Calculating pure rotational transitions of water molecule with a simple Lanczos method

We have calculated pure rotational transitions of water molecule from a kinetic energy operator (KEO) with the z-axis perpendicular to the molecular plane. We have used rotational basis functions which are linear combinations of symmetric top functions so that all matrix elements are real. The calculated spectra agree well with the observed values.     

玻色-爱因斯坦凝聚体中的超流现象

在玻色-爱因斯坦凝聚(BEC)的超流现象的研究中,人们通常采用平均场近似下求解Gross-Pitaevskii方程的方法,我们采用更严格的准确对角化的方法对弱排斥相互作用下两维旋转N-Boson体系的凝聚状态进行了研究.研究表明,弱相互作用下的基态并不是人们通常认为的单一凝聚态,而是一个碎裂凝聚态.通过碎裂态能谱与平均场方法给出的能谱之间的比较以及条件几率分布函数的计算,我们指出这种碎裂凝聚态有着内在的不稳定性,很容易破缺到一个单一凝聚状态;计算给出的条件几率分布可以用来揭示破缺后的状态,其分布图案与平均场近似下所得到的涡旋图形相类似.我们进一步注意到过去研究工作主要集中在弱相互作用极限下和强相互作用Thomas-Fermi近似极限下这两种极端情况.为考察两种极限间的中间过渡区域,我们研究了中等相互作用强度下体系的基态性质.     

基于接触有限元方法的镜面面形仿真技术研究

为考察在外载作用下某镜体镜面面形的变化是否满足设计要求,研究在预紧力及重力作用下镜面面形的变化规律,使用接触非线性有限元方法对镜体组件进行了仿真,采用基于Zernike多项式的光机集成仿真接口程序对面形数据进行了处理,得到了消除刚体位移后表征面形变化的参数和表示刚体位移系数的分布曲线。结果表明在预紧力和重力作用下刚体位移明显,镜面平移占据了刚体位移的主要方面,基于集成仿真技术的面形处理程序可有效地消除刚体位移;预紧力存在在不同方向重力作用下对面形的影响略有不同,与预紧力相比,重力作用对面形的影响较小。在预紧力作用下面形仿真数据对于镜体设计、装调具有一定指导意义,也说明基于接触方法面形仿真的工程适用性。     

基于预条件LANCZOS算法快速实现三维地电场正演计算

针对三维地电场正演计算过程中形成的超大规模稀疏线性方程组,采用不完全Cholesky分解方法进行预条件处理,经过条件数改善后形成的新线性方程组的系数矩阵变为一个近似的单位矩阵,再应用Lanczos算法将会提高数值计算的稳定性,加快迭代收敛的速度,通常在迭代次数远小于系数矩阵阶数时就能得到较好精确解的近似值,为下一步的电阻率三维反演计算打下了非常好的基础.     

载流子与铁磁物质耦合系统的严格对角化解与相干态变分方法

引用Schwinger的角动量谐振子理论将载流子与铁磁物质耦合系统变换为载流子与两类玻色子耦合的问题，对铁磁物质中束缚极化子的存在决定于介质中有无杂质势的规律进行了严格对角化求解. 得到的结论与普遍的看法一致，与相干态变分方法计算的基态能结果十分吻合，两种方法得到的波矢定性上也吻合，说明了相干态变分方法的可靠性和有较高的准确性，严格对角化解方法也可为其他的近似方法提供检验基础.     

玻色-爱因斯坦凝聚体中的超流现象

在玻色－爱因斯坦凝聚（BEC）的超流现象的研究中，人们通常采用平均场近似下求解Gross-Pitaveskii方程的方法，我们采用更严格的准确对角化的方法对弱排斥相互作用下两维旋转N－Boson体系的凝聚状态进行了研究，研究表明，弱相互作用下的基态并不是人们通常认为的单一凝聚态，而是一个碎裂凝聚态，通过碎裂态能谱与平均场方法给出的能谱之间的比较以及条件几率分布函数的计算，我们指出这种碎裂凝聚态有着内在的不稳定性，很容易破缺到一个单一凝聚状态；计算给出的条件几率分布可以用来揭示破缺石的状态，其分布图案与平均场近似下得到的涡旋图形相类似，我们进一步注意到过去研究工作主要集中在弱相互作用极限下和强相互作用Thomas-Fermi近似极限下这两种极端情况，为考察两种极限间的中间过渡区域，我们研究了中等相互作用强度下体系的基态性质。     

Recursive method for opacity expansion at finite temperature

Using a reaction operator approach,we derive the multiple-scattering induced gluon number distribution function to all orders in powers of opacity at finite temperature.The detailed balance effect is analyzed by taking into account both gluon emission and absorption in a thermal medium.We also calculate virtual corrections and show that the infrared divergence cancels out in the gluon distribution function at finite temperature.     

Recursive method for opacity expansion at finite temperature

Using a reaction operator approach, we derive the multiple-scattering induced gluon number distribution function to all orders in powers of opacity at finite temperature. The detailed balance effect is analyzed by taking into account both gluon emission and absorption in a thermal medium. We also calculate virtual corrections and show that the infrared divergence cancels out in the gluon distribution function at finite temperature.     

基于时域有限差分法的势垒透射过程的蒙特卡罗模拟

采用时域有限差分法,计算势垒透射过程中电子波的波函数和概率密度.根据蒙特卡罗随机方法,以随机点的密集程度代表概率密度的大小,模拟势垒透射的动态过程.     

Discrete ordinate method with a new and a simple quadrature scheme

Evaluation of the radiative component in heat-transfer problems is often difficult and expensive. To address this problem, in the recent past, attention has been focused on improving the performance of various approximate methods. Computational efficiency of any method depends to a great extent on the quadrature schemes that are used to compute the source term and heat flux. The discrete ordinate method (DOM) is one of the oldest and still the most widely used methods. To make this method computationally more attractive, various types of quadrature schemes have been suggested over the years. In the present work, a new quadrature scheme has been suggested. The new scheme is a simple one and does not involve complicated mathematics for determination of direction cosines and weights. It satisfies all the required moments. To test the suitability of the new scheme, four benchmark problems were considered. In all cases, the proposed quadrature scheme was found to give accurate results.     

New uncertainties in QCD—QED rescaling factors using quadrature method

In this paper we briefly outline the quadrature method for estimating uncertainties in a function which depends on several variables, and apply it to estimate the numerical uncertainties in QCD-QED rescaling factors. We employ here the one-loop order in QED and three-loop order in QCD evolution equations of the fermion mass renormalisation. Our present calculation is found to be new and also reliable when compared to the earlier values employed by various authors     

用不变量方法解具有非线性场和原子与场非线性耦合的Jaynes-Cummings模型

采用Lewis-Riesenfeld不变量方法研究了具有非线性场和任意形式原子与场相互作用的Jaynes-Cummings模型.该模型由于具有超对称代数结构,因此其Hamiltonian量可用超对称算符的线性组合表示.在算符N′的本征值子空间,用生成元算符构造出系统的不变量后,利用不变量方法求得了系统的一般波函数和时间演化算符,同时也计算了原子布居数和光子数的时间演化表达式.     

二维三角格点系统中的拓扑陈数

利用紧束缚模型对二维三角周期格点中各能带的陈数分布进行研究.通过严格对角化方法得到体系能量本征值和对应的本征态,再利用Kubo公式计算出量子化的霍尔电导、态密度及各扩展态对应的陈数.在傅里叶变换下将哈密顿量转换到k空间从而得到体系的能谱分布.研究表明：次近邻格点之间的跳跃积分t'的不同取值影响体系各能带对应的陈数分布,计算得到当t'=1/2时体系三个能带从低到高对应的陈数分布为{-4,5,-1},t'=-1/2时其对应陈数分布变化为{2,-4,2},而t'=±1/4时对应的陈数分布都为{2,-1,-1}.同时发现：能谱帯隙的宽度和对应霍尔平台的宽度一致,并且k空间的能带越平坦,其对应的在霍尔电导跳跃处的态密度峰就越高越尖锐,而该处霍尔电导跳跃就越陡峭.     

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以磁流体理论为基础,采用基于有限体积法的通量差分分裂格式数值求解具有双曲保守律形式的电阻磁流体方程组.编写C++程序对平板几何位形下的等离子体双撕裂模进行了长时间数值模拟,得到双撕裂模不稳定性的演化图景,捕捉到了双撕裂模非线性发展过程中磁场重联的几个典型阶段,讨论了等离子体电阻和两个有理面之间的距离对双撕裂模不稳定性非线性发展的影响.为研究磁流体动力学提供了一种可行的高精度数值算法.     

基于高斯伪谱方法的混沌系统最优控制

针对混沌系统最优控制问题,提出一种基于高斯伪谱方法的数值求解新算法. 首先在勒让德-高斯点上构造Lagrange插值多项式并近似表示混沌系统最优控制中的状态变量和控制变量;接着将连续空间的最优控制问题转化为非线性规划问题;然后通过序列二次规划（SQP）算法获得最优解;最后对三个典型混沌系统的仿真实验结果表明,新方法能有效和快速地实现混沌系统的最优控制. 关键词： 混沌系统 最优控制 高斯伪谱法 非线性规划     

基于有限体积法数值模拟双撕裂模非线性演化

以磁流体理论为基础,采用基于有限体积法的通量差分分裂格式数值求解具有双曲保守律形式的电阻磁流体方程组。编写C++程序对平板几何位形下的等离子体双撕裂模进行了长时间数值模拟,得到双撕裂模不稳定性的演化图景,捕捉到了双撕裂模非线性发展过程中磁场重联的几个典型阶段,讨论了等离子体电阻和两个有理面之间的距离对双撕裂模不稳定性非线性发展的影响。为研究磁流体动力学提供了一种可行的高精度数值算法。     

Buckling analysis of nanobeams with exponentially varying stiffness by differential quadrature method

We present the application of differential quadrature(DQ) method for the buckling analysis of nanobeams with exponentially varying stiffness based on four different beam theories of Euler-Bernoulli, Timoshenko, Reddy, and Levison.The formulation is based on the nonlocal elasticity theory of Eringen. New results are presented for the guided and simply supported guided boundary conditions. Numerical results are obtained to investigate the effects of the nonlocal parameter,length-to-height ratio, boundary condition, and nonuniform parameter on the critical buckling load parameter. It is observed that the critical buckling load decreases with increase in the nonlocal parameter while the critical buckling load parameter increases with increase in the length-to-height ratio.     

Free vibration of non-uniform nanobeams using Rayleigh–Ritz method

In this article, boundary characteristic orthogonal polynomials have been implemented in the Rayleigh–Ritz method to investigate free vibration of non-uniform Euler–Bernoulli nanobeams based on nonlocal elasticity theory. Non-uniform cross section of nanobeams has been considered by taking linear as well as quadratic variations of Young's modulus and density along the space coordinate. Detailed analysis has been reported for all the possible cases of such variations. The objective of the present study is to analyze the effects of nonlocal parameter, boundary condition, length-to-diameter ratio and non-uniform parameter on the frequency parameters. It is found that clamped nanobeams are having highest frequency parameters than other types of boundary conditions for a particular set of parameters. It is also observed that frequency parameters decrease with increase in scaling effect parameter. First four deflection shapes of non-uniform nanobeams have also been incorporated. In this analysis, some of the new results in terms of boundary conditions have also been included.     

Schwinger's method for the fermionic Casimir effect at finite temperature

The Casimir energy of a massive Dirac field at finite temperature and confined between two parallel infinite plates is computed using a method proposed by Schwinger. The boundary conditions are those of zero current through the plates, as inspired by quark confinement in the MIT bag model for hadrons. We use Schwinger's original regularization by a cutoff in proper-time. We comment on the analytical continuation method of regularization, which allows the employment of Epstein function techniques, and on the different possible expressions for the final answer.     

The black-box fast multipole method

A new O(N)$O(N)$ fast multipole formulation is proposed for non-oscillatory kernels. This algorithm is applicable to kernels K(x,y)$K(x\text{,}y)$ which are only known numerically, that is their numerical value can be obtained for any (x,y)$(x\text{,}y)$. This is quite different from many fast multipole methods which depend on analytical expansions of the far-field behavior of K  , for |x-y|$|x-y|$ large. Other “black-box” or “kernel-independent” fast multipole methods have been devised. Our approach has the advantage of requiring a small pre-computation time even for very large systems, and uses the minimal number of coefficients to represent the far-field, for a given L²$L^2$ tolerance error in the approximation. This technique can be very useful for problems where the kernel is known analytically but is quite complicated, or for kernels which are defined purely numerically.