最小二乘B样条函数在火箭发动机数据处理中的应用

在固体火箭发动机地面试验数据处理中,通过应用最小二乘三次B样条函数拟合的方法,进行野值辨识和修复。文中阐述了实际应用中的步骤及应注意的几点问题。为避免常规的控制序列中含有野值而影响数据辨识的问题,提出差别选取控制点循环过滤的方法,实现精度更高的野值辨识。进而采用门限判别方法,实现野值的修复。通过实测数据处理的应用表明,该算法对单个和成片野值的辨识度都很高,适用于火箭发动机地面试验数据处理。     

THE CONSTRUCTION OF WAVELET-BASED TRUNCATED CONICAL SHELL ELEMENT USING B-SPLINE WAVELET ON THE INTERVAL

Based on B-spline wavelet on the interval (BSWI), two classes of truncated conicalshell elements were constructed to solve axisymmetric problems, i.e. BSWI thin truncated conicalshell element and BSWI moderately thick truncated conical shell element with independent slope-deformation interpolation. In the construction of wavelet-based element, instead of traditionalpolynomial interpolation, the scaling functions of BSWI were employed to form the shape functionsthrough the constructed elemental transformation matrix,and then construct BSWI element viathe variational principle. Unlike the process of direct wavelets adding in the wavelet Galerkinmethod, the elemental displacement field represented by the coefficients of wavelets expansionwas transformed into edges and internal modes via the constructed transformation matrix. BSWIelement combines the accuracy of B-spline function approximation and various wavelet-basedelements for structural analysis. Some static and dynamic numerical examples of conical shellswere studied to demonstrate the present element with higher efficiency and precision than thetraditional element.     

里德伯钠原子经绝热快速通道的布居数跃迁相干控制

运用含时多态展开方法和B-样条函数研究了啁啾频率微波场中里德伯钠原子的量子态之间的布居数迁移.计算了里德伯钠原子n=70-77的开普勒频率.计算了在不同的微波场中六个态的布居数从n=70到n=77随时间的迁移,布居数跃迁到最终态n=77达到了98%,这可以通过连续的单光子跃迁来实现.结果表明,通过优化微波脉冲参数可以实现从低态到较高态的布居跃迁的相干控制.     

A Petrov-Galerkin method for equal width equation

The equal width equation is solved numerically by Petrov-Galerkin method using linear hat function and quadratic B-spline function as trial and test functions respectively. Product approximation has been used in this method. A linear stability analysis of the scheme is shown to be conditionally stable. Test problems including the single soliton and the interaction of solitons are used to validate the suggested method, which is found to be accurate and efficient. The Maxwellian initial condition pulse and the development of an undular bore are also studied.     

钫原子磁偶极超精细结构常数及其同位素的磁偶极矩的理论计算

应用基于B样条基组的相对论耦合簇理论方法,计算了~(212)Fr原子的n S (n=7—12), n P (n=7—12)和n D (n=6—11)态的磁偶极超精细结构常数.与精确实验值的比较说明这套理论方法能精确计算出磁偶极超精细结构常数,其中7P态的磁偶极超精细常数的理论值与实验值之间的差异小于1%.在忽略场移效应对Fr原子7P态超精细结构常数的影响下,通过结合实验值进一步定出了~(207-213,220-228)Fr核磁偶极矩μ,这些值与已有的测量值具有非常好的一致性.本文报道了12S, n P (n=9—12)和n D (n=10—11)态的磁偶极超精细结构常数.     

多曲面反射体的计算机辅助设计及优化

研究了自由曲面反射式照明系统的设计理论和方法.根据反射器的尺寸、位置以及配光要求按点光源设计得到曲面型值点初始坐标后,将双三次B样条曲面引入照明系统的设计,反算出控制顶点.给出了空间任意一条入射光线与反射器区块的交点及其曲面法线向量的求法,为了提高光路追迹的效率,针对多曲面反射体给出了一种快速判断相交区块的算法.探讨了用阻尼最小二乘法对B样条曲面反射器进行优化设计的方法,通过优化运算修正控制顶点Z轴坐标,使得曲面在使用扩展光源时光形分布尽可能满足设计要求.     

Quartic B-spline Galerkin approach to the numerical solution of the KdVB equation

The nonlinear Korteweg-de Vries–Burgers’ equation is solved numerically by method of Galerkin using quartic B-splines as both shape and weight functions over the finite intervals. Five test problems are studied to demonstrate the accuracy and efficiency of the proposed method. A comparison of numerical results of both algorithm and some published articles is done in computational section. The numerical results are found in good agreement with exact solutions.     

Debye屏蔽势下的Na原子

结合自由Na原子的l-依赖模型势, 采用B-样条基组展开方法计算了等离子体环境中Na原子的的基态能量、振子强度、偶极极化率、四极极化率、八极极化率等随Debye长度的变化. 其中原子的等离子体效应采用Debye屏蔽模型. 计算结果与其他研究者的结果符合得很好; 在Debye屏蔽等离子体环境下下基态能量的结果与Sahoo [Sahoo S Ho Y K 2006 Phys. Plasmas 13, 063301]和Li [Li H W and Kar S, 2012 Phys. Plasmas 19, 073303]用其他模型所得的结果基本一致; 电偶极、四极和八极极化率随Debye长度的变化趋势一致, 数值结果和Li和Kar [Li H W and Kar S, 2012 Phys. Plasmas 19, 073303] 的数量级一致.