Pulsatile flow between permeable beds

Pulsatile flow of a viscous fluid between two permeable beds is analyzed. The flow between and through the permeable beds are governed by the Navier-Stokes equations and Darcy's law, respectively. The velocity field and the volume flux are obtained for several cases and discussed. Further, when the permeability parameter k→0, the results agree with those of Wang (J. Appl. Mech. 38 (1971) 553).     

A volume integral equation method for periodic scattering problems for anisotropic Maxwell's equations

This paper presents a volume integral equation method for an electromagnetic scattering problem for three-dimensional Maxwell's equations in the presence of a biperiodic, anisotropic, and possibly discontinuous dielectric scatterer. Such scattering problem can be reformulated as a strongly singular volume integral equation (i.e., integral operators that fail to be weakly singular). In this paper, we firstly prove that the strongly singular volume integral equation satisfies a Gårding-type estimate in standard Sobolev spaces. Secondly, we rigorously analyze a spectral Galerkin method for solving the scattering problem. This method relies on the periodization technique of Gennadi Vainikko that allows us to efficiently evaluate the periodized integral operators on trigonometric polynomials using the fast Fourier transform (FFT). The main advantage of the method is its simple implementation that avoids for instance the need to compute quasiperiodic Green's functions. We prove that the numerical solution of the spectral Galerkin method applied to the periodized integral equation converges quasioptimally to the solution of the scattering problem. Some numerical examples are provided for examining the performance of the method.     

体积差的等周不等式

首次提出并建立了凸体的体积差函数的等周不等式,它是经典等周不等式的推广.作为应用,对星体建立了体积差函数的对偶等周不等式和广义对偶等周不等式.     

Direct numerical simulation of thermocapillary flow based on the Volume of Fluid method

A numerical method for direct simulation of thermal Marangoni effects at dynamically deformable interface of two-phase incompressible fluids is developed. The approach is based on the Volume of Fluid (VOF) method with special focus on the numerical treatment of the temperature surface gradient because of its decisive role as the driving force of the flow. The surface gradient calculation is split into computing its length and direction in order to satisfy the correct thermal boundary condition at the interface without losing mobility of the interface. The method is applied to three different types of thermocapillary flow, namely thermocapillary migration of a droplet in an ambient fluid with linear temperature gradient, thermocapillary convection in a liquid layer under linear temperature gradient along the interface, and Marangoni convection due to Bénard–Marangoni instability. In the first case, different aspects of the dynamics of the migration are considered for validation such as the terminal migration velocity, the initial acceleration and quantification of the wall effects. The simulation also considers high convective heat transfer and covers a wide range of Marangoni numbers up to 5000, where good agreement with both theoretical and experimental results is achieved. In the second case, the convection velocity in the liquid layer is compared with an analytical result. In the final application, pattern formation due to the Bénard–Marangoni instability in a liquid layer in square geometry of small aspect ratio is investigated for realistic Biot number and dynamically deformable fluid interface. The results show good agreement with experiments from literature, where our numerical simulation also predicts cell pattern for a particular aspect ratio which is outside the limitation of the above cited experimental work.     

对合理确定考试题量的探讨

本文根据抽样理论对考试题量从考试实质、影响试题量的因素、建立题量的数学模型及题量计算等几方面进行了讨论和研究。     

体积相位全息光栅的设计与制备

本文指出全息干版薄膜在曝光后处理过程中的收缩性和折射率变化对制备全息光栅的周期、倾斜度、布喇格入射角及衍射角的影响问题,并根据实验数据对光栅设计进行修正,再结合Kogelnik衍射方程及折射率调制度和曝光量的线性关系,在实验中基本上能准确设计出指定周期、倾斜度和衍射效率的全息光栅。     

4维完备Einstein流形的一些注释

本文给出了在开的定向的4维流形上存在有界曲率的完备Einstein度量的障碍．     

298.15K下ccl4在CH3OH—C6H6混合物中的偏摩尔体积

有若干原因促使人们使用混合溶剂,例如对溶解度的技术要求,欲改变溶剂的介电常数,都常常改变溶剂的组成。人们研究溶剂结构及其对溶质性质的影响,则把潜溶剂加入水中就会对溶剂的结构产生影响。关于混合溶剂中各种化学问题的讨论,都必须考虑组份内和组份间的这两种相互作用,体积函数比较直观,有助于对其它偏摩尔数量的理解。近年来,由于商品密度计的开发,对溶液密度的直接测量前进了一步,此种密度计仅需要较小体积的溶液和提供了10~(-6)(克)的准确度。本文采用“高精度读数式液体流动密度计”,测定四氯化碳在甲醇—苯体系中偏摩尔体积。以第三组分在二元混合物中偏摩尔性质变化,探讨三元系中分子间相互作用和机理。     

Auto LISP语言在轴对称类锻件体积计算中的应用

本文介绍了用ＡｕｔｏＬＩＳＰ语言编程计算轴对称类锻件的体积。该程序应用ＡｕｔｏＬＩＳＰ函数对ＡｕｔｏＣＡＤ实体图形的访问功能，自动检索轴对称锻件半个轴截面轮廓的数值，代入公式计算体积。程序运行时无需人工干预。程序简单、实用。     

一个单形问题的矩阵证明

本文利用“磨光变换”的思想和矩阵方法证明了:在表面积为一定的一切n维单形(n≥2)中以正则单形的体积为最大。