Extended Symmetry of Generalized Variable-Coefficient Kadomtsev-Petviashvili Equation

In this paper, the extended symmetry of generalized variable-coeFficient Kadomtsev-Petviashvili （vcKP） equation is investigated by the extended symmetry group method with symbolic computation. Then on the basis of the extended symmetry, we can establish relation among some different kinds of vcKP equations. Thus the exact solutions of these veKP equations can be constructed via the simple veKP equations or constant-coefficient KP equations.     

基于点插值的配点型无网格法解Helmholtz问题

基于点插值法的思想,用三角函数作为基函数在局部支持域内构造具有Kroneckerδ函数性、单位分解性、高阶连续性、再生性和紧支性的形函数.用配点法离散微分方程,得到了具有稀疏带状性的系数矩阵,用GMERS方法求解代数方程组,分别研究了Helmholtz问题的边界层问题和波传播问题.通过数值算例可以发现,给出的数值结果非常接近于精确解,且随着节点的增加,其精确度越来越高,具有良好的收敛性.     

锐钛矿二氧化钛纳米颗粒水热结晶过程研究

以钛酸四丁酯(TBOT)为钛源,氨水为矿化剂,在水热条件下,反应结晶制备锐钛矿TiO2纳米颗粒.并对锐钛矿TiO2进行X射线衍射(XRD)、拉曼光谱(Raman)、扫描电子显微镜(SEM)、投射电子显微镜(TEM)表征,分析其物相组成及形貌.结果表明,反应时间是锐钛矿TiO2形成和生长控制的关键因素.利用JMA方程对锐钛矿TiO2结晶生长进行动力学分析.结果表明,随着钛源浓度增加,Avrami指数n逐渐变大.     

水热法制备钛酸铋钠粉体及其生长机理研究

以钛酸四丁酯Ti(OC4H9)4和五水硝酸铋Bi(NO3)3·5H2O为原料,NaOH为矿化剂,通过水热法制备钛酸铋钠(Na0.5Bi0.5TiO3)粉体.通过X射线衍射仪(XRD)、扫描电子显微镜(SEM)、透射电子显微镜(TEM)对反应制备的粉体进行物相分析.结果表明,反应温度、反应时间及矿化剂浓度均是影响钛酸铋钠粉体制备的关键因素.利用JMA方程对其进行动力学计算分析,结果表明,在反应温度为120～ 180℃时,NBT颗粒的Avrami指数n随温度的升高而减小,而反应速率k则相反,反应活化能Ea为50.14 kJ·mol-1.     

MEMS稀薄气体内部流动模拟中的信息保存法

首先综述了处理低速稀薄气体流动的一些方法: 线化Boltzmann方程方法、Lattice Boltzmann方法(LBM)、加滑移边界的Navier-Stokes方程、以及DSMC方法, 并讨论它们在模拟MEMS中过渡领域低速流动特别是内部流动所遇到的困难, 其中表明了LBM现有方案不适合模拟过渡领域中的MEMS流动问题. 信息保存(IP)法通过保存一个模拟分子所代表的大量分子的平均信息,克服了流速低使得信息噪声比小而引起统计模拟的困难. 本文给出了方法的一些理论证实. MEMS中内部流动的特点, 即流速低和大的长宽比的特点, 引起椭圆性问题, 即出入口边界条件相互影响需要协调的问题. 通过对(长约几千微米的)微槽道流动应用IP方法的算例,演示了采用守恒形式的质量守恒方程和超松弛法可成功地解决这一问题. 借助同样的方法,用IP方法求解了真实长度(1\,000\,$\mu$m)硬盘驱动器读写头在过渡领域的薄膜支撑问题, 压力分布与具有严格气体动理论基础的概括化Reynolds方程完全相符, 而在此之前, DSMC方法只对短的读写头(5\,$\mu$m)与Reynolds方程做了校验. 作者建议将原来用于求解读写头润滑问题的Reynolds方程退化来求解过渡领域中的微槽道流动问题, 从而提供了一个有严格气体动理论品性的检验方法来验证求解MEMS内部流动的各种方法.      

New Exact Solutions to （2＋1）-Dimensional Variable Coefficients Broer-Kaup Equations

In this paper, using the variable coefficient generalized projected Rieatti equation expansion method, we present explicit solutions of the （2＋1）-dimensional variable coefficients Broer-Kaup （VCBK） equations. These solutions include Weierstrass function solution, solitary wave solutions, soliton-like solutions and trigonometric function solutions. Among these solutions, some are found for the first time. Because of the three or four arbitrary functions, rich localized excitations can be found.     

Integrating Factors and Conservation Theorems of Lagrangian Equations for Nonconservative Mechanical System in Generalized Classical Mechanics

The conservation theorems of the generalized Lagrangian equations for nonconservative mechanical system are studied by using method of integrating factors. Firstly, the differential equations of motion of system are given, and the definition of integrating factors is given. Next, the necessary conditions for the existence of the conserved quantity are studied in detail. Finally, the conservation theorem and its inverse for the system are established, and an example is given to illustrate the application of the result.     

A Secondary Operator Ordering Problem for a Charged Rigid PlanarRotator in Uniform Magnetic Field

When the motion of a particle is constrained, an excess term exists using hermitian form of Cartesian momentum pi(i= 1, 2, 3) in usual kinetic energy (1/2μ)∑Pi^2, and the correct kinetic energy turns out to be (1/2μ)∑(1/fi)pifipi, where the fi are dummy factors in classical mechanics and nontrivial in quantum mechanics. In this paper the explicit form of the dummy functions f i is given for a charged rigid planar rotator in the uniform magnetic fieM.     

A Generalized F-expansion Method and Its Application in High-Dimensional Nonlinear Evolution Equation

A generalized F-expansion method is introduced and applied to （3＋1 ）-dimensional Kadomstev-Petviashvili（KP） equation. As a result, some new Jacobi elliptic function solutions of the equation are found, from which the trigonometric function solutions and the solitary wave solutions can be obtained. The method can also be extended to other types of nonlinear evolution equations in mathematical physics.     

Giant Vortex States in a Long Superconducting Cylinder with a Hole in Center

We have theoretically studied the nucleation of superconductivity in doubly connected superconductors in the form of long superconducting cylinders. The giant vortex states are investigated with the nonlinear Ginzburg-Landau theory. The solutions of Ginzburg-Landau equations are solved numerically with relaxation method. The quantum size effect is clearly shown through the calculation of free energy.