用B-样条函数研究静电场中锂原子里德伯态的性质

用B-样条函数展开方法，结合原子的单电子势模型研究了静电场中锂原子里德伯态的性质. 所得到的Stark能级图、反交叉位置、反交叉宽度以及振子强度与已有的实验和其他理论结果符合得很好. 表明该方法是一种有效的研究静电场中碱金属原子性质的方法. 最后，在数值上研究了锂原子里德伯态振子强度谱随静电场场强的演化特征.     

Recursive polynomial curve schemes and computer-aided geometric design

A class of polynomial curve schemes is introduced that may have widespread application to CAGD (computer-aided geometric design), and which contains many well-known curve schemes, including Bézier curves, Lagrange polynomials, B-spline curve (segments), and Catmull-Rom spline (segments). The curves in this class can be characterized by a simple recursion formula. They are also shown to have many properties desirable for CAGD; in particular they are affine invariant, have the convex hull property, and possess a recursive evaluation algorithm. Further, these curves have shape parameters which may be used as a design tool for introducing such geometric effects as tautness, bias, or interpolation. The link between probability theory and this class of curves is also discussed.Communicated by Klaus Höllig.     

Numerical solutions of the modified Burgers’ equation by Petrov-Galerkin method

The modified Burgers’ equation (MBE) is solved numerically by the Petrov-Galerkin method using a linear hat function as the trial function and a cubic B-spline function as the test function. Product approximation has been used in this method. A linear stability analysis of the scheme shows it to be unconditionally stable. The accuracy of the presented method is demonstrated by two test problems. The numerical results are found in good agreement with the exact solutions.     

B-splines methods with redefined basis functions for solving fourth order parabolic partial differential equations

In this work, we discuss two methods for solving a fourth order parabolic partial differential equation. In Method-I, we decompose the given equation into a system of second order equations and solve them by using cubic B-spline method with redefined basis functions. In Method-II, the equation is solved directly by applying quintic B-spline method with redefined basis functions. Stability of these methods have been discussed. Both methods are unconditionally stable. These methods are tested on four examples. The computed results are compared wherever possible with those already available in literature. We have developed Method-I for fourth order non homogeneous parabolic partial differential equation from which we can obtain displacement and bending moment both simultaneously, while Method-II gives only displacement. The results show that the derived methods are easily implemented and approximate the exact solution very well.     

基于外推和级联积分梳状滤波器的多普勒插值方法

INS/GPS深组合导航系统的本地码和载波数控振荡器(NCO)控制量的计算需要利用滤波修正后的惯导位置信息或速度信息,其中的多普勒频移计算需要同时利用位置和速度信息。基带I、Q信息的更新率通常为1 kHz,利用惯导信息解算出的多普勒频移为100 Hz,利用级联积分梳状(CIC)滤波器进行插值有效解决了二者更新率的匹配问题。此外,导航滤波器的更新频率通常为1 Hz,惯导解算频率为100 Hz,对于低精度惯导系统,在滤波修正周期之间误差累积较快,利用外推方法有效控制了惯导解算误差。通过半实物仿真分析,基于外推和CIC滤波器的在线插值结果与基于B-样条插值结果对比,误差标准差约为1 Hz,误差的频谱被限定在0.02 Hz以内,结果表明了该方法的有效性。     

A nonrational B-spline profiled horn with high displacement amplification for ultrasonic welding

A new horn with high displacement amplification for ultrasonic welding is developed. The profile of the horn is a nonrational B-spline curve with an open uniform knot vector. The ultrasonic actuation of the horn exploits the first longitudinal displacement mode of the horn. The horn is designed by an optimization scheme and finite element analyses. Performances of the proposed horn have been evaluated by experiments. The displacement amplification of the proposed horn is 41.4% and 8.6% higher than that of the traditional catenoidal horn and a Bézier-profile horn, respectively, with the same length and end surface diameters. The developed horn has a lower displacement amplification than the nonuniform rational B-spline profiled horn but a much smoother stress distribution. The developed horn, the catenoidal horn, and the Bézier horn are fabricated and used for ultrasonic welding of lap-shear specimens. The bonding strength of the joints welded by the open uniform nonrational B-spline (OUNBS) horn is the highest among the three horns for the various welding parameters considered. The locations of the failure mode and the distribution of the voids of the specimens are investigated to explain the reason of the high bonding strength achieved by the OUNBS horn.     

圆板弹塑性弯曲的简单样条积分方程法

提出了圆板弹塑性弯曲的简单样条积分方程法.以径向转角作为未知量建立积分方程并结合B样条函数进行求解.这一方法具有域积分容易处理、精度高和计算简单的优点.计算结果表明本文解与文[2]解吻合良好.     

三次均匀B样条在服装CAD中的应用

服装设计中三维向二维的转换是服装 CAD当今研究的重要课题之一 .依据投影原理寻找到三维衣片的边界点在平面上的对应位置 ,并利用三次均匀 B样条拟合二维边界点以实现三维衣片向二维衣片的转换 .经上机调试、运行、得到比较满意的结果 ,为今后深入研究奠定了基础     

利用提升格式构造稳定的对偶小波

近年来 ,产生了一种称为“提升格式”的新的小波构造方法 [7,8,9] ,它从一个较简单的多尺度分析 (MRA)出发 ,利用尺度函数相同的多尺度分析之间的相互关系 ,逐步地得到所需性质的多尺度分析 .本文仅考虑双正交滤波的提升格式 .当选定一初始双正交滤波后 ,利用提升格式构造的双正交滤波仍是双正交的 ,而这双正交滤波能否生成双正交小波 Riesz基即稳定的对偶小波 ?更进一步 ,如何从一些较为简单的不能生成双正交小波 Riesz基的双正交滤波出发 ,利用提升格式构造出具有 Riesz基性质的双正交滤波 ?这在目前有关提升格式的文章中没作回答 .本…     

Computing parallel curves on parametric surfaces

Generating parallel curves on parametric surfaces is an important issue in many industrial settings. Given an initial curve (called the base curve or generator) on a parametric surface, the goal is to obtain curves on the surface that are parallel to the generator. By parallel curves we mean curves that are at a given distance from the generator, where distance is measured point-wise along certain characteristic curves (on the surface) orthogonal to the generator. Except for a few particular cases, computing these parallel curves is a very difficult and challenging problem. In fact, only partial, incomplete solutions have been reported so far in the literature. In this paper we introduce a simple yet efficient method to fill this gap. In clear contrast with other existing techniques, the most important feature of our method is its generality: it can be successfully applied to any differentiable parametric surface and to any kind of characteristic curves on surfaces. To evaluate our proposal, some illustrative examples (not addressed with previous methods) for the cases of section, vector-field, and geodesic parallels are discussed. Our experimental results show the excellent performance of the method even for the complex case of NURBS surfaces.