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In this paper, the sparse direct adaptive equalization based on the recently developed proportionate recursive least squares (PRLS) adaptive filtering algorithm is investigated for multiple-input multiple-output (MIMO) underwater acoustic (UWA) communications. First, performance analysis is made for the PRLS, and simulation results show its gain over a standard recursive least squares algorithm under sparse systems. The fast implementation of the PRLS, named the proportionate stable fast transversal filters (PSFTF), is revisited to implement a direct adaptive decision-feedback equalizer which outperforms the existing PSFTF direct adaptive linear equalizer. The PSFTF direct adaptive equalizers (DAEs) are then compared with the selective zero-attracting stable fast transversal filter DAEs (SZA-SFTF-DAEs) enabled by the SZA-SFTF adaptive filtering algorithm. The SZA-SFTF algorithm is designed with the zero-attracting sparsity-promoting principle, which is in parallel to the proportionate updating principle used to design the PSFTF algorithm. Experimental results of an at-sea MIMO UWA communication trial show that PSFTF-DAEs outperform the SZA-SFTF-DAEs.This paper studies the interactions of two plane waves in elastic solids with quadratic nonlinearity. In particular, the necessary and sufficient conditions for resonant mixing of two plane waves are derived. It is shown that the conventional resonance condition for resonant mixing of plane waves is only a necessary condition, not sufficient. Based on the newly derived necessary and sufficient conditions, resonant mixing of various types of plane waves are investigated and specific conditions for generating a resonant mixed wave are obtained for each case. These results are useful for developing nonlinear ultrasonic nondestructive evaluation techniques using the wave mixing method.The paper describes the beamforming procedures in an acoustic waveguide based on representing the field on the antenna as a superposition of several stable components formed by narrow beams of rays [A. L. Virovlyansky, J. Acoust. Soc. Am. 141, 1180-1189 (2017)]. A modification of the matched field processing method is proposed, based on the transition from comparing the measured and calculated fields on the antenna to comparing their stable components. The modified approach becomes less sensitive to the inevitable inaccuracies of the environmental model. In the case of a pulsed source, the stable components carry signals whose arrival times can be taken as input parameters in solving the inverse problems. The use of the stable components as the initial fields on the aperture of the emitting antenna makes it possible to excite narrow continuous wave beams propagating along given ray paths.Considered herein is a small wedge-shaped block that contacts a rough surface on its angled face, with contact maintained by precompressed springs. The wedge is connected to a large mass that is subjected to a harmonic excitation. Sacituzumab govitecan concentration begins with a derivation of equations for the normal and friction forces, which are shown to depend on the displacement and acceleration of the wedge as well as the external force. Enforcing Coulomb's law for sliding leads to a differential equation of motion in which the effective inertia and stiffness coefficients switch values according to whether the wedge advances or retreats. Algebraic expressions for the displacement in either state are supplemented by an assessment of sticking based on Coulomb's static friction rule. The solutions for motion and the assessment of sticking are assembled in a simple, yet general, algorithm that only requires calculation of algebraic formulas. Transient waveforms of displacement, acceleration, and transmitted force are calculated for a harmonic excitation at the natural frequency of the frictionless system. It is found that very large viscous damping ratios would be required to obtain the same steady-state amplitude.Three-dimensional finite element (FE) modelling, with representation of materials at grain scale in realistic sample volumes, is capable of accurately describing elastic wave propagation and scattering within polycrystals. A broader and better future use of this FE method requires several important topics to be fully understood, and this work presents studies addressing this aim. #link# The first topic concerns the determination of effective media parameters, namely, scattering induced attenuation and phase velocity, from measured coherent waves. This work evaluates two determination approaches, through-transmission and fitting, and it is found that these approaches are practically equivalent and can thus be used interchangeably. For the second topic of estimating modelling errors and uncertainties, this work performs thorough analytical and numerical studies to estimate those caused by both FE approximations and statistical considerations. It is demonstrated that the errors and uncertainties can be well suppressed by using a proper combination of modelling parameters. For the last topic of incorporating FE model information into theoretical models, this work presents elaborated investigations and shows that to improve agreement between the FE and theoretical models, the symmetry boundary conditions used in FE models need to be considered in the two-point correlation function, which is required by theoretical models.The second-harmonic generation of the fundamental antisymmetric Lamb wave at a closed parallel crack in an elastic plate is studied by numerical analysis. The closed crack is modeled as a spring-type interface with quadratic nonlinearity. Based on a perturbation method, the problem of nonlinear Lamb wave scattering is decomposed into two linearized problems, i.e., for the linear reflection/transmission of the incident Lamb wave at the crack and for the generation/radiation of the second-harmonic Lamb waves due to the contact nonlinearity. The reduced problems are solved by the finite element method in the frequency domain. Numerical results demonstrate significant effects of the crack resonance on the linear and nonlinear Lamb wave scattering responses, which appear as sharp peaks/dips in the reflection/transmission spectra and enhanced second-harmonic amplitudes at some frequencies. Two simple frequency selection rules are established which explain the enhanced generation of the second-harmonic Lamb waves. The time-domain analysis is also carried out to supplement the frequency-domain analysis, which confirms that the incident Lamb wave interacts with the crack at some specific frequencies in its bandwidth in a selective manner and enhances the generation of the second-harmonic components.