Breaking of stationary waves in nonlinear dispersive media

A nontrivial behaviour of a nonlinear wave under influence of small disturbing factors like dissipation, smooth inhomogeneity of medium parameters, etc. is considered by the example of sine-Gordon equation. The stage of slow “adiabatic” variation of the parameters of quasi-stationary wave is shown to change at some finite distance due to strong instability. The wave form becomes essentially nonstationary (breaking of stationary wave structure). The breaking condition is defined by the extremum of the wave adiabatic invariant. The behaviour of a wave at the nonadiabatic stage is described using a Galerkin procedure.     

Ultrasonic wave propagation in human cancellous bone: application of Biot theory

Ultrasonic wave propagation in human cancellous bone is considered. Reflection and transmission coefficients are derived for a slab of cancellous bone having an elastic frame using Biot's theory modified by the model of Johnson et al. [J. Fluid Mech. 176, 379-402 (1987)] for viscous exchange between fluid and structure. Numerical simulations of transmitted waves in the time domain are worked out by varying the modified Biot parameters. The variation is applied to the governing parameters and is about 20%. From this study, we can gain an insight into the sensitivity of each physical parameter used in this theory. Some parameters play an important role in slow-wave wave form, such as the viscous characteristic length lambda and pore fluid bulk modulus Kf. However, other parameters play an important role in the fast-wave wave form, such as solid density rhos and shear modulus N. We also note from these simulations that some parameters such as porosity phi, tortuosity alpha(infinty), thickness, solid bulk modulus Ks, and skeletal compressibility frame Kb, play an important role simultaneously in both fast and slow wave forms compared to other parameters which act on the wave form of just one of the two waves. The sensitivity of the modified Biot parameters with respect to the transmitted wave depends strongly on the coupling between the solid and fluid phases of the cancellous bone. Experimental results for slow and fast waves transmitted through human cancellous bone samples are given and compared with theoretical predictions.     

Inverse problems in cancellous bone: estimation of the ultrasonic properties of fast and slow waves using Bayesian probability theory

Quantitative ultrasonic characterization of cancellous bone can be complicated by artifacts introduced by analyzing acquired data consisting of two propagating waves (a fast wave and a slow wave) as if only one wave were present. Recovering the ultrasonic properties of overlapping fast and slow waves could therefore lead to enhancement of bone quality assessment. The current study uses Bayesian probability theory to estimate phase velocity and normalized broadband ultrasonic attenuation (nBUA) parameters in a model of fast and slow wave propagation. Calculations are carried out using Markov chain Monte Carlo with simulated annealing to approximate the marginal posterior probability densities for parameters in the model. The technique is applied to simulated data, to data acquired on two phantoms capable of generating two waves in acquired signals, and to data acquired on a human femur condyle specimen. The models are in good agreement with both the simulated and experimental data, and the values of the estimated ultrasonic parameters fall within expected ranges.     

Features of nonlinear wave propagation in a layer of a granular medium

Computer simulation was performed to study compression wave propagation in a granular medium in a gravity field. It is shown that in a layer with spherical granules, periodic wave structures can be formed and their parameters depend on the granule size and layer thickness. If the layer is compressed, the wave structures fail to emerge and wave attenuation is much weaker. Wave processes in a layer of granular medium with nonspherical granules were also studied. It is shown that the medium is characterized by very strong wave attenuation and by the absence of wave structure formation and is highly sensitive to its initial stress state.     

弯曲型Lamb波传播特性与固井质量相关性研究

轻质水泥在油田固井中的广泛应用使得传统测井方式无法有效的对固井水泥胶结质量做出评价。为了研究新的可行的评价方法,本文采用传递矩阵方法对套管中传播的弯曲型Lamb波进行建模,并通过对所建模型进行数值计算研究了套管外水泥等介质的声学参数变化对弯曲型Lamb波衰减率的影响。数值计算的结果表明,弯曲型Lamb波的衰减率与水泥的声学参数以及水泥与套管的胶结状况有较强相关性,据此可对水泥与套管胶结状况进行评价。本文的计算结果与分析对弯曲型Lamb波在水泥胶结评价中的应用具有一定的参考意义。     

Parametric interaction and compression of optical pulses in field of high-power pump wave

It is shown that, in the undepleted pump approximation, the nonlinear problem of the three-wave parametric interaction under the conditions of phase mismatch can be reduced to a problem of linear interaction of the signal and idle waves with a strong low-frequency pump wave. The whole wave packet formed by the two waves breaks down to partial pulses whose dynamics is controlled by effective dispersion parameters. This can be accompanied by the compression of either one of the pulses that comprises the wave packet or the whole wave packet.     

Dynamics of electron wave packets in topological insulators

Dynamics of wave packets formed by surface (edge) electronic states in topological insulators has been investigated. The spin and electron probability density, as well as zitterbewegung, of wave packets have been calculated analytically and numerically for various values of the Hamiltonian parameters. The effects of the main parameters (size and spin polarization) of the wave packets on a change in the packet shape and oscillations of their average velocity have been considered.     

Theoretical Study of Millimeter Wave Harmonic Oscillator Stabilized with a Transmission Cavity

An equivalent circuit model of millimeter wave second harmonic oscillator stabilized with a transmission cavity has been proposed for constructing analytical formulations between performance parameters of the oscillator and parameters of the circuit. The model consists of an equivalent circuit of fundamental wave and that of second harmonic wave. Each of the circuits comprises circuit models of main cavity, transmission waveguide, and transmission cavity. Absorbing material placed between the transmission waveguide and the transmission cavity can suppress additional resonances originated from transmission cavity. The behavior of the second harmonic oscillator can be effectively described by the circuit model. Furthermore, based on this model, mechanical tuning characteristics have been studied at first, and then analytical formulas for quality factor and efficiency depending on circuit parameters have been derived. The circuit parameters can be conveniently extracted by electromagnetic field simulation. Hence the formulas exhibit both compact form and enough accuracy. Thereafter, general rules of performance parameters varying with circuit parameters have been deduced for the harmonic oscillators. Then some design considerations have been derived according to the corresponding analysis. The equivalent circuit model is useful for designing and adjusting millimeter wave second harmonic stabilizing oscillator with a transmission cavity.     

装置参数对狭缝天线激发的等离子体表面波传播的影响

采用时域有限差分法对矩形结构装置的等离子体表面波传播进行了三维数值模拟.研究了装置参数(如介质板相对介电常数、厚度以及介质板上方空气间隙)对天线阵列激发的等离子体表面波传播的影响,给出了合适的介质板相对介电常数和厚度,并指出空气间隙的存在会严重削弱天线阵列对表面波的激发.计算结果可为大面积矩形表面波等离子体源装置的优化设计提供参考. 关键词： 时域有限差分法 等离子体表面波 狭缝天线     

管流中注入粒子的非定常波系的数值研究

使用二维有限体积方法,对在管流中固定位置处注入静止固体粒子的可压缩含灰气体流动进行数值模拟,讨论流场和粒子在过程中的耦合,研究质量增加和热量变化所产生的非定常波系,分析物理参数在过程中的变化.结果表明,在添质和加热过程中,流场会产生不同类型和不同强度的非定常波,在分析其物理规律的同时,讨论添质和加热相互作用导致的波系间转换,最后求解流场中各区域的热力学参数,得到不同的流场速度和粒子温度情况下各非定常波波强的相图,定量解释改变参数引起的非定常波变化规律.     

Polarization of light transmitted through a polymer film with nanosized droplets of liquid crystal

A method is developed for analyzing the state of polarization of a plane wave transmitted through a polymer-dispersed liquid-crystal (PDLC) film with nanosized liquid-crystal (LC) droplets. This method is based on the anisotropic-dipole approximation for describing scattering by a separate droplet and on the Foldy-Twersky approximation for describing propagation of light in a film. Equations are obtained that relate the ellipsometric parameters of coherent (direct) light transmitted through a PDLC film to the order parameters that characterize the morphological and structural properties of the film. Elliptic and circular polarizations and the rotation of the plane of polarization of a wave transmitted through a film are investigated under the normal illumination of the PDLC film by a linearly polarized plane wave. The order parameters of the PDLC film are determined as a function of a control field under the transition from a partially ordered structure of optical axes of LC droplets to a homeotropic structure.     

Parameter measurement of the cylindrically curved thin layer using low-frequency circumferential Lamb waves

The characteristic parameters of a cylindrically curved thin layer include its elastic constants, thickness and curved radius. A layer is considered thin if the echoes from the front and back surfaces of the layer cannot be separated in the time domain, and/or that the wave arrivals corresponding to longitudinal and shear wave part cannot be identified in the time or space domain. This paper describes a low-frequency circumferential Lamb wave method to characterize those parameters of a cylindrically curved thin layer. The technique is based on the measurement of circumferential Lamb wave phase velocity and the unknown parameter is estimated through minimizing the mean square error obtained by comparing theoretical and experimental phase velocities. The sensitivity and accuracy of the proposed technique to different parameters are analyzed. Using the present technique, a cylindrically curved thin layer with thickness down to ten percent of the longitudinal wavelength can be successfully measured with an average relative error less than two-percent in our experiment.     

Statistical characteristics of an intense wave behind a two-dimensional phase screen

An analysis of the parameters of nonlinear waves transmitted through a layer of a randomly inhomogeneous medium is carried out. The layer is modeled by a two-dimensional phase screen. Passing through the screen plane, the wave acquires a random phase shift. The wave front becomes distorted, and randomly located regions of ray convergence and divergence are formed, in which the nonlinear evolution of the wave alters profoundly. The problem is solved in the approximation of geometrical acoustics. The ray pattern of a plane wave transmitted through the regular screen is constructed. The solution that describes the spatial structure of the field and the evolution of an arbitrary temporal wave profile behind the screen is obtained. Statistical characteristics of the discontinuity amplitude are calculated for different distances from the screen. A random modulation is shown to result in a faster (in comparison with the case of a homogeneous medium) nonlinear attenuation of the wave and in the smoothing of the shock profile. The distribution function of the wave field parameters becomes broader because of random focusing effects.     

Investigation of a silicon-based one-dimensional phononic crystal plate via the super-cell plane wave expansion method

The super-cell plane wave expansion method is employed to calculate band structures for the design of a silicon-based one-dimensional phononic crystal plate with large absolute forbidden bands. In this method, a low impedance medium is introduced to replace the free stress boundary, which largely reduces the computational complexity. The dependence of band gaps on structural parameters is investigated in detail. To prove the validity of the super-cell plane wave expansion, the transmitted power spectra of the Lamb wave are calculated by using a finite element method. With the detailed computation, the band-gap of a one-dimensional plate can be designed as required with appropriate structural parameters, which provides a guide to the fabrication of a Lamb wave phononic crystal.     

基于黄金分割搜索算法的行波管测量方法

为了提供声学材料的测试环境,该文通过有源吸声技术在行波管中建立了一套测量系统,声管中实现了模拟无限水域的行波场环境,从而对样品的声学参数进行测量。提出了一种利用黄金分割搜索算法对最佳时延与幅值进行搜索从而完成行波场建立的方法。在上述行波场建立的基础上,利用双水听器法分别对水柱与钢板样品的声学参数进行了声学测量,透射系数测量值与理论值符合较好。该方法为声学参数的测量方法提供了有意义的参考。     

Trapped rossby waves

The possibility of tidal dynamics at strictly imaginary Lamb parameters has been known for more than three decades. The present paper explores the prevailing physics in this parameter regime. To this end, basic features of the global circulation such as baroclinicity and geostrophy have to be incorporated into tidal dynamics. The tidal equations of the thermal wind are readily obtained in the framework of spherical bishallow water theory. Density surfaces of a circulation with available potential energy alter the spatial inhomogenities of the generic tidal problem. Wave dynamics in an inhomogeneous medium are characterized not only by a dispersion relation but also by a wave guide geography: significant wave amplitudes are trapped in specific regions of frequency-dependent width. As an inherently global issue, evaluation of the Rossby wave guide geography for a given circulation cannot rely on the familiar regional filters of tidal theory. On the global domain, the Rossby wave specification is given by the Margules filter. A thermal wind is stable against nondivergent Rossby wave disturbances. Rossby waves propagating with a geostrophic wind are governed by prolate dynamics (real Lamb parameters) while imaginary Lamb parameters emerge for the oblate dynamics of Rossby waves running against a geostrophic wind. Oblate Rossby wave dynamics include pole-centered wave guides and very low-frequency disturbances propagating eastward against a westward wind.     

Correction of aberration for a high-resolution electron hologram by means of the amplitude contrast criterion of image wave

In order to further improve the resolution for a high-resolution electron hologram, the aberration working on the hologram must be corrected. Since it is rather difficult to precisely control aberration coefficients in the experimental stage, we proposed an amplitude contrast D criterion of imaging wave to determine the working aberration from the hologram itself. In the determination or correction of the aberration, we assume a symmetrical aberration function is parameterized only by a spherical aberration coefficient and a defocus value. First, D is calculated from a holographically reconstructed imaging wave of YBa(2)Cu(3)O(7-x) for each combination of these parameters. The working aberration on the imaging wave is determined from the combination of the parameters by noting the maximum or minimum D of the imaging wave at some specifically chosen thickness regions. The theoretical validity for the D criterion is then proved with three-beam dynamical diffraction formula. Finally, the 'experimental' examination for the D criterion is successfully performed on the reconstructed image wave for the Sigma=9 interface structure of a wedge-shaped silicon sample.     

Nonlinear Evolution of a Gaussian Wave Perturbation in the Presence of a High Power Electromagnetic Plane Wave in the F Region Ionosphere

The interaction of a high power electromagnetic plane wave of uniform intensity with a weak electromagnetic Gaussian wave has been studies analytically. The two waves propagate vertically with almost the same frequency in the F region ionosphre. It is seen that the Gaussian wave acquires an oscillatory structure due to the nonlinear coupling of the strong plane wave and the weak Gaussian wave and the amplitude of these fluctuations grows with height. The growth, however, occurs only above a certain altitude z₀, which is determined by the plasma and wave parameters.     

1D waves in a random poroelastic medium with large fluctuations

We examine the problem of wave propagation in a random poroelastic medium. The porous medium is modelled as a Biot poroelastic solid whose constitutive parameters fluctuate substantially over finite distances. Our main results are asymptotic analytical expressions for the mean velocity-stress wave; this solution incorporates two distinct length scales. The effect of the fluctuations appears on the regular depth coordinate while the parameters of the effective medium arise on a shorter scale of distance. Thus the method that we apply, the theory of averaging, allows us to give a rigorous derivation of the effective medium parameters. It also provides the correction terms which are caused by the fluctuations in the random medium; we find that the relative effect of the latter increases in proportion to ω^1/2 where ω denotes the wave frequency. We also show that the fluctuations introduce significant attenuation of the fast Biot compressional wave and dispersion of the slow Biot wave. These results are illustrated by numerical examples using real oilfield data.     

Gaussian beam decomposition of high frequency wave fields using expectation–maximization

A new numerical method for approximating highly oscillatory wave fields as a superposition of Gaussian beams is presented. The method estimates the number of beams and their parameters automatically. This is achieved by an expectation–maximization algorithm that fits real, positive Gaussians to the energy of the highly oscillatory wave fields and its Fourier transform. Beam parameters are further refined by an optimization procedure that minimizes the difference between the Gaussian beam superposition and the highly oscillatory wave field in the energy norm.