Nonlinear shear wave interaction in soft solids

This paper describes nonlinear shear wave experiments conducted in soft solids with transient elastography technique. The nonlinear solutions that theoretically account for plane and nonplane shear wave propagation are compared with experimental results. It is observed that the cubic nonlinearity implied in high amplitude transverse waves at f(0)=100 Hz results in the generation of odd harmonics 3f(0), 5f(0). In the case of the nonlinear interaction between two transverse waves at frequencies f(1) and f(2), the resulting harmonics are f(i)+/-2f(j)(i,j=1,2). Experimental data are compared to numerical solutions of the modified Burgers equation, allowing an estimation of the nonlinear parameter relative to shear waves. The definition of this combination of elastic moduli (up to fourth order) can be obtained using an energy development adapted to soft solid. In the more complex situation of nonplane shear waves, the quadratic nonlinearity gives rise to more usual harmonics, at sum and difference frequencies, f(i)+/-f(j). All components of the field have to be taken into account.     

Simulation of frictional energy dissipation in a fiber contact subjected to normal and tangential oscillation

This paper presents a numerical study on the frictional contact between two crossed fibers subject to both normal and tangential oscillation. The results from simulation using the method of dimensionality reduction show that the frictional energy dissipation increases firstly with coefficient of friction, and then almost symmetrically decreases to a constant. The fiber aspect ratio has an important effect on the energy dissipation and this effect becomes more significant for larger coefficient of friction. The simulation results for very large coefficient of friction show a good agreement with the analytical solution for the case of infinite coefficient of friction.     

Nonlinear acoustic wave generation in a three-phase seabed

Generation of an acoustic wave by two pump sound waves is studied in a three-phase marine sediment, which consists of a solid frame and the pore water with air bubbles in it. To avoid shock-wave formation, the interaction is considered in the frequency range where there is a significant sound velocity dispersion. Nonlinear equations are obtained to describe the interaction of acoustic waves in the presence of air bubbles. An expression for the amplitude of the generated wave is obtained and numerical analysis of its dependence on distance and resonance frequency of bubbles is performed.     

Nonlinear dynamics of an interface between shear bands

We study numerically the nonlinear dynamics of a shear banding interface in two-dimensional planar shear flow, within the nonlocal Johnson-Segalman model. Consistent with a recent linear stability analysis, we find that an initially flat interface is unstable with respect to small undulations for a sufficiently small ratio of the interfacial width l to cell length L(x). The instability saturates in finite amplitude interfacial fluctuations. For decreasing l/L(x) these undergo a nonequilibrium transition from simple traveling interfacial waves with constant average wall stress, to periodically rippling waves with a periodic stress response. When multiple shear bands are present we find erratic interfacial dynamics and a stress response suggesting low dimensional chaos.     

固体粗糙界面与超声的非线性相互作用研究

本文提出了一种随机弹性接触界面与超声的非线性相互作用理论. 首先建立了描述随机弹性接触界面的模型, 然后分别研究了界面间应力-应变关系在线性简化模型、指数模型、高斯模型下与超声的非线性相互作用. 数值仿真和实验研究结果均表明高斯模型更适合描述固体接触界面. 本文在介观结构上解释了固体界面与超声的相互作用, 对工业超声无损检测裂缝、缺陷及损伤有指导意义. 关键词： 超声无损检测 固体粗糙界面 非线性效应     

Nonlinear equations for a slow magnetogasdynamic quasi-monochromatic wave in a medium with dispersion and dissipation

Evolutionary equations are obtained in the vicinity of a singularity for a slow wave with allowance for the quadratic nonlinearity, dispersion, and dissipation. It is demonstrated that the propagation of quasi-monochromatic waves in a current-conducting gas—liquid mixture is described by ordinary differential equations for the amplitudes in the aforementioned region.     

Generation of higher acoustic harmonics at a flat rough interface between two solids

The results of experimental studies of the influence of a static pressure applied to a flat rough interface between two solids on its nonlinear elastic properties are presented. The studies were performed by the spectral method on the basis of an analysis of the efficiency of generation of higher acoustic harmonics, which arise upon the reflection of a longitudinal elastic wave of finite amplitude from the boundary and the passage through it. A nonmonotonic dependence of the amplitudes of acoustic harmonics on the value of the external reversible static pressure applied to the interface was revealed: pronounced amplitude maxima for the amplitudes of the second and third harmonics were observed with a decrease in the external static pressure. It was also found that the amplitudes of the second, third, and fourth acoustic harmonics increase with a decrease in the external static pressure (in comparison with their values at the same pressure values during its increase). The experimentally determined power dependence of the higher acoustic harmonics on the amplitude of the first acoustic harmonic significantly differed from the classical indices for these harmonics. The influence of the external pressure on the values of the nonlinear second- and third-order elastic parameters was analyzed. The experimental results were analyzed on the basis of nonclassical acoustic nonlinearity.     

Analysis of nonlinear beam-wave interaction of gyro-peniotron at harmonics

An analysis of the nonlinear beam-wave interaction of the gyro-peniotron at high harmonic is presented in this paper. It bases on a ballistic large-signal theory of the gyropeniotron assuming a given RF field distribution in the resonator. The proposed method is applicable to arbitrary harmonic numbers and to arbitrary TE modes. Analytical results of its operational characteristics are given using computer simulations. E. g. an efficiency of 45% for the third harmonic has been calculated. The results show that the gyro-peniotron could be potentially a high efficiency, high power millimeter-wave device at a low magnetic field.     

Reflected and transmitted second harmonics generation by an obliquely p-polarized laser pulse incident on a vacuum-plasma interface

The theoretical investigation is developed for the phenomenon of second-harmonic (SH) generation by a p-polarized laser pulse at oblique incidence on a vacuum-plasma interface. We considered the simultaneous SH generation inside the plasma as well as vacuum due to the reflected component of the laser pulse. The results approved that the SH conversion efficiency drastically increases, for both transmitted and reflected components, when the incident angle approaches to its critical value. We found that the maximum SH efficiency is greater for transmitted component, however, the reflected component is more proper for technical and experimental applications.     

Resonant absorption of shear instabilities in flow systems with energy dissipation

It is shown that hydrodynamic and electrohydrodynamic waves excited in two-layer dissipative systems due to shear instabilities experience resonant absorption of two types: at the rotational frequency of particles of the medium and the frequency of their collision with the lattice.     

Few-cycle-driven XUV laser harmonics: generation and focusing

We have investigated the use of sub-10-fs near-infrared laser pulses to generate high-order harmonic radiation efficiently in the wavelength region between 30 to 10 nm. The ultrashort rise time of the driver pulses allows harmonics to be produced at low ionization levels and hence to grow coherently over propagation lengths becoming comparable to the XUV absorption lengths in the noble gas medium. As a result, absorption-limited harmonic generation has been extended to the 10-nm range for the first time. Harmonic conversion efficiencies of (3-4)᎒^ъ in the range of 10-13 nm in neon and some two orders of magnitude higher at around 30 nm in argon have been obtained in simple gas tube targets under these conditions. Preliminary focusing tests with 13-nm harmonic radiation have been carried out with a specially designed zoneplate and a spherical Mo/Si multilayer mirror and have resulted in spot sizes of about 2 microns. Our experiments aim at paving the way to nonlinear optics in the soft-X-ray regime.     

A generalized approach to beam wave interaction with a dielectric interface

New phenomena have been reported recently in connection with Gaussian beam interaction with a plane dielectric interface, namely, the deterioration of the reflected and refracted beams from shapes predicted by geometric optics, and the generation of higherorder components that cause angular beam deflection. Any bounded, symmetric beam, which is not necessarily Gaussian, can be comprised in terms of an angular spectrum of plane waves. Utilizing such a modal expansion, a model of the interaction process that seems to point out the generality of the phenomena involved for bounded symmetrical beams with any cross-section is presented. The procedure is applied to a Cauchy profile, and analytical results are given. Comparison with previous results obtained for the Gaussian beam and careful examination of the respective spectral functions demonstrate close correspondence between the results. This adds credence to the general approach presented here which can be applied to bounded symmetrical beams of general shape.     

Nonlinear interaction of acoustic emission pulses with a harmonic test wave

Phase modulation of weak, high-frequency, monochromatic waves interacting with strong pulsed signals is investigated. Some estimates are obtained for the interaction between the acoustic emission pulses caused by the crack formation in the Arctic ice cover and a high-frequency test wave.     

Nonlinear shift of spatial solitons at a graded dielectric interface

We investigate total internal reflection of optical spatial solitons at the interface between two regions of nematic liquid crystals with different optical densities. Due to nonlinear molecular reorientation, the solitons experience a penetration depth, hence, a lateral shift that depends on the excitation, with lateral shifts from 0.7 to 1.2 mm as input powers increased from 1.6 to 9.3 mW.