Effective medium method of slightly compressible elastic media permeated with air-filled bubbles

An effective medium method is developed for the slightly compressible elastic media permeated with air-filled bubbles, according to the nonlinear oscillation of the bubble, which happens when compressional wave travels through the porous media. The effective Lame coefficients of the porous medium and the nonlinear elastic wave equation are deduced, based on the fact that the micro-unit of the effective medium should have the same stress and strain as the micro-unit of the porous media. The linearized properties obtained by this method are in good agreement with the results of Gaunaurd’s classic theory [Gaunaurd G.C. and überall H., J. Acoust. Soc. Am., 1978, 63: 1699–1711]. Furthermore, the nonlinear coefficient, which is an important property of the porous media, can also be acquired by this method. __________ Translated from Acta Acustica, 2006 (in Chinese) (in press)     

含气泡弱可压缩弹性材料的等效媒质法

声波在含气泡弹性材料中传播时不仅使固相介质产生形变,而且会使气泡非线性振动,据此建立了含气泡弱可压缩弹性材料的等效媒质法。利用等效媒质的微单元与含气泡材料的微单元具有相同的应力和应变,求得了含气泡材料的等效Lame系数,并得到了含气泡材料的非线性波动方程。其线性化结果与Gaunaurd的经典理论相比较,有很好的一致性。本方法还可给出含气泡弱可压缩弹性材料的另一重要参数——非线性系数。     

Influence of the surrounding pressure on acoustic properties of slightly compressible porous media permeated with air-filled bubbles

The effective wave velocity, attenuation, and nonlinear properties of slightly compressible porous media permeated with air-filled bubbles are studied numerically by employing the nonlinear Hooke’s law for different surrounding pressures. Numerical simulations show that the acoustic properties of porous media are greatly affected by the surrounding pressure if the shear modulus of the elastic medium is very small due to the fact that the acoustic wave propagation in porous media are strongly influenced by the nonlinear oscillation of bubbles; moreover, the oscillation of a bubble depends on the equilibrium bubble radius, which is affected by the surrounding pressures. Published in Russian in Akusticheskiĭ Zhurnal, 2006, Vol. 52, No. 4, pp. 490–496. The text was submitted by the authors in English.     

Propagation of acoustic wave in viscoelastic medium permeated with air bubbles

Based on the modification of the radial pulsation equation of an individual bubble, an effective medium method (EMM) is presented for studying propagation of linear and nonlinear longitudinal acoustic waves in viscoelastic medium permeated with air bubbles. A classical theory developed previously by Gaunaurd (Gaunaurd GC and \"{U}berall H, {\em J. Acoust. Soc. Am}., 1978; 63: 1699--1711) is employed to verify the EMM under linear approximation by comparing the dynamic (i.e. frequency-dependent) effective parameters, and an excellent agreement is obtained. The propagation of longitudinal waves is hereby studied in detail. The results illustrate that the nonlinear pulsation of bubbles serves as the source of second harmonic wave and the sound energy has the tendency to be transferred to second harmonic wave. Therefore the sound attenuation and acoustic nonlinearity of the viscoelastic matrix are remarkably enhanced due to the system's resonance induced by the existence of bubbles.     

梯度圆柱颗粒复合介质的有效非线性响应

应用非线性微分有效偶极近似方法,导出了关于非线性梯度圆柱颗粒的等效线性介电常数和三阶非线性极化率的微分式,研究了稀释极限下,圆柱形梯度颗粒无规置入线性介质中组成的复合介质的有效线性介电常数和三阶非线性极化率.作为应用,数值计算了具有幂指数梯度分布的介电常数的颗粒复合介质的有效非线性响应,及梯度金属电介质颗粒复合介质的表面plasmon共振效应.     

随机多孔介质逾渗模型渗透率的临界标度性质

研究了一类非零键渗透率满足均匀分布的随机多孔介质逾渗模型-数值计算了该模型系统渗透率在临界点处的标度指数-结果表明该指数并不能看作是普适常数,而与均匀分布的参数有关-这意味着即使非零键渗透率值的概率密度函数满足负一阶矩存在条件,系统渗透率在逾渗临界点处的标度指数仍然依赖于分布函数的具体参数,并不是常数-这一数值结果与Sahimi对此问题的结论不同- 关键词： 逾渗 随机多孔介质 标度指数 渗透率     

用格子玻尔兹曼方法研究流动-反应耦合的非线性渗流问题

根据格子玻尔兹曼计算技术以及相应渗流理论，对多孔介质内流动-反应(矿物介质的溶解等)耦合这一非线性渗流问题进行了数值研究，计算结果与解析解基本符合.数字图像重构技术反映的结果表明流体流动和反应之间可以发生强烈的耦合和反耦合作用，同时可以形成条带结构这一自组织现象，与实验和其他理论分析结果符合也很好. 关键词： 非线性渗流 耦合反应 数值模型     

Nonlinear optical properties in double-sided nonlinear media with Z-scan technique based on the Huygens——Fresnel principle

We present a theoretical model to analyse the propagation of a Gaussian laser beam through double-sided nonlinear media. This model is based on the Huygens--Fresnel diffraction integral method. This theoretical model is not only consistent with the cascade structure model for a small nonlinear phase-shift but also can be used for a large nonlinear phase-shift. It has been verified that it is suitable to characterize the double-sided nonlinear media compared with the cascade structure model. A good agreement between the experimental data and the results from the theoretical model is obtained. It will be useful for the design of multi-sided nonlinear materials.     

绝缘颗粒液体主体基质复合介质的非线性光学性质

利用Maxwell-Garnett近似，并结合谱表示方法，理论研究了具有一般非线性的绝缘颗粒，无规则浸入液体主体基质复合体系的非线性光学性质-在弱非线性条件下，数值研究了体系的有效线性介电函数和光学非线性随体积分数的变化，并发现体系的线性介电函数比光学非线性更依赖于绝缘颗粒组分的体积分数-在一般非线性条件下，研究体系的有效介电函数随入射光强度的依赖关系，还研究了s方向和p方向极化的总反射率的行为- 关键词： 复合介质 谱表示 非线性光学性质     

两组份复合材料光学非线性性质的临界行为

对两组份非线性复合材料的光学非线性性质的临界行为进行了研究。考虑第一组份为非线性材料,其电流、电压间服从I=g1V x1V^β关系;而第二组份为线性材料,电流、电压间满足I—g2V,其中g1,x1是第一组份的线性电导和光学非线性极化率,g2是第二组份的线性电导,β是第一组份材料的光学非线性指数。分别采用了有效介质近似和相对电阻涨落的标度理论两种方法计算了系统有效响应的临界指数随光学非线性指数及维数的变化规律。用不同的方法得到系统的有效线性电导g和有效光学非线性极化率xe(β)的临界指数M(β)和N(β)的结论也不同。有效介质近似得到M(β)=1和N(β)=(β 1)/2,即M(β)与β和d都无关,而N(β)只与有β关而与d无关;而相对电阻涨落标度理论方法得到的M(β)和N(β)与β和d都有关。     

Monte-Carlo simulation of light scattering in fractal porous media

Monte-Carlo simulation of light propagation in a porous medium with a mass fractal morphology was carried out. It was shown that the simulation results can be used to analyze experimental data on light scattering and to study the porous medium structure. __________ Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 75, No. 2, pp. 193–196, March–April, 2008.     

多孔介质内溶解与沉淀过程的格子Boltzmann方法模拟

本文采用格子Boltzmann方法模拟了多孔介质内的溶解和沉淀现象, 并分析了雷诺数、施密特数、达姆科勒数对多孔介质孔隙结构及浓度分布的影响. 结果表明: 对于多孔介质内的溶解(沉淀)过程, 当雷诺数越大时, 孔隙率越大(小), 平均浓度值越小(大); 当达姆科勒数或施密特数较小时, 溶解和沉淀过程均受反应控制, 此时反应在多孔介质的固体表面较为均匀的发生; 当达姆科勒数或施密特数较大时, 溶解和沉淀过程均受扩散控制, 此时反应主要发生在上游及大孔隙区域.     

Homotopy Continuation Approach to Electrostatic Boundary-Value Problems of Nonlinear Media

The homotopy continuation method is employed to solve electrostatic boundaryvalue problems of nonlinear media. The difficulty associated with matching the inherently nonlinear boundary conditions on the interface is overcome by the mode expansion method, by which the nonlinear partial differential equations of the original problem are transformed into an infinite set of nonlinear ordinary differential equations. In this regard, the homotopy method has to be modified to handle the nonlinear boundary conditions. As an illustration, we study two cases:(a) nonlinear inclusion in linear host and (b) linear inclusion-in nonlinear host, both in two dimensions. The homotopy method is validated by comparing the results with the exact solution of case (a) and the results derived by perturbation method in case (b).     

Simulation of the relationship between porosity and tortuosity in porous media with cubic particles

Tortuosity is an important parameter used in areas such as vascular medicine,neurobiology,and the field of soil permeability and diffusion to express the mass transport in porous media.It is a function of the porosity and the shape and distribution of particles.In this paper,the tortuosity of cubic particles is calculated.With the assumption that the porous medium is homogeneous,the problem is converted to the micro-level over a unit cell,and geometry models of flow paths are proposed.In three-dimensional(3D) cells,the flow paths are too complicated to define.Hence,the 3D models are converted to two-dimensional(2D) models to simplify the calculation process.It is noticed that the path in the 2D model is shorter than that in the 3D model.As a result,triangular particles and the interaction are also taken into consideration to account for the longer distance respectively.We have proposed quadrate particle and interaction(QI) and quadrate and triangular particle(QT) models with cubic particles.Both models have shown good agreement with the experimental data.It is also found that they can predict the toruosities of some kinds of porous media,like freshwater sediment and Negev chalk.     

Nonlinear Schrödinger equation for optical media with quintic nonlinearity

A nonlinear quintic Schrödinger equation (NLQSE) is developed and studied in detail. It is found that the NLQSE has soliton solutions, the stability of which is analysed using variational method. It is also found that the soliton pulse width in the materials supporting NLQSE is small compared to soliton pulse width of the commonly studied nonlinear cubic Schrödinger equation (NLCSE).     

含定向非均匀体固体材料的横观各向同性有效弹性模量

针对非均匀体定向指向的情况,将非均匀体对弹性波的散射等效为球形有效体对弹性波的散射,推导出了呈现横观各向同性的有效弹性模量.理论分析表明:本文得到的有效模量公式至少具有二阶精度.数值计算表明:本文的有效模量随孔隙度增加而降低,不会出现Hudson模型中在孔隙度超过一定阈值后不减反增的问题.另外,在非均匀体指向随机的情况,本文得到的有效模量公式归结为Kuster-Toks z模型的公式.对于由扁状裂隙作为非均匀体的孔隙岩石,裂隙内液体主要影响横观各向同性对称轴方向的纵波模量.     

Analysis of Nonlinear TE Waves in a Periodic Refractive Index Structure with a Nonlinear Cladding

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N-Soliton Solutions of General Nonlinear Schrodinger Equation with Derivative

The bilinear equation of the genera/nonlinear Schrodinger equation with derivative （GDNLSE） and the N-soliton solutions are obtained through the dependent variable transformation and the Hirota method, respectively. The bilinear equation of the nonlinear Schrodinger equation with derivative （DNLSE） and its multisoliton solutions are given by reduction.     

Interaction trajectory of solitons in nonlinear media with an arbitrary degree of nonlocality

The interaction trajectory of solitons in nonlocal nonlinear media is investigated. A simple differential equation describing the interaction trajectories is derived based on the light ray equation. Numerical calculations are carried out to illustrate the interaction trajectories with different parameters. The results show that the degree of nonlocality greatly affects the interaction of solitons. For a strongly nonlocal case, the interaction trajectory can be described by a cosine function. Analytical expressions describing the trajectory and the oscillation period are obtained. For generally and weakly nonlocal cases, the interaction trajectories still oscillate periodically, however it is no longer sinusoidal and the oscillation period increases with the nonlocal degree decreasing. In addition, the trajectory of two solitons launched with a relative angle at the entrance plane is investigated. It is found that there exists a critical angle. When the initial relative angle is larger than the critical angle, the two solitons do not collide on propagation. The influence of the degree of nonlocality on the critical angle is also discussed.