard-to-reach places inside a living body and emitting signals that can be detected by common equipment used in ultrasound and photoacoustic imaging procedures. This kind of biosensor is the focus of the present article, where we critically review the emergent sensing technologies based on acoustically driven oscillations of bubbles in liquids and bodily fluids. This review is intended for a broad biosensing community and transdisciplinary researchers translating novel ideas from theory to experiment and then to practice. To this end, all discussions in this review are written in a language that is accessible to non-experts in specific fields of acoustics, fluid dynamics and acousto-optics.

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In this paper we study the generation and behavior of subharmonics in a bubbly liquid confined in an acoustic resonator, through numerical simulations carried out at finite-amplitude acoustic pressure. Several configurations in terms of resonator length and driving frequency are considered here. Our results show that these frequency components, created from a higher-frequency signal at the source (ultrasound), are due to the nonlinearity of the medium at high acoustic-pressure amplitude and to the configuration of the resonator (geometry and boundaries). We also show that they have an amplitude-threshold dependence, which is in concordance with the literature. The response of these subharmonics to different sequences of pressure amplitudes also reveals the hysteretic nature of the bubbly liquid.

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Frequency combs (FCs)-spectra containing equidistant coherent peaks-have enabled researchers and engineers to measure the frequencies of complex signals with high precision, thereby revolutionising the areas of sensing, metrology and communications and also benefiting the fundamental science. Although mostly optical FCs have found widespread applications thus far, in general FCs can be generated using waves other than light. Here, we review and summarise recent achievements in the emergent field of acoustic frequency combs (AFCs), including phononic FCs and relevant acousto-optical, Brillouin light scattering and Faraday wave-based techniques that have enabled the development of phonon lasers, quantum computers and advanced vibration sensors. In particular, our discussion is centred around potential applications of AFCs in precision measurements in various physical, chemical and biological systems in conditions where using light, and hence optical FCs, faces technical and fundamental limitations, which is, for example, the case in underwater distance measurements and biomedical imaging applications. This review article will also be of interest to readers seeking a discussion of specific theoretical aspects of different classes of AFCs. To that end, we support the mainstream discussion by the results of our original analysis and numerical simulations that can be used to design the spectra of AFCs generated using oscillations of gas bubbles in liquids, vibrations of liquid drops and plasmonic enhancement of Brillouin light scattering in metal nanostructures. We also discuss the application of non-toxic room-temperature liquid-metal alloys in the field of AFC generation.

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This paper reports a numerical study of the sensitivity and applicability of the Nonlinear Coda Wave Interferometry (NCWI) method in a heterogeneous material with a localized microcracked zone. We model the influence of a strong pump wave on the localized microcracked zone as a small average increase in the length of each crack. Further probing of this microcracked zone with a multiply scattered ultrasonic wave induces small changes to the coda-type signal, which are quantified with coda wave interferometry. A parametric sensitivity study of the CWI observables with respect to the changes in crack length is established via numerical simulations of the problem using a 2D spectral element method (SEM2D). The stretching of the signal, proportional to the relative variation in effective velocity, is found to be linearly proportional to the global change in crack length, while the other CWI parameter, the remnant decorrelation coefficient, is found to be quadratically proportional to the crack length change. The NCWI method is shown to be relevant for the detection of different damaged material states in complex solids. The reported numerical results are especially significant in the context of quantitative nondestructive evaluation of micro-damage level of a heterogeneous materials using nonlinear ultrasound signals.

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Acoustic wave propagation in ultrasonic flow measurements is typically assumed to be linear and reciprocal. However, if the transmitting transducer generates a sufficiently high pressure, nonlinear wave propagation effects become significant. In flow measurements, this would translate into more information to estimate the flow and therefore a higher precision relative to the linear case. In this work, we investigate how the generated harmonics can be used to measure flow. Measurements in a custom-made flow loop and simulations using the Khokhlov-Zabolotskaya-Kuznetsov (KZK) equation will show that the second harmonic component provides similar transit time differences to those obtained from the fundamental component, their linear combination results in more precise flow measurements compared to the estimations with the fundamental component alone.

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Action potentials in neurons are known to annihilate each other upon collision, while there are cases where they might penetrate each other. The fate of two waves upon collision is critically dependent on the underlying mechanism of propagation and therefore an understanding of possible outcomes of collision under different conditions is important. Previously, compression waves that travel within the plasma membrane of a neuron have been proposed as a thermodynamic basis for the propagation of action potentials. In this context, it was recently shown that two-dimensional compressive shock waves in the model system of lipid monolayers behave strikingly similar to action potentials in neurons and can even annihilate each other upon head-on collision. However, even a qualitative mechanism remained unclear. To this end, we summarise the fundamentals of shock physics as applied to an interface and recap how it explained the observation of threshold and saturation of shockwaves in the lipid monolayer (all - or - none). We then compare the theory with the soliton model that has the same fundamental premise, i.e. the conservation laws and thermodynamics, and was previously proposed as a model for the nerve pulse propagation. We elaborate on how the two approaches make different predictions with regards to collisions and the detailed structure of the wave-front. As a case study and a new qualitative result, we finally show that previously unexplained annihilation of shock waves in the lipid monolayer is a direct consequence of the nature of state changes, i.e. jump conditions, within these shockwaves.

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For tissue characterization, it is desirable to determine B/A using high-frequency transducers. Moreover, an accurate estimate of B/A at elevated frequencies (or at least the assumption of frequency independence of B/A) is required to evaluate the safety of high-frequency systems. However, common finite-amplitude approaches become increasingly inaccurate at high frequencies. In this article, a practical variation of the finite-amplitude method is proposed which combines experiments with numerical simulations of the Khokhlov-Zabolotskaya-Kuznetsov equation and can be used at elevated frequencies. The results at low frequencies show that the proposed approach is accurate with lower uncertainties compared with the finite-amplitude method because it avoids assumptions and approximations. The measured values of B/A versus frequency for water at 2.25-20 MHz show that there is no statistically significant variation in B/A values with frequency, and therefore the assumption of frequency independence of B/A is realistic.

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The entropic lattice Boltzmann method for the simulation of compressible flows is studied in detail and new opportunities for extending operating range are explored. We address limitations on the maximum Mach number and temperature range allowed for a given lattice. Solutions to both these problems are presented by modifying the original lattices without increasing the number of discrete velocities and without altering the numerical algorithm. In order to increase the Mach number, we employ shifted lattices while the magnitude of lattice speeds is increased in order to extend the temperature range. Accuracy and efficiency of the shifted lattices are demonstrated with simulations of the supersonic flow field around a diamond-shaped and NACA0012 airfoil, the subsonic, transonic, and supersonic flow field around the Busemann biplane, and the interaction of vortices with a planar shock wave. For the lattices with extended temperature range, the model is validated with the simulation of the Richtmyer-Meshkov instability. We also discuss some key ideas of how to reduce the number of discrete speeds in three-dimensional simulations by pruning of the higher-order lattices, and introduce a new construction of the corresponding guided equilibrium by entropy minimization.

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As a sound transmitting device based on the nonlinear acoustic theory, parametric acoustic array (PAA) is able to generate high directivity and low frequency broadband signals with a small aperture transducer. Due to its predominant technical advantages, PAA has been widely used in a variety of application scenarios of underwater acoustic engineering, such as sub-bottom profile measurement, underwater acoustic communication, and detection of buried targets. In this review paper, we examine some of the important advances in the PAA since it was first proposed by Westervelt in 1963. These advances include theoretical modelling for the PAA, signal processing methods, design considerations and implementation issues, and applications of the PAA in underwater acoustic engineering. Moreover, we highlight some technical challenges which impede further development of the PAA, and correspondingly give a glimpse on its possible extension in the future. This article provides a comprehensive overview of some important works of the PAA and serves as a quick tutorial reference to readers who are interested to further explore and extend this technology, and bring this technology to other application areas.

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Tube/Pipe (TP) 304 stainless steel has been widely used in industry, but a change in its microstructures may endanger its service safety, and it is essential to evaluate its microstructural evolution. In this work, a pulse-echo nonlinear method is proposed to characterize the microstructural evolution of the TP304 stainless steel. The detailed pulse-echo nonlinear experimental process is presented, and it is shown that the absolute nonlinear parameter can be determined when the effect of attenuation is taken into account. The microstructural evolution of TP304 stainless steel is artificially controlled by annealing treatments before it is evaluated by using nonlinear ultrasonic method and metallographic method. The results show that the grain sizes increase as the annealing time increases, which leads to the performance degradation of the TP304 steel and an increase in the nonlinear parameters, with the reason discussed considering the variation in the microstructure. The present pulse-echo nonlinear method is easier to conduct than the traditional transmission-through method and the absolute nonlinear parameter can be determined for quantitative characterization. The variation in determined nonlinear parameters provides a reference to evaluate the microstructural evolution of TP304 stainless steel.

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We present a model developed for studying the generation of stable cavitation bubbles and their motion in a three-dimensional volume of liquid with axial symmetry under the effect of finite-amplitude phased array focused ultrasound. The density of bubbles per unit volume is determined by a nonlinear law which is a threshold-dependent function of the negative acoustic pressure reached in the liquid, in which nuclei are initially distributed. The nonlinear mutual interaction of ultrasound and bubble oscillations is modeled by a nonlinear coupled differential system formed by the wave and a Rayleigh-Plesset equations, for which both the pressure and the bubble oscillation variables are unknown. The system, which accounts for nonlinearity, dispersion, and attenuation due to the bubbles, is solved by numerical approximations. The nonlinear acoustic pressure field is then used to evaluate the primary Bjerknes force field and to predict the subsequent motion of bubbles. In order to illustrate the procedure, a medium-high and a low ultrasonic frequency configurations are assumed. Simulation results show where bubbles are generated, the nonlinear effects they have on ultrasound, and where they are relocated. Despite many physical restrictions and thanks to its particularities (two nonlinear coupled fields, bubble generation, bubble motion), the numerical model used in this work gives results that show qualitative coherence with data observed experimentally in the framework of stable cavitation and suggest their usefulness in some application contexts.

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Techniques based on ultrasound in nondestructive testing and medical imaging analyze the response of the source frequencies (linear theory) or the second-order frequencies such as higher harmonics, difference and sum frequencies (nonlinear theory). The low attenuation and high directivity of the difference-frequency component generated nonlinearly by parametric arrays are useful. Higher harmonics created directly from a single-frequency source and the sum-frequency component generated nonlinearly by parametric arrays are attractive because of their high spatial resolution and accuracy. The nonlinear response of bubbly liquids can be strong even at relatively low acoustic pressure amplitudes. Thus, these nonlinear frequencies can be generated easily in these media. Since the experimental study of such nonlinear waves in stable bubbly liquids is a very difficult task, in this work we use a numerical model developed previously to describe the nonlinear propagation of ultrasound interacting with nonlinearly oscillating bubbles in a liquid. This numerical model solves a differential system coupling a Rayleigh-Plesset equation and the wave equation. This paper performs an analysis of the generation of the sum-frequency component by nonlinear mixing of two signals of lower frequencies. It shows that the amplitude of this component can be maximized by taking into account the nonlinear resonance of the system. This effect is due to the softening of the medium when pressure amplitudes rise.

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The acoustic streaming behaviour below an ultrasonic sonotrode in water was predicted by numerical simulation and validated by experimental studies. The flow was calculated by solving the transient Reynolds-Averaged Navier-Stokes equations with a source term representing ultrasonic excitation implemented from the predictions of a nonlinear acoustic model. Comparisons with the measured flow field from Particle Image Velocimetry (PIV) water experiments revealed good agreement in both velocity magnitude and direction at two power settings, supporting the validity of the model for acoustic streaming in the presence of cavitating bubbles. Turbulent features measured by PIV were also recovered by the model. The model was then applied to the technologically important area of ultrasonic treatment of liquid aluminium, to achieve the prediction of acoustic streaming for the very first time that accounts for nonlinear pressure propagation in the presence of acoustic cavitation in the melt. Simulations show a strong dependence of the acoustic streaming flow direction on the cavitating bubble volume fraction, reflecting PIV observations. This has implications for the technological use of ultrasound in liquid metal processing.

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Nonlinear constitutive mechanical parameters, predominantly governed by micro-damage, interact with ultrasound to generate harmonics that are not present in the excitation. In principle, this phenomenon therefore permits early stage damage identification if these higher harmonics can be measured. To understand the underlying mechanism of harmonic generation, a nonlinear micro-mechanical approach is proposed here, that relates a distribution of clapping micro-cracks to the measurable macroscopic acoustic nonlinearity by representing the crack as an effective inclusion with Landau type nonlinearity at small strain. The clapping mechanism inside each micro-crack is represented by a Taylor expansion of the stress-strain constitutive law, whereby nonlinear terms arise. The micro-cracks are considered distributed in a macroscopic medium and the effective nonlinearity parameter associated with compression is determined via a nonlinear Mori-Tanaka homogenization theory. Relationships are thus obtained between the measurable acoustic nonlinearity and the Landau-type nonlinearity. The framework developed therefore yields links with nonlinear ultrasound, where the dependency of measurable acoustic nonlinearity is, under certain hypotheses, formally related to the density of micro-cracks and the bulk material properties.

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Omnidirectional sound sources are needed to perform a large variety of tests in acoustics. Typically, they consist of conventional speaker drivers arranged in a dodecahedron. However, the directivity of the speaker drivers sharpens with frequency, which induces an intense decrease of the sound pressure levels at the edges of the dodechaedron. In this work, the problem is mitigated by building an Omnidirectional Parametric Loudspeaker (OPL), which contains hundreds of small ultrasound transducers set on a sphere. Each transducer emits an ultrasonic carrier wave modulated by an audible signal. Thanks to nonlinear propagation, the air itself demodulates the signal bringing it back to the audible range. The construction of an OPL prototype is challenging. The structure has been built by 3D-printing a set of pieces that conform to the sphere. Each piece contains the exact location of the transducers, which are aligned in parallels to facilitate the structural assembly and the wiring. The performance of the OPL has been tested in an anechoic chamber. Measurements show that the OPL has a good omnidirectional behavior for most frequencies. It clearly improves the directivity of dodechaedral sources in the high frequency range, but performs worse at low frequencies.

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The relative dislocation density of aluminum and copper samples is quantitatively measured using linear Resonant Ultrasound Spectroscopy (RUS). For each metallic group, four samples were prepared with different thermomechanical treatments in order to induce changes in their dislocation densities. The RUS results are compared with Nonlinear Resonant Ultrasound Spectroscopy (NRUS) as well as Second Harmonic Generation (SHG) measurements. NRUS has a higher sensitivity by a factor of two to six and SHG by 14⁻62%. The latter technique is, however, faster and simpler. As a main result, we obtain a quantitative relation between the changes in the nonlinear parameters and the dislocation density variations, which in a first approximation is a linear relation between these differences. We also present a simple theoretical expression that explains the better sensitivity to dislocation content of the nonlinear parameters with respect to the linear ones. X-Ray diffraction measurements, although intrusive and less accurate, support the acoustics results.

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Nerve impulses, previously proposed as manifestations of nonlinear acoustic pulses localized at the plasma membrane, can annihilate upon collision. However, whether annihilation of acoustic waves at interfaces takes place is unclear. We previously showed the propagation of nonlinear sound waves that propagate as solitary waves above a threshold (super-threshold) excitation in a lipid monolayer near a phase transition. Here we investigate the interaction of these waves. Sound waves were excited mechanically via a piezo cantilever in a lipid monolayer at the air-water interface and their amplitude is reported before and after a collision. The compression amplitude was observed via Förster resonance energy transfer between donor and acceptor dyes, measured at fixed points along the propagation path in the lipid monolayer. We provide direct experimental evidence for the annihilation of two super-threshold interfacial pulses upon head-on collision in a lipid monolayer and conclude that sound waves propagating in a lipid interface can interact linearly, nonlinearly, or annihilate upon collision depending on the state of the system. Thus we show that the main characteristics of nerve impulses, i.e. solitary character, velocity, couplings, all-or-none behaviour, threshold and even annihilation are also demonstrated by nonlinear sound waves in a lipid monolayer, where they follow directly from the thermodynamic principles applied to an interface. As these principles are equally unavoidable in a nerve membrane, our observations strongly suggest that the underlying physical basis of action potentials and the observed nonlinear-pules is identical.

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