The scattering of flexural waves by random fractal inhomogeneities in a thin plate

The scattering of flexural waves by small statistical fractal inhomogeneities in a thin plate is considered. An expression for the average intensity of the fluctuations of the scattered wave field is obtained. A relation of the intensity to the plate parameters and to the fractal dimension of the inhomogeneities is determined. An expected frequency dependence of the attenuation of flexural waves in a plate due to the scattering by fractal inhomogeneities is discussed.     

Laser excitation of flexural waves and their scattering by fractal inhomogeneities in a thin plate

The excitation of flexural waves in a thin plate (film) by harmonically modulated laser radiation and their scattering by small fractal inhomogeneities are considered. An expression for the mean fluctuation intensity for the scattered wave field is obtained. A relationship between the intensity, parameters of the laser radiation and the plate, and the fractal dimension of inhomogeneities is found. The expected frequency dependence of the flexural wave attenuation in the plate due to their scattering by fractal inhomogeneities is discussed.     

Qualitative theory of amplitude and phase fluctuations in a medium with anisotropic turbulent irregularities

Abstract

Wave propagation in an anisotropic turbulent medium is studied assuming that the anisotropy coefficient η is constant for all scales of inhomogeneities. A qualitative method of studying the amplitude and phase fluctuations is developed. Formulae have been obtained for the phase structure functions and scintillation index for the medium with spectrum power index 3<μ<5 and anisotropy coefficient η≥1. Two particular cases have been studied in detail—propagation along and across the axis of the stretching of irregularities. During propagation along a short axis of inhomogeneities the fluctuations are decreasing and the phase structure function and scintillation index turn out to be η^μ?2 times smaller as compared with isotropic case. At the same time, during propagation along the long axis of inhomogeneities the phase structure function in vertical plane and the scintillation index are η times greater than in the isotropic medium.     

Computer modeling of sound propagation in the ocean with fractal inhomogeneities

The wave-field computer code based on the wide-angle parabolic equation is modified and adapted to the problems of sound scattering in a medium with anisotropic inhomogeneities of fractal type. To verify the computer code, a model numerical experiment on determining the angular dependence of the scattered sound field is performed for different anisotropy coefficients of the sound speed inhomogeneities. The comparison of the computed data with the theoretical dependences shows their rather good agreement and indicates that the computer code can be applied to calculations of sound propagation in the ocean with fine-structure inhomogeneities possessing fractal properties.     

Liquid transport due to light scattering

Using experiments and theory, we show that light scattering by inhomogeneities in the index of refraction of a fluid can drive a large-scale flow. The experiment uses a near-critical, phase-separated liquid, which experiences large fluctuations in its index of refraction. A laser beam traversing the liquid produces a interface deformation on the scale of the experimental setup and can cause a liquid jet to form. We demonstrate that the deformation is produced by a scattering-induced flow by obtaining good agreements between the measured deformations and those calculated assuming this mechanism.     

Some features of the fractal structure of the developed small-scale ionospheric turbulence

We present the results of the first studies of the fractal structure of the developed small-scale ionospheric turbulence (SSIT) during special experiments on radio-raying of the midlatitude ionosphere by signals from orbital satellites in 2005–2006. It is established that under conditions of developed turbulence, typical values of the fractal dimension of the space occupied by natural SSIT inhomogeneities are, as a rule, close to the topological dimension of their embedding space, and the true values of the spectral index of isotropic SSIT only slightly differ from the corresponding generally accepted nominal values in the embedding space. Nevertheless, even small differences in the mentioned parameters detected in the experiment witness a sharply nonuniform distribution of the local fractal structures of the developed SSIT in space. We propose a stochastic model of the nonstationary process for fast amplitude fluctuations of signals during their propagation in the ionosphere with nonuniform spatial distribution of small-scale electron-density fluctuations. Eventually, namely this nonuniform distribution of small-scale electron-density fluctuations leads to the specific multifractal structure of the amplitude records of received signals. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 51, No. 4, pp. 287–294, April 2008.     

分形海面的微波电磁散射计算模型

利用2维Weierstrass带限函数建立了模拟粗糙海面形状的模型,讨论了分形维数、频率幅度尺度因子等分形参数对海面形状的影响。以粗糙海面形状模型为基础,针对模拟的分形海面形状,从亥姆霍兹积分出发,利用基尔霍夫近似推导出2维分形海面的电磁散射系数,并进行了数值模拟。对微波电磁散射特性随分形维数、频率幅度尺度因子、入射波入射角变化的规律做了进一步讨论分析。在低掠射角时电波会受海面的遮挡,用遮挡函数对散射系数进行修正。研究表明:随着分形维数的增大,散射峰分布变均匀。频率幅度尺度因子越大,散射也越分散。随着入射角的增大,后向散射也逐渐增强,而前向散射逐渐减弱。     

Amplitude fluctuations in the theory of radio-wave refraction scattering

We consider some aspects of the theory of radio-wave scattering with respect to studies of radiation intensity fluctuations behind a random phase screen. The expressions for a piecewise approximation of the function of distribution of intensity fluctuations in the near zone and in the region of random focusing behind the screen are found. The expressions obtained are used to calculate the radio-wave scintillation index in these regions. The corresponding calculations are performed with allowance for the finite dimensions of external and internal scales of turbulent inhomogeneities of the phase screen. It is shown that the radio-wave refraction scattering, as a rule, is characterized by a pronounced random focusing of the radiation intensity behind the phase screen. However, under strongly developed turbulence of the radio-wave propagation medium (phase screen) the above phenomenon may be absent.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 39, No. 9, pp. 1114–1124, September, 1996.This paper was supported by the Russian Foundation for Fundamental Research under project 95-02-03716.     

Determining the structural parameters of fractal and nonfractal objects in multiple small-angle neutron scattering experiments

An experimental procedure employing setups with standard resolution characteristics for multiple small-angle neutron scattering in fractal and nonfractal media is described. Specific features of the proposed method, which are related to a limited resolution of the spectrometer, are considered in the case of large-scale inhomogeneities with the characteristic size exceeding the inverse spatial resolution. A new approach to the extraction of information about the fractal dimension of the system studied is demonstrated, which takes into account the dependence of the attenuation and broadening of the transmitted neutron beam on the sample thickness.     

Studying the structural features of oxide nanoclusters of cerium and titanium in a silicate glass by means of the small-angle neutron scattering

The features of the formation of Ce-Ti-O complex oxide nanoclusters in a silicate glass are studied by means of the small-angle neutron scattering technique. It is found that bounded regions of density fluctuation of the glass material are formed in the initial glass matrix without the addition of titanium and cerium oxides. These regions could serve as nucleation centers for oxide clusters of cerium and titanium upon their introduction into the matrix. The calculated average size of these inhomogeneities does not exceed 30 ± 1 nm, and their surface volume equals 0.72 ± 3 nm³. A structural mechanism for Ce-Ti-O oxide formation in a silicate glass, in which the nanoclusters are formed within a bounded region of glass material inhomogeneities at low concentrations of the initial cerium oxide (CeO₂), is proposed. At high cerium oxide concentrations, oxide nanocluster growth occurs predominantly on the surface of these inhomogeneities. This leads to a sharp change in the nanocluster sizes and their fractal dimension.     

一维带限Weierstrass分形分层地面与矩形截面导体柱复合电磁散射FDTD研究

运用时域有限差分方法研究一维带限分形分层粗糙地面与矩形截面导体柱的复合电磁散射,计算复合电磁散射的双站散射系数,得到复合散射系数随散射角的变化,讨论粗糙面高度起伏均方根、分维、中间层介质、下层介质及矩形截面导体柱的参数等对复合散射系数的影响.     

分形大地土壤表面与部分埋藏目标复合散射特性

采用土水混合物介电常数的Topp方程模型表示大地土壤的介电特性,应用带限Weierstrass-Mandelbrot分形粗糙面模型和Monte Carlo方法模拟大地土壤表面,运用矩量法研究了带限分形大地土壤表面与部分埋藏矩形截面柱复合模型的电磁散射,得出了复合散射系数的角分布曲线;计算了复合散射系数随带限分形大地土壤表面分维、空间基频、高度起伏均方根、土壤含水率、矩形截面柱几何参数、埋藏深度、倾角、入射波频率等的变化情况,并做了详细分析与讨论;结果表明,土壤表面分维等参数对复合散射系数的影响是非常复杂的,镜像附近的角分布曲线具有明显的分形特征。     

二维导体粗糙面电磁散射的分形特征研究

采用二维归一化带限Brown分形函数来模拟二维分形粗糙面,主要利用基尔霍夫近似给出了该导体粗糙面的电磁散射场.导出了平均散射场、平均散射系数和散射强度方差的计算公式.讨论了散射场分布与分维的关系,获得了散射场波峰拟合线的斜率与分维D满足线性关系这一重要结论. 关键词：     

Microwave scattering by tropospheric fluctuations in an evaporation duct

Numerical analysis of the centimeter wave propagation in an evaporation duct with allowance for scattering by correlated turbulent fluctuations of the tropospheric refraction index is carried out. It is shown that energy leakage from the duct leads to an additional decrease in the average wave power. The amplitude of random power variations above the duct turns out to be significantly higher compared with the variations inside the duct. An increase in the vertical correlation radius of refraction-index inhomogeneities leads to an increase in the vertical correlation radius of the radio-wave intensity. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 52, No. 4, pp. 307–317, April 2009.     

Classical chaos and nonlinear dynamics of rays in inhomogeneous media

An investigation is made of the classical nonlinear resonance and the classical stochastic dynamics of rays in waveguide media with irregular inhomogeneities. Analytic and numerical methods are used to study the characteristics of the ray trajectories, their confinement in a nonlinear resonance, and the development of chaotic behavior in waveguides with longitudinal periodic inhomogeneities. It is established that the localization of the rays has fractal properties; in particular, the cycle length of a ray and the time and velocity of propagation of a signal depend on the initial parameters of the ray in the form of a "devil's staircase." A waveguide with an inhomogeneous index of refraction and a periodically corrugated wall is considered.     

The angular dependence of the coefficient of sound reflection from anisotropic volume inhomogeneities of the ocean

The small perturbation method is used to consider the scattering of sound by random volume inhomogeneities of the ocean. The inhomogeneities are assumed to be horizontally anisotropic with their horizontal dimensions far exceeding the vertical ones. Expressions are obtained for the angular dependence of the scattering coefficient. Vertical and horizontal sections of the scattering pattern are presented, and the angular widths of its maxima are analytically estimated.     

具有二维fBm特征的分层介质粗糙面电磁散射的特性研究

运用微扰法研究了平面波入射分层介质粗糙面的电磁散射,推出了不同极化状态下的双站散射系数公式.采用二维fBm分形粗糙面来模拟实际的分层介质粗糙面,结合二维fBm分形粗糙面的功率谱导出了平面波入射二维fBm分形分层介质粗糙面的散射系数计算公式.通过数值计算得到了HH极化下双站散射系数随散射角的变化曲线,讨论了分维、底层介质介电常数、中间介质介电常数和厚度及入射波频率对双站散射系数的影响,得到了二维fBm分形分层介质粗糙面散射系数的分维特征、基本特征、分区特征和随频率变化的特征. 关键词： 电磁散射 二维fBm分形粗糙面 分层介质 微扰法     

Scattering of radiation by a quasiperiodic two-dimensional medium

We study the scattering of radiation by a medium presenting inhomogeneities distributed in a quasiperiodic way. We show the existence of quasiperiodic solutions of the two-dimensional stationary wave equation, under certain conditions on the index of refraction, using a technique based on Dinaburg-Sinai method for one-dimensional Schrödinger equation with a quasiperiodic potential. Moreover we show that the energy spctrum contains a nonempty absolutely continuous component, with a subset having high degeneracy, provided the inhomogeneities are small enough.     

随机分布烟尘团簇粒子辐射特性研究

基于分形理论,采用蒙特卡罗方法对随机分布的烟尘团簇粒子结构进行了仿真模拟,利用离散偶极子近似(discrete dipole approximation, DDA)方法研究了随机分布的烟尘团簇粒子的辐射特性,分析讨论了分形维数、原始微粒粒径和数量以及复折射率对随机分布烟尘团簇粒子辐射特性的影响.研究表明,在给定分形维数的情况下,烟尘团簇粒子的辐射特性取决于原始微粒粒径、数量及复折射率;原始微粒较小的团簇粒子,当分形维数较小时,吸收截面变化不明显,但当分形维数大于2时,吸收截面骤然增大,然而,对于具有比较大的原始微粒粒径、数量及复折射率的烟尘团簇粒子,吸收截面随着分形维数的增大而单调递减;随着分形维数的增大,团簇粒子的散射截面、消光截面及单次散射反照率均单调递增;从整体上来讲,团簇粒子的辐射特性与等效球形粒子的辐射特性存在着比较大的差别,并且这种差别随着分形维数的增大而减小.该工作对研究气溶胶粒子的辐射及气候效应具有重要的科学价值. 关键词： 烟尘团簇粒子 辐射特性 离散偶极子近似方法