Beam breakup and modulational instability in a bulk type I quadratic medium

The effect of a small modulation superimposed on a strip (1D) solitary wave propagating in a bulk quadratic medium was investigated both analytically and numerically near Type I phase matching. General, exact results were obtained. By using first order perturbation theory, we obtained the gain coefficient for the modulational instability and the modulation cut-off frequency and we investigated their dependence on various beam and material parameters. The wave evolves into a clean periodic sequence of solitary waves and does not reproduce the incident beam. We showed that the beam breakup observed experimentally is due entirely to noise induced modulational instability.     

The influence of external tensile stress on surface elastic waves on piezoelectric ceramic plates

Experimental results on the output voltage via a propagating surface elastic wave and the convolution output of two oppositely propagating surface elastic waves on a piezoelectric ceramic plate are described as a function of external tensile stress. The convolution output increases with the cummulative load, while the output voltage via the surface elastic wave decreases. The variation of the output voltage is considered to be due to the change in nonlinearity that arises from the external load.     

Pulse dynamics in an optical fiber with linear intermode coupling and Kerr nonlinearity dispersion

The effect of Kerr nonlinearity dispersion on the envelope duration and the velocity of the envelope maximum for a wave packet propagating in an optical fiber and formed by two coupled copropagating waves is studied. The critical (threshold) energy of wave packet collapse can substantially be diminished and the supraluminal mode of propagation of the pulse envelope maximum in a nonamplifying medium can be realized owing to a significantly higher nonlinearity dispersion in such systems in comparison with “single-wave” ones.     

Random generation of coherent solitary waves from incoherent waves

The random generation of coherent solitary waves from incoherent waves in a medium with an instantaneous nonlinearity has been observed. One excites a propagating incoherent spin wave packet in a magnetic film strip and observes the random appearance of solitary wave pulses. These pulses are as coherent as traditional solitary waves, but with random timing and a random peak amplitude.     

Two-dimensional wave propagation in a rotating elastic solid with voids

Two-dimensional wave propagation is studied in an isothermal linear isotropic elastic material with voids rotating with constant angular velocity based on a theory of elastic material with voids developed by Ie?an (1986) in the thermoelastic context. It is found that there exist three coupled plane waves propagating with distinct phase speeds. The presence of voids and the rotation of the medium are responsible for this coupling. In the absence of voids, the classical longitudinal and transverse waves are found to be coupled through the rotation of the medium. At very large frequency or when the angular rotation is very small relative to the wave frequency the waves are decoupled and propagate with distinct phase speeds. These are (i) a longitudinal wave, (ii) a transverse wave and (iii) a longitudinal wave corresponding to the change in void volume fraction. The first two correspond to the waves of classical elasticity, while the third is new and arises from the presence of the voids. The results are illustrated graphically.     

Bending wave propagation of carbon nanotubes in a bi-parameter elastic matrix

This article studies transverse waves propagating in carbon nanotubes (CNTs) embedded in a surrounding medium. The CNTs are modeled as a nonlocal elastic beam, whereas the surrounding medium is modeled as a bi-parameter elastic medium. When taking into account the effect of rotary inertia of cross-section, a governing equation is acquired. A comparison of wave speeds using the Rayleigh and Euler-Bernoulli theories of beams with the results of molecular dynamics simulation indicates that the nonlocal Rayleigh beam model is more adequate to describe flexural waves in CNTs than the nonlocal Euler-Bernoulli model. The influences of the surrounding medium and rotary inertia on the phase speed for single-walled and double-walled CNTs are analyzed. Obtained results turn out that the surrounding medium plays a dominant role for lower wave numbers, while rotary inertia strongly affects the phase speed for higher wave numbers.     

Experimental study of nonlinear acoustic effects in a granular medium

Results of a series of experimental studies of nonlinear acoustic effects in a granular medium are presented. Different effects observed in the experiments simultaneously testify that the nonlinearity of granular media is governed by the weakest intergrain contacts. The behavior of the observed dependences suggests that the distribution function of contact forces strongly increases in the range of forces much smaller than the mean force value, which is inaccessible for conventional experimental measuring techniques. For shear waves in a granular medium, the effects of demodulation and second harmonic generation with conversion to longitudinal waves are studied. These effects are caused by the nonlinear dilatancy of the medium, i.e., by the nonlinear law of its volume variation in the shear stress field. With the use of shear waves of different polarizations, the anisotropy of the nonlinearity of the medium is demonstrated. The observation of the cross-modulation effect shows that the nonlinearity-induced modulation components of the probe wave are much more sensitive to weak nonstationary perturbations of the medium, as compared to the linearly propagating fundamental harmonic. The nonlinear effects under study offer promise for diagnostic applications in laboratory measurements and in seismic monitoring systems.     

Axisymmetric Nonlinear Modulated Waves in a Cylindrical Shell

A quasi-hyperbolic equation is derived that simulates the axisymmetric propagation of bending waves in a cylindrical shell, which interacts with a nonlinearly elastic medium. With the correct asymptotic procedure, the study of a wave process reduces to analysis of a nonlinear Schrödinger equation. It is established that the development of modulation instability requires a “soft” nonlinearity of the medium surrounding the shell. Operating modes that allow the propagation of stable light envelope solitons are revealed.     

Impulsive fracture of silicon by elastic surface pulses with shocks

During nonlinear evolution of surface acoustic waves (SAWs) stress increases with propagation, and may cause fracture of brittle materials. This effect was used to evaluate the strength of crystalline silicon with respect to impulsive load in the nanosecond time scale without using seed cracks. Short SAW pulses propagating in the [11(macro)2] direction on the Si(111) plane induce fracture at significantly lower SAW amplitudes than the mirror symmetric wave propagating in the [112(macro)] direction. This effect is explained by the differences in elastic nonlinearity of the two propagation directions.     

Rayleigh wave propagation along the boundary of a non-Newtonian fluid-saturated porous medium

The Frenkel-Biot theory is used to study the reflection of elastic waves from the boundary of a non-Newtonian (Maxwell) fluid-saturated porous medium. The velocity and attenuation of a Rayleigh surface wave propagating along the boundary of the medium are determined. Two models of a fluid-saturated porous medium are used for calculation: with pore channels of a fixed diameter and with a lognormal distribution of pore channels in size. The results of calculations show that, when the fluid in the porous medium is characterized by a small Deborah number (i.e., exhibits non-Newtonian properties), the velocity of Rayleigh waves exhibits a considerable frequency dispersion. The results also suggest that, in principle, it is possible to estimate the Deborah number from the measured frequency dispersion of the Rayleigh wave velocity.     

Numerical simulations of random sound waves

We perform one-dimensional numerical simulations of both driven and impulsively generated sound waves propagating through a medium whose mass density admits time-independent, random fluctuations. While the amplitude of both types of wave is always attenuated, driven sound waves can be either retarded or speeded up depending on their wavenumber and amplitude and on the strength of the random field. The speed of a pulse propagating in the random medium is also altered, in agreement with the findings for the driven waves. The concomitant action of nonlinearity and randomness results in wave speeding for wavenumbers which are of the order of the size of an average random density fluctuation, whereas it gives retardation for larger wavenumbers.     

基于Biot-喷射流统一模型Maxwell流体饱和孔隙介质中的弹性波

推广Biot-Tsiklauri声学模型的同时借鉴Dvorkin和Nur的工作,建立了具有任意孔径分布并顾及喷射流动机制的非牛顿流体饱和孔隙介质声学模型,研究了非牛顿流体(Maxwell流体)饱和孔隙介质中的弹性波的衰减和频散特性.着重讨论充孔隙Maxwell流体的非牛顿流效应对弹性波的频散和衰减的影响.研究表明,饱和流体的非牛顿流效应和喷射流动机制均是引起弹性波波频散和衰减的重要因素.依据非牛顿流体(Maxwell流体)饱和各向同性孔隙介质的Biot-喷射流声学模型,喷射流动只影响纵波的频散和衰减,而饱和流体的非牛顿流效应不仅影响纵波,而且还影响横波的频散和衰减.     

Rayleigh wave at the boundary of an inhomogeneous nonlinear viscoelastic half-space

In the approximation of weak nonlinearity and weak viscosity of the medium, we obtain an equation describing the spectral density of the particle horizontal velocity for a Rayleigh wave propagating along the boundary of a half-space. The coefficients of nonlinear interaction between the wave harmonics are found on the assumption that the third-order elastic moduli arbitrarily depend on the depth. We find expressions for the complex correction to the wave frequency due to small relaxation corrections to the elastic moduli and small variations in the medium density, which arbitrarily depend on the depth as well. The imaginary part of this correction to the frequency determines the decay of the linear Rayleigh wave due to small relaxation corrections to the elastic moduli arbitrarily dependent on the depth. Using numerical simulation (with allowance for the interaction of 500 harmonics), we study distortions of an initially harmonic Rayleigh wave for a particular dependence of variations in the nonlinear moduli on the depth. An integral equation is derived for the nonlinear elastic moduli as functions of the depth. It is shown that for independent spatio-temporal distributions of the viscous moduli, functions determining the dependence of the viscosity on the depth are described by an analogous integral equation. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 50, No. 3, pp. 212–226, March 2007.     

Resonant excitation and nonlinear evolution of waves in the equatorial waveguide in the presence of the mean current

We study interactions of planetary waves propagating across the equator with trapped Rossby or Yanai modes, and the mean flow. The equatorial waveguide with a mean current acts as a resonator and responds to planetary waves with certain wave numbers by making the trapped modes grow. Thus excited waves reach amplitudes greatly exceeding the amplitude of the incoming wave. Nonlinear saturation of the excited waves is described by an amplitude equation with one or two attracting equilibrium solutions. In the latter case spatial modulation leads to formation of characteristic defects in the wave field. The evolution of the envelopes of long trapped Rossby waves is governed by the driven complex Ginzburg-Landau equation, and by the damped-driven nonlinear Schr?dinger equation for short waves. The envelopes of the Yanai waves obey a simple wave equation with cubic nonlinearity.     

Theoretical studies on frequency doubling in glass optical fibers in constant-intensity approximation

Theoretical consideration of the second harmonic generation in the constant-intensity approximation with account of the inverse effect of the excited wave on a stimulation wave through account of the phase change of interaction waves is presented. The behavior of harmonic wave intensity in a fiber for different parameters of the problem has been studied, the self-action of the light both in glass optical fiber and inside the homogeneous medium has been analyzed. In this approximation a decrease of conversion efficiency and a change of parameters of the curves of synchronism versus the pump intensity, in particular, the change of positions of intensity minima that does not take place in the constant-field approximation, are observed. The propagation of a plane wave packet in the homogeneous medium with quadratic nonlinearity and in an optical fiber accompanied by the self-phase modulation and leading to the change of the Gaussian pulse spectrum is analyzed with account of the phase changes of all the interacting waves.     

Modulation instability of wave packets in the presence of linear and nonlinear mode coupling

Conditions for modulation instability of a wave packet consisting of two codirected linearly coupled waves propagating in a light guide with Kerr-type nonlinearity are formulated. The development of the instability with regard to light guide parameters, linear and nonlinear mode coupling, and input power is analyzed for symmetric and antisymmetric light guide excitations. Unlike in single-mode light guides, here modulation instability may arise in the frequency ranges of normal material dispersion and at the zero perturbation frequency.     

Radiation of caustic beams from a collapsing bullet

We show both theoretically and experimentally that a collapsing (2+1)-dimensional wave packet in a medium with cubic nonlinearity and a two-dimensional dispersion of an order higher than parabolic irradiates untrapped dispersive waves. The studies are performed for a spin-wave bullet propagating in an in-plane magnetized ferrimagnetic film. An induced uniaxial anisotropy in such a medium leads to the formation of narrow spin-wave caustic beams whose angles to the bullet's propagation direction are modified by the motion of the source.     

Localization of a transverse elastic wave in a semibounded acoustic superlattice of ferrimagnetic and superconducting layers: 3. Leaky surface modes and associated resonances

In terms of the effective medium method, conditions for the existence of leaky shear surface acoustic waves in a semibounded fine-layered magnetic superlattice consisting of ferrimagnetic and superconducting layers are determined. On this basis, the possibility of a resonance interaction between a surface elastic SH wave propagating in the magnetic superlattice and a shear bulk wave propagating in the adjacent nonmagnetic medium is investigated.     

Specificity of the phenomenon of acoustoelasticity in a two-dimensional internally structured medium

A two-dimensional model of a microstructured medium is considered in the form of a square lattice consisting of elastically interacting circular particles with translational and rotational degrees of freedom. The interactions between the particles are modeled by a set of elastic springs. Differential equations are derived to describe the propagation and interaction of acoustic waves in such a medium. The relation between the velocities of wave propagation and the small strain arising in the structure under external action is determined. Analytical expressions that determine the difference between the squares of the velocities of both longitudinal and shear waves propagating in two mutually perpendicular directions in a medium with an externally induced anisotropy are derived and analyzed.     

Interaction of acoustic waves with polycrystals

We analyze theoretically the structure of the field created in a semi-infinite polycrystal by an acoustic wave, coming from an isotropic homogeneous medium and incident normally onto its surface. The elastic anisotropy of the polycrystal is supposed to be small, and the perturbation theory is applied. It is shown that the effective medium approach is not valid. In addition to the transmitted wave propagating in the polycrystal with an effective sound speed, there is one more bulk wave, whose amplitude decreases at a distance of the order of the mean size of the grain from the interface. The structure of the reflected wave is the same as when reflecting from an isotropic solid. However, the relation between the amplitudes of reflected and transmitted waves differs from that in an isotropic solid.