Finite element method for strong reflection of water waves

In this study, the propagation of monochromatic water waves over an arbitrarily varying topography is numerically investigated. A finite element model is developed by formulating the diffraction of waves caused by depth changes. Not only the propagating mode but also the evanescent modes are included in the model. The model developed is applied to the study of strong reflection of monochromatic waves over a sinusoidally varying topography. Predicted reflection coefficients are compared with those of available laboratory experiments and the eigenfunction expansion method. A very good agreement is observed.     

Two-dimensional scattering and diffraction of P- and SV-waves around a semi-circular canyon in an elastic half-space: An analytic solution via a stress-free wave function

A well-defined boundary-valued problem of wave scattering and diffraction in elastic half-space should have closed-form analytic solutions. This two-dimensional (2-D) scattering around a semi-circular canyon in elastic half-space subjected to seismic plane and cylindrical waves has long been a challenging boundary-value problem. In all cases, the diffracted waves will consist of both longitudinal (P-) and shear (S-) rotational waves. Together at the half-space surface, these in-plane longitudinal P- and shear SV-waves are not orthogonal over the infinite half-space flat-plane boundary. Thus, to simultaneously satisfy both the zero normal and shear stresses at the flat-plane boundary, some approximation of the geometry and/or wave functions often has to be made, or in some cases, relaxed (disregarded). This paper re-examines this two-dimensional (2-D) boundary-value problem from an applied mathematics points of view and redefines the proper form of the orthogonal cylindrical-wave functions for both the longitudinal P- and shear SV-waves so that they can together simultaneously satisfy the zero-stress boundary conditions at the half-space surface. With the zero-stress boundary conditions satisfied at the half-space surface, the most difficult part of the problem will be solved, and the remaining boundary conditions at the finite-canyon surface are then comparatively less complicated to solve. This is now a closed-form analytic solution of the 2-D boundary-valued problem satisfying the half-space zero-stress boundary conditions exactly.     

稳定电流场的反射、透射、衍射——波动性

稳定电流场是否有反射、透射现象,它们服从什么规律,以及稳定电流场是否具有波动性等问题,本文将予以探讨。 一、稳定电流场的反射与透射 在用“电像法”解点电流源平界面问题时,一般用反射、透射的概念,并用虚源等效地代替界面,指的是全界面的、源的“反射”与“透射”,要求界面为无限平面,其结果没有普遍性。因此,尚不能当作一般的物理规律来看待。从弹性波与稳定电流场的类比中,有人曾     

基于麦夸特算法的X射线衍射物相定量分析的影响因素研究

X射线衍射物相定量分析方法很多,新近提出的麦夸特算法(Levenberg-Marquardt)在XRD物相定量分析中具有明显的优势,但在实际应用过程中,哪些因素会对该方法计算结果的准确度产生影响仍不清楚。为了指导实际操作过程并提高麦夸特算法在X射线衍射物相定量分析中的准确度和处理效率,本研究通过Matlab软件,将已知配比含量的刚玉、石英、方解石和钠长石与其计算值进行比较,探讨衍射峰强度、衍射峰背底、样品数量等因素对麦夸特算法应用于X射线衍射物相定量分析中计算结果的影响。结果表明:通过前三强峰法的计算结果比通过最强峰法的计算结果具有更高的准确度;由于物相晶体结构及衍射特性的差异,衍射峰背底对不同物相定量结果的影响程度各异,扣除背底后各物相计算结果的准确度整体上都有不同程度的提高;在利用麦夸特算法进行批量分析过程中,当样品数低于一定阈值时,样品数越多,计算结果的准确度提高越明显,但当计算的样品超过一定阈值时准确度不会有明显的提高。     

亮点周围的衍射模式

将衍射问题研究中的回波解析奇性归结为探讨含参量的振荡积分的渐近性态问题,并利用广义函数的算子理论,以十分简捷的方式给出了上述振荡积分的稳定位相公式,以及结合Ｔｈｏｍ理论逐一地算出非退化奇点、岐点和脐点周围的衍射模式．     

尾矿的砷污染试验研究及治理措施

金矿尾矿是砷污染的重要来源,不同冶炼工艺形成的尾矿中砷的赋存状态有很大差异,不同的砷形态会直接影响其在环境中的迁移转化行为,确认砷的存在形态是修复砷污染场地研究中的重要内容。本文针对浮选法和生物氧化法两种不同浸金方法的尾矿,采用pH计和氧化还原电位自动测定仪测量尾矿的物理性质（pH、氧化还原电位）,采用X射线衍射和X射线荧光光谱分析尾矿的矿物物相和主要成分,电子探针分析砷的存在形态。表征结果表明,浮选法尾矿和生物氧化法尾矿的物理性质都会因堆置环境的变化而变化,其Eh、pH和零电荷点都大致相同,pH≈8.5,样品零电荷点（pH_PZC）大约为8.5。由于两种尾矿都属于碱性环境,因此在修复方法的选择上也受到限制,如只适合在酸性条件下进行的电动修复法就不适用于这两种尾矿,修复试剂的选择也以碱性物质和铁的氧化物（氢氧化物）为主。浮选法尾矿的主要矿物类型为石英、白云石和黏土矿物,化学主要成分是Si和Al,尾矿呈灰白色,其中砷的含量约为754 μg/g左右,主要以毒砂（FeAsS）形式存在;而生物氧化法尾矿的主要矿物类型为石膏,化学主要成分是Fe、Ca和S,尾矿呈红棕色,其中砷的含量约为26350 μg/g,主要以毒砂（FeAsS）和五氧化二砷（As₂O₅）形式存在。两种浸金工艺每一道工序的不同,都会造成两种尾矿在矿物相、主要成分和其中砷存在形态上的差异。因此在进行尾矿原位修复工作时,应考虑不同浸金方法对尾矿堆置环境和砷存在形态的影响,从而选择出一种更加合适、廉价、高效的修复方法和试剂。

     

应用X射线衍射-红外光谱等技术研究滑石在机械力研磨中的形貌和晶体结构变化及影响机制

滑石的颗粒粒径、形貌、晶型等对其应用的实效性、终端产品的性能产生极大影响,目前主要研究其表面改性,而有关微观形貌及晶体结构研究较少。本文利用X射线荧光光谱、X射线衍射分析、红外光谱、粒度分析仪结合高分辨场发射扫描电镜(FE-SEM)技术对辽宁滑石粉在高强度机械力研磨作用下的微形貌和晶体结构变化特征进行系统研究。结果表明滑石粉原矿混合物中MgO与SiO2的分子个数比约为0.45,该数值明显低于纯滑石粉晶体中MgO与SiO2的分子个数比0.75。此类滑石为典型的单斜晶系,研磨作用使滑石粉由晶态转变为非晶态结构,其层状结构的有序化和键合作用发生了明显的变化。滑石粒度随研磨时间变化呈现减小-增大-减小的循环过程。研磨后粉体形貌存在差异,细化的小颗粒粉体因团聚而呈"准球体",且随着研磨的进行出现细化-团聚-细化的反复过程。此结论对于滑石的深加工与应用及其相关矿物粉体的研究具有一定的参考价值。     

Simulation of diffraction of ocean waves by a submerged sphere in finite depth

Based on the linear diffraction theory, an investigation is made on the interaction of water waves with a completely submerged sphere in water of finite depth in this paper. The method of multipole expansions is used to obtain the fluid velocity potential in the form of double series of the associated Legendre functions with the unknown coefficients of the infinite set of infinite matrix equations. The truncation property of the matrices and the convergence of the multipole series coefficients are investigated for various wavelengths and depths. The systematic numerical simulation, based on our analytical solution, is carried out and the fields of the hydrodynamic diffraction pressure and fluid velocity around the sphere, the three-dimensional free surface elevation, and total exciting forces acting on the sphere are graphically presented for a wide range of the body submergences, ocean depths and wavelengths.     

Nonlinear wave interaction with a vertical circular cylinder: wave forces

Second-order wave forces on a large diameter vertical circular cylinder, computed according to a semi-analytic nonlinear diffraction theory, are compared to results of 22 laboratory experiments with regular waves. In general, predicted forces agree quite well with measured forces. In most tests, both measured and predicted maximum forces exceeded linear theory by 5 to 15%. In a few cases, however, the measured forces were less than those predicted by linear theory, in contrast to the second-order predictions. It is shown that these results are related to the phasing of various linear and nonlinear wave force components, and are consistent with those obtained by other investigators.     

广义散射层析成像反演

本文详细地给出了基于非均匀介质的体散射广义散射层析成像反演的基本理论.广义散射层析成像反演可以描述为波场的反向传播和对成像场进行局部波数域滤波的过程.在数值算例中,利用背景速度沿深度方向均匀变化的v（z）介质中的简单的方块作为速度异常体的模型,通过对该模型产生的低频的Born数据和声波的正演数据的测试,在对采集系统进行有限频率带宽和空间孔径的校正来进行局部成像矩阵谱的恢复中,可以看出模型中各点的谱在恢复后的质量无论从覆盖的面积范围还是幅值的均一性上都有着明显的提高;在对速度模型的重建中,广义散射层析成像反演能够很好地恢复速度模型的低频分量,即便是方块速度异常体相对于背景速度的平均速度扰动是23%也能很好地重建模型中的速度,且对于不同的背景速度模型基本上都能很好地恢复Marmousi速度模型的低频分量.所以该方法将基于Born模型的层析成像反演适应范围进行了一定程度的扩展.