Scattering of shear waves by an elliptical cavity in a radially inhomogeneous isotropic medium

Complex function and general conformal mapping methods are used to investigate the scattering of elastic shear waves by an elliptical cylindrical cavity in a radially inhomogeneous medium. The conformal mappings are introduced to solve scattering by an arbitrary cavity for the Helmholtz equation with variable coefficient through the transformed standard Helmholtz equation with a circular cavity. The medium density depends on the distance from the origin with a power-law variation and the shear elastic modulus is constant. The complex-value displacements and stresses of the in.homogeneous medium are explicitly obtained and the distributions of the dynamic stress for the case of an elliptical cavity are discussed. The accuracy of the present approach is verified by comparing the present solution results with the available published data. Numerical results demonstrate that the wave number, inhomogeneous parameters and different values of aspect ratio have significant influence on the dynamic stress concentration factors around the elliptical cavity.

SOLVING THE PROPAGATION OF ELECTROMAGNETIC WAVE IN A SIMPLE TWO-DIMENSIONALINHOMOGENEOUS MEDIUM BASED ON SYMPLECTIC GEOMETRICAL THEORY

A new symplectic geometrical high-frequency approximation method for solving the propagation of electromagnetic wave in the two-dimensional inhomogeneous medium is used in this paper. The propagating caustic problem of electromagnetic wave is translated into non-caustic problem by the coordinate transform on the symplectic space. The high-frequency approximation solution that includes the caustic region is obtained with the method combining with the geometrical optics. The drawback that the solution in the caustic region can not be obtained with geometrical optics is overcome by this method. The results coincide well with that of finite element method.

Dynamics of the Moving Ring Load Acting in the System“Hollow Cylinder+Surrounding Medium”with Inhomogeneous Initial Stresses

This paper studies the influence of the inhomogeneous initial stress state in the system consisting of a hollow cylinder and surrounding elastic medium on the dynamics of the moving ring load acting in the interior of the cylinder.It is assumed that in the initial state the system is compressed by uniformly distributed normal forces acting at infinity in the radial inward direction and as a result of this compression the inhomogeneous initial stresses appear in the system.After appearance of the initial stresses,the interior of the hollow cylinder is loaded by the moving ring load and so it is required to study the influence of the indicated inhomogeneous initial stresses on the dynamics of this moving load.This influence is studied with utilizing the so-called threedimensional linearized theory of elastic waves in elastic bodies with initial stresses.For solution of the corresponding mathematical problems,the discrete-analytical solution method is employed and the approximate analytical solution of these equations is achieved.Numerical results obtained within this method and related to the influence of the inhomogeneous initial stresses on the critical velocity of the moving load and on the response of the interface stresses to this load are presented and discussed.In particular,it is established that the initial inhomogeneous initial stresses appearing as a result of the action of the aforementioned compressional forces cause to increase the values of the critical velocity of the moving load.

The Scattering of SH Wave in a Nano Hole Embedded the Infinite Inhomogeneous Medium

Scattering of the shear waves by a nano-sized cylindrical hole embedded the inhomogeneous is investigated in this study. The Helmholtz equation with a variable coefficient is transformed the standard Helmholtz equation by the complex function method and the conformal mapping method. By wave function expanding method, the analytical expressions of the displacement field and stress field in the inhomogeneous medium are obtained. Considering the surface effect and using the generalized Young-Laplace equation, we obtain the boundary conditions at nano arbitrary-shaped hole, then the field equations satisfying boundary conditions are attributed to solving a set of infinite algebraic equations. Numerical results show that when the radius of the cylindrical cavity shrinks to nanometers, surface energy becomes a dominant factor that affects the dynamic stress concentration factor (DSCF) around the cylindrical cavity. The influence the density variation of the inhomogeneity on the DSCF is discussed at the same time.

SOME PROPERTIES OF FAR FIELD PATTERNS OF ACOUSTIC WAVES IN AN INHOMOGENEOUS MEDIUM

In this paper, by using functional analysis and integral equation method, we obtain some results about the properties of far field of acoustic waves in an inhomogeneous medium. And we also discuss some ill-posed inverse scattering problems by Tikhonov regularization method.

INVERSE CONDUCTIVE MEDIUM SCATTERING WITH UNKNOWN BURIED OBJECTS

This paper is concerned with inverse acoustic scattering in an inhomogeneous medium with a conductive boundary condition and the unknown buried impenetrable objects inside.Using a variational approach,we establish the well-posedness of the direct problem.For the inverse problem,we shall numerically reconstruct the inhomogeneous medium from the far-field data for different kinds of cases.For the case when a Dirichlet boundary condition is imposed on the buried object,the classical factorization method proposed in[1]is justified as valid for reconstructing the inhomogeneous medium from the far-field data.For the case when a Neumann boundary condition is imposed on the buried object,the classical factorization method of[1]cannot be applied directly,since the middle operator of the factorization of the far-field operator is only compact.In this case,we develop a modified factorization method to locate the inhomogeneous medium with a conductive boundary condition and the unknown buried objects.Some numerical experiments are provided to demonstrate the practicability of the inversion algorithms developed.

基于蒙特卡洛法的喷管中强非均匀性介质辐射换热问题求解加速策略

固体火箭发动机喷管内的辐射换热不可忽视,使用传统蒙特卡洛法模拟效率低下,而现有蒙特卡洛法加速策略研究多局限于辐射物性跨越1个数量级的情况,这与实际喷管中的强非均匀性特点不符。因此,辐射物性跨越2~3个数量级时,以零碰撞蒙特卡洛法为基准,对加权零碰撞蒙特卡洛法和分解蒙特卡洛法两种加速策略进行比较探究,分别考察了灰介质立方体、非灰介质圆柱体算例。结果表明:加权零碰撞蒙特卡洛法在零碰撞衰减系数取全局最大值的60%以上、分解蒙特卡洛法在控制介质辐射物性取全局最大值的3%以内时,二者均可在保证计算精度的前提下缩减计算用时;相较分解蒙特卡洛法,加权零碰撞蒙特卡洛法的加速性能更好,其在非灰算例中的效率提升最高可达14%。此外,还提出了一种改进的轴对称网格定位方法,在几种典型路径中计算用时可缩减43%以上。

Peculiarities of Sound Wave in Moving Medium

Generalized equation for linear gravity waves in moving medium has been obtained. Sound wave is considered as a particular case and it is shown that in inhomogeneous medium at rest it is propagated in full concordance with the Doppler law and principle of motion relativity, i.e. these laws are invariant with reference to properties of medium (homogeneity or inhomogeneity). In moving medium they are fair only in the case of its homogeneity. In strongly inhomogeneous moving medium, propagation of sound is absolutely impossible.

Forced Vibration of the Non-Homogeneously Pre-Stressed System Consisting of the Hollow Cylinder and Surrounding Medium

The paper deals with the study of the influence of the non-homogeneous prestresses in the system consisting of the hollow cylinder and surrounding elastic medium on the frequency response of this system caused by the time-harmonic ring load acting in the interior of the cylinder.The axisymmetric problem is considered and it is assumed that in the initial state,the system is compressed in the radial direction with homogeneously distributed static forces as a result of which,non-homogeneous pre-stresses(or initial stresses)appear in that.It is also assumed that after these pre-stresses appear in the interior of the cylinder,the point-located(with respect to the axial coordinate directed along the cylinder’s central axis)additional time-harmonic ring load acts.Thus,it is required to determine how the pre-stresses influence the frequency response of the system to the noted additional time-harmonic loading.This influence,which is the non-linear effect,is studied within the scope of the so-called three-dimensional linearized equations and relations of the theory of elastic waves in pre-stressed bodies.The solution to the corresponding boundary value problems is found by employing the discrete analytical solution method and numerical results on the influence of the pre-stresses on the frequency response of the interface stresses which appear as a result of the action of the additional time-harmonic forces,are presented and discussed.In particular,it is established that the pre-stresses mentioned above cause to decrease the magnitude of the interface dynamic stresses appearing as a result of the additional time-harmonic loading.

混合散射体的分解方法

考虑混合散射体在时谐声波散射下的反散射问题,该散射体是由具有导电传输边界的可穿透非齐次介质和具有阻抗边界的不可穿透障碍物组成。首先利用变分方法证明正问题解的适定性,然后基于远场数据利用分解方法同时反演混合散射体的位置和形状,最后给出数值算例来验证提出的反演算法的有效性。

Chemical inhomogeneity inhibits grain boundary fracture:A comparative study in CrCoNi medium entropy alloy

Grain boundary(GB)fracture is arguably one of the most important reasons for the catastrophic failure of ductile polycrystalline materials.It is of interest to explore the role of chemical distribution on GB defor-mation and fracture,as GB segregation becomes a key strategy for tailoring GB properties.Here we report that the inhomogeneous chemical distribution effectively inhibits GB fracture in a model CoCrNi medium entropy alloy compared to a so-called‘average-atom’sample.Atomic deformation kinematics combined with electronic behavior analysis reveals that the strong charge redistribution ability in chemical disor-dered CrCoNi GBs enhances shear deformation and thus prevents GB crack formation and propagation.Inspects on the GBs with different chemical components and chemical distributions suggest that not only disordered chemical distribution but also sufficient“harmonic elements”with large electronic flexibility contribute to improving the GB fracture resistance.This study provides new insight into the influence mechanism of GB chemistry on fracture behavior,and yields a systematic strategy and criterion,from the atoms and electrons level,forward in the design of high-performance materials with enhanced GB fracture resistance.

Scintillations of optical vortex in randomly inhomogeneous medium

The comparative numerical and analytical analysis of scintillation indices of the vortex Laguerre–Gaussian beam and the nonvortex doughnut hole and Gaussian beams propagating in the randomly inhomogeneous atmosphere has been performed. It has been found that the dependence of the scintillation index at the axis of the optical vortex on the turbulence intensity at the path has the form of a unit step. It has been shown that the behavior of scintillations in the cross sections of vortex and nonvortex beams differs widely. Despite the scintillation index of vortex beams has been calculated only for the simplest LG10 mode, the obtained results are quite general, because they demonstrate the main properties inherent in scintillations of vortex beams of any type.

A numerical study of shock-interface interaction and prediction of the mixing zone growth in inhomogeneous medium

The growth of mixing zone on an interface induced by Richtmyer-Meshkov(RM)instability occurs frequently in natural phenomena and in engineering applications.Usually,the medium on which the RM instability happens is inhomogeneous,the effect of medium inhomogeneity on the growth of the mixing zone during the RM instability is still not clear.Therefore,it is necessary to investigate the RM instability in inhomogeneous medium.Based on a high-order computational scheme,the interactions of a density interface with an incident shock wave(ISW)in inhomogeneous medium are numerically simulated by solving the compressible Navier-Stokes equations.The effect of the inhomogeneity on the interface evolution after the passage of ISW through the interface is investigated.The results show that the interface morphology develops in a distinctive "spike-spike"structure in inhomogeneous medium.Particularly,the spike structure on the bottom of the interface is due to the reverse induction of RM instability by curved ISW or reflected shock wave.With the increase of inhomogeneity,the growth rate of the mixing zone width on interface increases,and the wave patterns caused by interaction between the shock wave and interface are more complex.Compared with RM instability in homogeneous medium,the inhomogeneous distribution of the density in medium further enhances the baroclinic effect and induces larger vorticity in flow field.Therefore,the interface is stretched much more significantly under the induction of enhanced vorticity in inhomogeneous medium.Based on above analyses,a model for predicting the growth of mixing zone width on the interface after the passage of ISW is proposed,in order to provide a useful method for evaluations of perturbation growth behavior during the RM instability in inhomogeneous medium.

Simple equivalent systems for GRIN lenses in inhomogeneous medium

Simple single-lens equivalent systems for graded-index （GRIN） lenses in inhomogeneous medium obtained using matrix optics are proposed in this letter. Due to its simplicity, the equivalent optical system enables quick analysis of the imaging properties of GRIN lens rod immersed in inhomogeneous medium. This facilitates the optical analysis of complicated optoelectronics systems in inhomogeneous medium utilizing GRIN lens rods.

基于随机介质理论的热障涂层随机孔隙模型构建

基于随机介质理论、采取统计学方法,将热障涂层(TBCs)中孔隙和裂纹引起的局部密度和弹性模量起伏用空间自相关函数及某些统计参数来描述,借助极值搜索法对连续随机介质模型进行改造,并针对涂层孔隙率及各向异性取向等进行模型参数优化,提出并建立了TBCs随机孔隙模型。将模型模拟结果与ZrO2涂层SEM观察结果进行对比表明,所建立的模型能够较好地描述热障涂层中的孔隙、裂纹形貌特征。本研究对于确定TBCs孔隙特征与涂层性能的理论关系以及涂层性能计算研究具有较大意义。

长白山天池火山区介质非均匀性

高频S波随着传播距离的增大其均方根(RMS)包络逐渐变宽,我们把这种现象称为S波包络展宽现象.S波传播路径上随机分布的非均匀体对S波的多次前向散射和绕射作用是导致S波包络展宽现象的主要原因,因此可用S波包络展宽现象来研究介质非均匀性.本文采用S波包络峰值延时来对S波包络展宽现象进行量化.S波包络峰值延时定义为S波初至与其均方根包络峰值最大值之间的时间差.本文选用长白山天池火山区的小震记录,运用S波包络峰值延时对长白山天池火山口地区的介质非均匀性进行了评价.结果发现长白山天池火山区呈现强烈的介质非均匀性,在0-2 km深度范围内介质非均匀性表现出南部强北部弱的空间分布特征;在2-5 km深度范围内介质非均匀性的空间分布特征与频率具有相关性;天池火山区介质非均匀性具有明显的多尺度特性;强弱非均匀性接触带,往往是地震频发地带.根据地震与非均匀体在空间分布的相对位置,我们认为火山区介质非均匀性可能反映了火山早期喷发堆积物介质结构的差异.

非均匀P-偏振电磁波在导电界面的类全反射横向偏移

利用非均匀P-偏振电磁波(电场平行于入射面)在导电界面反射系数所产生的附加相角导出了非均匀电磁波在导电介质界面的横向偏移,并给出了一个低频电磁波算例,绘制了横向偏移随入射角的变化曲线.计算结果表明,入射角在相移常数临界角、衰减常数临界角和90°处,横向偏移曲线存在三个间断点;当入射角等于这三个角时,电磁波将沿界面传播;当入射角在这三个角附近时,横向偏移效应影响较大;在其他角度入射时横向偏移与波长在一个数量级.论文还讨论了横向偏移效应对电磁波测井测量结果所产生的误差,并给出了误差计算方法和算例.

非均匀电磁波在导电媒质界面反射的横向偏移

由电磁场边值关系给出了非均匀电磁波在导电媒质界面反射时反射系数所产生的附加相角.利用这一附加相角导出了非均匀电磁波在导电介质界面的横向偏移,并进行了横向偏移的相关计算,绘出了横向偏移随入射角的变化曲线.结果表明:在导电媒质界面反射电磁波的横向偏移随入射角的增大而增大,当入射角接近90°时,电磁波在界面要传播较长时间后才返回第一种媒质.在同一入射角电场偏振化方向在入射面的电磁波要比电场偏振化方向垂直于入射面的电磁波的横向偏移大,随着电磁波频率的增加横向偏移变小.

电场垂直入射面的非均匀电磁波在导电媒质界面的类全反射横向偏移

利用电磁波在导电媒质界面反射系数的附加相角,导出了电场垂直于入射面的非均匀电磁波在导电介质界面的类全反射横向偏移,并对横向偏移进行了相关计算,绘出了横向偏移随入射角的变化曲线.结果表明:入射角在相移常数临界角、衰减常数临界角和90°处,横向偏移曲线存在三个间断点.当入射角等于这三个角时,横向偏移为无穷大,即电磁波将沿界面传播;当入射角在这三个角附近时,横向偏移变得非常大.

非均匀介质的光学常数

提出了一种计算非均匀介质光学常数的新方法,该方法仔细地考虑了光在非均匀介质中的吸收和散射.研究了非均匀介质层的厚度、介质中颗粒粒径、衬底反射性能等对介质光学常数的影响.这种研究将有利于同有关的测量实验结合和比较.