计算二维静电场的非正交有限差分算法

讨论了计算二维维静电场的非正交有限差分算法，给出了数值计算公式，通过对一些实例的以及与理论解的比较，结果表明非正交有限差分算法具有数值网格的合的特点，只要较少用网格就可以达到较高的精度，是求解复杂边界情况下二维静电问题的一种有效方法。     

非正交曲线坐标下三维粘性流动数值分析

本文基于非正交曲线坐标与相应的非正交速度分量下导得的守恒型N—S方程，讨论了求解三维粘性流动的数值方法，计算中显式时间推进算法与Baldwin—Lomax湍流模型被采用，应用本工作发展的程序，作为算例计算了一个沿径向非等截面环形叶栅的三维粘性流场，得到了诸如三维压力分布，总压损失分布以及十分清晰的二次流动图景等丰富的流场信息。     

利用非均匀正交激光选择谐波发射短量子路径

理论研究了谐波发射的量子路径在非均匀正交激光场下的调控机制.结果表明,在适当的双色激光偏振角和非均匀参数的组合下,不仅谐波截止能量有明显增大;谐波发射的短量子路径可以被单独选择出来对谐波连续区起到贡献作用.并且,该方案在长脉宽激光下依然适用.最后,利用谐波连续区可以获得脉宽在50 as的孤立阿秒脉冲.     

捷联水平基准的非正交性标定

介绍了单轴旋转调制水平基准消除机抖激光陀螺漂移和加速度计偏置的原理,并对IMU安装误差原理做了理论分析,利用矩阵旋转变换法推导出安装误差角的计算公式。用得到的安装误差角进行标校大大降低了水平基准的姿态误差,并在工程中得到了良好的应用。     

陈氏混沌系统的非反馈控制

通过对陈氏混沌系统施加非共振参数激励实现非反馈混沌控制.将远大于系统特征频率的周期信号作为控制输入，利用平均法和Lyapunov方法证明控制方案的可行性，并得出控制参数应满足的条件.数值研究表明此方法可以使受控系统迅速达到稳定状态，且具有较强的抗干扰性能.     

非理想强度差起伏量子非破坏性测量的实验方案

提出了一种强度差起伏量子非破坏性（QND）测量的实验方案,该方案通过一个非简并光学参量放大腔实现。推导了在非理想状态下该系统的传输系数和量子态制备能力的关系式,分别讨论了探针输入噪声谱和探测系统测量效率对其测量的影响。结果表明：探针输入噪声越小,测量效率越高,则其测量质量就越好,且对测量效率越敏感。     

非共线相位匹配的参量增益分析

对非共线Ⅱ类相位匹配的ＫＴＰ飞秒光学参量振荡器进行了分析和理论研究，用数值方法得出参量增益的变化曲线和参量光的光强分布，与共线相位匹配相比，非共线方案具有更高的参量增益，更好的光束质量，特别适合飞秒光学参量的振荡器。     

非微扰色动力的新途径

本文首先对于所谓光前ＱＣＤ作一概述，然后阐述Ｋ．Ｇ．Ｗｉｌｓｏｎ等人最近提出和发展的非微扰ＱＣＤ理论方案的基本内容。     

在非交错网格上求解非正交曲线坐标系下N-S方程

介绍一种在非交错网格上,求解非正交曲线坐标系下的流动控制方程的方法。为解决在三维非正交曲线坐标系下采用非交错网格时所遇到的压力波动问题,将一种网格界面速度插值方法进行推广,并导出了相应的计算公式。运用所建立的方法对90°方截面弯管流动问题进行了数值模拟。结果是令人满意的,从而表明计算方法及所开发程序的可靠性。     

非正交轴系激光经纬仪反向运动学线性模型

为满足大尺寸测量仪器性能与制造水平提升的需求,基于非正交轴系架构理念对激光经纬仪进行设计。针对非正交轴系经纬仪在无参考末端情况下计算反向运动旋转角度的难题,提出反向运动线性模型,以实现旋转角度的快速、高精度计算。首先,基于李群李代数基本理论构建非正交轴系经纬仪正向运动学模型。其次,构建空间目标点与视准轴位姿参数间的约束关系,并结合旋转角度误差传递模型,确立用于求解旋转角度误差修正值的线性方程组。最终通过旋转角度初始估计值与误差修正值线性相加,获取高精度的反向旋转角度值。仿真结果表明,该方法所计算的旋转角度误差趋近于0,真实实验的旋转角度误差均小于0.02 mrad,验证了所提反向运动学线性模型的可行性与实用性。     

Optimized local basis set for Kohn–Sham density functional theory

We develop a technique for generating a set of optimized local basis functions to solve models in the Kohn–Sham density functional theory for both insulating and metallic systems. The optimized local basis functions are obtained by solving a minimization problem in an admissible set determined by a large number of primitive basis functions. Using the optimized local basis set, the electron energy and the atomic force can be calculated accurately with a small number of basis functions. The Pulay force is systematically controlled and is not required to be calculated, which makes the optimized local basis set an ideal tool for ab initio molecular dynamics and structure optimization. We also propose a preconditioned Newton–GMRES method to obtain the optimized local basis functions in practice. The optimized local basis set is able to achieve high accuracy with a small number of basis functions per atom when applied to a one dimensional model problem.     

Energy basis via decoherence

The question of the emergence of a preferred basis which is generally understood as that basis in which the reduced density matrix is driven to a diagonal (classically interpretable) form via environment induced decoherence is addressed. The exact solutions of the Caldeira-Leggett Master Equation are analyzed for a free particle and a harmonic oscillator system. In both cases, we see that the reduced density matrix is driven diagonal in the energy basis, which is momentum for the free particle and the number states for the harmonic oscillator. This seems to single out the energy basis as the preferred basis which is contrary to the general notion that it is the position basis which is selected since the coupling to the environment is via the position coordinates     

Application of modal wavelets to PIV measurements by selecting basis function

A modal wavelet transform, which overcomes the intrinsic data number limitation of power of two to conventional wavelet transform, has been applied to analysis of axial and eddy pseudo velocity fields, standard PIV velocity field and experimental PIV measurement. The modal wavelet transform is compared with the discrete wavelet transform in order to select the optimum basis function among Neumann, Dirichlet and Green function types basis functions. Consequently, it is verified that Neumann type function is the best basis because the correlation of Neumann type basis function is higher and the root mean square is lower than the other basis functions. Also, the decomposition vector patterns by Neumann type are similar to that by conventional Daubechies basis function of 4th order.     

应用改进的特征基函数法和自适应交叉近似算法快速分析导体目标电磁散射特性

特征基函数的构造是特征基函数法的关键步骤之一, 传统方法在构造特征基函数时, 需要在每个子域设置足够多的入射波激励, 生成的特征基函数个数较多, 奇异值分解时间较长. 为了加快特征基函数的构造, 本文提出了一种改进的特征基函数法. 该方法充分考虑每个子域之间的耦合作用, 求出每个子域的次要特征基函数, 从而降低入射波激励的个数, 大大减少了特征基函数的个数; 并且结合自适应交叉近似算法加速阻抗矩阵元素的计算, 提高了次要特征基函数求解和缩减矩阵构建过程中的矩阵矢量相乘的速度. 数值结果证明了本文方法的精确性和高效性. 关键词： 电磁散射 矩量法 特征基函数法 自适应交叉近似     

一种基于压缩感知的三维导体目标电磁散射问题的快速求解方法

提出了一种将压缩感知和特征基函数结合的方法来计算三维导体目标的雷达散射截面.利用压缩感知理论,将随机选择的矩量法阻抗矩阵作为测量矩阵,将激励电压视为测量值,然后再用恢复算法可实现二维或二维半目标感应电流的求解.对于三维导体目标,使用Rao-Wilton-Glisson基函数表示的感应电流在常用的离散余弦变换基、小波基等稀疏基上不稀疏.为此,本文将计算出的目标特征基函数作为稀疏基,用广义正交匹配追踪算法作为恢复算法来加速恢复过程,并应用到三维导体目标的雷达散射截面计算中.数值结果证明了本文方法的准确性与高效性.     

Molecular properties with dual basis set methods

The dual basis set approach has proven to be very successful for accurately estimating total energies with large basis sets. This study extends the applications of this technique to the calculation of molecular properties, including energy derivatives with respect to nuclear positions and to an external electric field. All energy derivatives have been calculated numerically via finite-differences. Molecular gradients and Hessians as well as dipole moments and polarizabilites have been calculated at the HF and MP2 levels using two alternative versions of the dual basis set method. The accuracy of these approaches is discussed in the context of quality of basis sets used in calculations. It is shown that even quite poor results obtained with the 6-311G basis set are significantly improved in dual basis set calculations with the 6-311G(d,p) and 6-311G(3df,3dp) basis sets.     

The accuracy of local MP2 methods for conformational energies

The relative energies of 95 conformers of four peptide models are studied using MP2 and LMP2 methods and correlation consistent basis sets ranging from double-zeta to augmented quintuple-zeta quality. It is found that both methods yield quite similar results, and the differences between MP2 and LMP2 decrease systematically with increasing basis set. Due to reduced intramolecular basis set superposition effects (BSSE), the LMP2 results converge more slowly to the basis set limit for most of these rather small systems. However, for larger peptides, the BSSE has a very large effect on the energy difference between extended and helical structures, leading to a very strong basis set dependence of the canonical MP2 results. It is demonstrated for alanine octapeptides that the basis set error exceeds 30 and 20kJ mol^?1, respectively, if augmented double-zeta and triple-zeta basis sets are used. On the other hand, the LMP2 results are only slightly affected by the basis set size, and, even with augmented double-zeta basis sets, reasonably accurate results are obtained. Furthermore, for the larger systems, the computation times for the LMP2 calculations are shown to be up to one order or magnitude shorter than for canonical MP2 calculations with the same basis set.     

基于关联基的壳模型截断计算

提出了一种新的用于壳模型截断计算的基矢空间的构建方法,即关联基的方法。关联基是利用壳模型中每个粒子数分布下哈密顿量的本征态作为基矢。在此基矢之上,可以很自然地通过考虑能量相对较低的关联基矢进行相应的截断计算。当所有的关联基矢都被考虑时,计算结果回到一般jj耦合给出的结果。最后,对关联基下壳模型的计算与标准的壳模型计算进行了比较,计算结果表明,关联基下壳模型能量和波函数有着良好的收敛性,同时表明关联基计算的有效性。     

计算分子二阶超极化率的基组选择

设计和使用了扩展的6-31G,D95, ANO,aug-cc-pVDZ基组以及Hypol基组,用各种相关能级别的方法SCF,MP2,MP3,MP4D,MP4DQ,MP4SDQ,MP4, CCSD,CCSD(T),计算了H2O,CO,HF,H2,N2等分子的二阶超极化率.分别以4-aug-cc-pVTZ基组在不同方法下的二阶超极化率结果,和CCSD(T)/4-aug-cc-pVTZ水平上的结果作为标准,求得各水平计算相对应的平均相对偏差.结果发现:MP2/aug-cc- pVDZ+是计算二阶超极化率最优的水平.综合讨论认为:可在MP2/aug-cc-pVDZ+水平上计算分子的二阶超极化率,其结果是可靠的.而且如果同时要计算分子极化率和一阶超极化率,其结果也是可靠的.     

Optimized effective potentials in finite basis sets

The finite basis optimized effective potential (OEP) method within density functional theory is examined as an ill-posed problem. It is shown that the generation of nonphysical potentials is a controllable manifestation of the use of unbalanced, and thus unsuitable, basis sets. A modified functional incorporating a regularizing smoothness measure of the OEP is introduced. This provides a condition on balanced basis sets for the potential, as well as a method to determine the most appropriate OEP and energy from calculations performed with any finite basis set.