Multi-variable special polynomials using an operator ordering method

Using an operator ordering method for some commutative superposition operators, we introduce two new multi-variable special polynomials and their generating functions, and present some new operator identities and integral formulas involving the two special polynomials. Instead of calculating complicated partial differential, we use the special polynomials and their generating functions to concisely address the normalization, photocount distributions and Wigner distributions of several quantum states that can be realized physically, the results of which provide real convenience for further investigating the properties and applications of these states.     

Finite element modelling of natural-convection-controlled change of phase

The problem of phase change in the presence of natural convection has been investigated. A model has been proposed based on the treatment of the release/absorption of latent heat as a heat source/sink in combination with the standard Galerkin finite element method with a primitive variable formulation on a fixed grid. To demonstrate the capabilities of the model, three cases of phase change of an aluminium alloy in the presence of natural convection arc considered, i.e. solidification, melting and combined solidification and melting. The solidification of water in a square cavity is modelled as another example, taking into account the density extremum, and the results are compared with a previously published work.     

折衍混合复消色差望远物镜设计的PWC方法

将衍射结构视为折射率无限大的薄透镜,研究了衍射透镜高折射率表示的折衍混合复消色差望远物镜设计的PWC方法;设计了焦距为2000mm、相对孔径为1/15的双片型折衍混合复消色差望远物镜,并与常规三片型纯折射复消色差望远物镜进行了比较,结果表明双片型折衍混合复消色差望远物镜具有更好的二级光谱校正能力,色球差更小,因此具有更好的成像质量.     

方形自聚焦透镜的研制

经过方形玻璃丝的加工、离子交换及成品的精密加工等过程,成功制出了方形自聚焦透镜.并采用聚焦成像和雅明干涉等方法对其光学特性进行测试,得出了方形自聚焦透镜本身所具有的一些特性：中心部分畸变较小,成像性能好;四个棱角内的球差较大,像质较差;折射率分布不具有旋转对称性,而是与方向和半径有关.     

流-固界面波的激光激发与光偏转检测

基于光偏转原理,研制了可用于流-固界面波探测的光纤传感装置.在此基础上,建立了以调Q Nd∶YAG激光为流-固界面波激发光源的实验系统.实验上探测了激光在空气-铝、水-铝和酒精-铝等界面上激发的界面波波形.根据实验波形,算得在这三种界面上的泄漏Rayleigh波和Scholte波的速度分别为2889 m/s和339 m/s、2916 m/s和1512 m/s、2872 m/s和1184 m/s,此实验值与理论计算值相比,偏差小于5％.     

混合纤芯光子晶体光纤超平坦色散的研究

利用平面波展开法,系统地研究了一种具有混合纤芯结构的光子晶体光纤的色散特性. 数值计算结果表明,通过优化结构参量,这种新型结构的光子晶体光纤在通信窗口1.55 μm 附近可以获得带宽超过800 nm的超平坦色散区域（色散曲线的变化范围不超过 ±0.6 ps·km－1·nm－1）.     

连续梁在周期荷载下的动力稳定性简化分析方法

对于一般任意支撑的连续梁结构动力稳定性问题,已有的计算方法求解过程都很复杂,给工程设计带来极大的不便．本文提出了一个简化的分析方法,利用现有的商业软件,只需求得连续梁的自然频率及静力屈曲（失稳）荷载,就可容易得到结构的动力失稳区域,当考虑结构阻尼对不稳定区域的影响时,可将阻尼矩阵表达为Rayleigh阻尼的形式．研究结果表明：采用本文计算方法与已有的理论计算方法得到的连续梁主参数共振的不稳定边界非常吻合,而本文计算方法更为简单,计算结果可靠,计算精度高,可满足工程设计的需要．     

Numerical approach for generic three-phase flow based on cut-cell and ghost fluid methods

In this paper, we introduce numerical methods that can simulate complex multiphase flows. The finite volume method, applying Cartesian cut-cell is used in the computational domain, containing fluid and solid, to conserve mass and momentum. With this method, flows in and around any geometry can be simulated without complex and time consuming meshing. For the fluid region, which involves liquid and gas, the ghost fluid method is employed to handle the stiffness of the interface discontinuity problem. The interaction between each phase is treated simply by wall function models or jump conditions of pressure, velocity and shear stress at the interface. The sharp interface method “coupled level set (LS) and volume of fluid (VOF)” is used to represent the interface between the two fluid phases. This approach will combine some advantages of both interface tracking/capturing methods, such as the excellent mass conservation from the VOF method and good accuracy of interface normal computation from the LS function. The first coupled LS and VOF will be generated to reconstruct the interface between solid and the other materials. The second will represent the interface between liquid and gas.     

THE DETERMINATION OF THE COMPUTATIONAL DEGREES OF FREEDOM OF BAR SYSTEMS1)

为了简化和统一结构力学教材中杆件体系计算自由度$W$的算法,本文提出了“直接法”。该方法以相邻节点间的杆件和结点为分析对象,对于含$m$根杆件、$g$ 个单刚结点和$h$个单铰结点的平面杆件体系,直接法给出计算自由度公式$W=3m-(3g+2h$)。相比于已有方法,直接法研究对象清晰,数学运算统一,适合于编程计算,便于初学者准确而快速计算复杂体系的$W$;也为结构超静定次数的确定提供了一种简单有效的数值算法。     

A STUDY OF LOW CYCLE FATIGUE PROPERTIES OF MATERIALS BASED ON THE FUNNEL-SHEET SPECIMENS1)

根据能量等效方法,针对漏斗薄片试样,提出了关联Ramberg-Osgood 幂律参数、试样几何参数的载荷-位移半解析统一模型。采用有限元数值模拟,正、反向验证了该模型的有效性。在此基础上,提出了通过漏斗薄片试样低循环试验实现材料低周疲劳性能的预测方法。基于薄片试样低循环试验数据,完成了SS316L, N18及SAPH440 三种材料的低周疲劳性能预测,预测结果与标准试样试验结果具有良好的一致性。并利用该方法完成了N18与SAPH在不同温度条件下的低周疲劳性能预测。