基于变分几何的参数化设计绘图方法

本文提出了一种基于变分几何的参数化设计绘图方法。该方法根据对实际工程图纸的分析，将图纸信息分解为结构图元与轮廓图元两大部分，并对传统变分几何的设计方法作了大量的改进，从而提高了设计绘图效率。

HyCAD：一个基于结构化变分几何的变参设计系统

ＨｙＣＡＤ是一个支持参数化的新一代设计系统，它根据对实际工程设计过程的分析，将设计对象分解为主元与从元两大部分，并结合了变分法设计和结构化设计的优点，从而提高了设计效率和可靠性．本文主要介绍了该系统的基本设计思想及系统体系结构．

HyCAD：一个基于结构化变分几何的变参设计系统

ＨｙＣＡＤ是一个支持参数化的设计系统，它根据对实际工程设计过程的分析，将设计对象分解为主元与从元两大部分，并结合了变分法设计和结构化设计的优点，从而提高了设计效率和可靠性．本文主要介绍了该系统的基本设计思想及系统体系结构．

基于变分几何的参数化绘图系统HyVDS

ＨｙＶＤＳ是一个支持参数化的新一代二维绘图系统，它根据对实际工程图纸的分析，将图纸信息分解为结构图元与轮廓图元两大部分，并对变分几何的设计方法作了大量的改进，从而提高了设计绘图效率。本文主要介绍了该系统的基本设计思想、数据模型和系统体系结构。

基于变分几何的参数化造型系统的研究与开发

基于约束的参数化几何造型技术是一种新型、快速的造型方法。本文应用变分几何技术开发了一个参数化几何造型系统——VGPDA。该系统具有自动搜索约束关系,生成约束方程组,进行约束关系一致性识别以及采用符号微分方程法快速求解约束方程组等功能。

基于变分几何的2D参数化造型

本文研究和开发了一个变分几何的参数化造型系统(VGPDA)。该系统能自动生成约束方程,较好地处理约束一致性问题,并将约束一致性判断与约束方程的求解相结合,使得求解过程方便、快速;此外,VGPDA 的另一独特之处在于运用符号微分方法提高了算法的精度和可靠性。

基于总变分和形态学的航空图像道路检测算法

高分辨率航空图像中道路通常表现为较狭窄的面,这给分类算法创造了机会.文中提出了一种新的基于分类的航空图像道路自动提取方法——基于总变分和形态学分析方法,它首先根据邻域总变分和直方图得到分割道路所需的合适阈值并从图像中分割出道路区域,然后根据基于区域总变分和几何测度的准则函数及其模式频谱得到形态学普通开运算的阈值,最后用此准则及阈值对图像进行形态学普通开运算以去除和路面具有相似光谱特性的物体的干扰.初步实验证明,该方法具有良好的稳定性和较强的环境适应能力.

弹性膜结构动力学的各类非传统Hamilton型变分原理

根据古典阴阳互补和现代对偶互补的基本思想,通过罗恩早已提出的一条简单而统一的新途径,系统地建立了弹性膜结构动力学的各类非传统Hamilton型变分原理.这种新的非传统Hamilton型变分原理能反映这种动力学初值-边值问题的全部特征.文中首先给出膜结构动力学的广义虚功原理的表式,然后从该式出发,不仅能得到膜结构动力学的虚功原理,而且通过所给出的一系列广义Legendre变换,还能系统地成对导出弹性膜结构动力学的5类变量(pα,pβ,pγ,vα,vβ,vγ,Nα,Nβ,Sαβ,εα,εβ,εαβ,u,v,w)、4类变量(pα,pβ,pγ,Nα,Nβ,Sαβ,εα,εβ,εαβ,u,v,w)、3类变量(Nα,Nβ,Sαβ,εα,εβ,εαβ,u,v,w)和2类变量(Nα,Nβ,Sαβ,u,v,w)非传统Hamilton型变分原理的互补泛函、以及相空间(pα,pβ,pγ,vα,u,v,w)非传统Hamilton型变分原理的泛函与1类变量(u,v,w)非传统Hamilton型变分原理势能形式的泛函.同时,通过这条新途径还能清楚地阐明这些原理的内在联系.

几何变分问题近期发展

本文回顾与平均曲率相关的几何变分理论的最新研究进展,主要讨论极小超曲面的Morse理论,并重点介绍常平均曲率(constant mean curvature,CMC)曲面的变分理论、重数一猜想、极小超曲面的典范空间分布、自由边界极小曲面的变分理论及在等变情形下的推广.

Development of Turbocharger for Improving Diesel Engine Matching Performance

The two development ways of turbocharger technology to solve the problem of matching performance with diesel were presented. The ways of waste valve gate turbocharger and variable geometry turbocharger can solve the problem of engine’s low speed torque and achieve lower smoke level. Especially for variable geometry turbocharger, it covers all conditions of engine. It can not only improve the low engine’s speed torque and keep the power performance at high engine speed, but also cover wide engine speed performance that keeps lower fuel consumption and exhaust gas temperature in full load and part load matching. The results of theory analysis and experiment research showed that it’s the ideal solution to solve the matching problem of diesel engines.

In situ analysis of multi-twin morphology and growth using synchrotron polychromatic X-ray microdiffraction

Synchrotron polychromatic X-ray microdiffraction（micro-XRD） was applied to study in situ deformation twinning of commercially AZ31（Mg-3Al-1Zn） strip subjected to uniaxial tension.The morphology and growth of twins were analyzed in situ under the load level from 64 to 73 MPa.The X-ray microdiffraction data,collected on beamline 12.3.2 at the Advanced Light Source,were then used to map an area of 396μm x 200μm within the region of interest.The experimental set-up and X-ray diffraction microscopy with a depth resolution allow the position and orientation of each illuminated grain to be determined at the submicron size.A list of parent grains sorted by crystallographic orientation were selected to examine their twinning behavior.The results depict twin variant selection,local misorientation fluctuation and mosaic spread for multi-twins within the same parent grain.As load increases,the amplitude of misorientation fluctuation along twin trace keeps increasing.This is attributable to the accumulation of geometrically necessary dislocations.

Development of analysis model for geometric error in turning processes

A finite element model was established for analyzing the geometric errors in turning operations and a two-step analyzing process was proposed. In the first analyzing step, the cutting force and the cutting heat for the cutting conditions were obtained using the AdvantEdge. Also, the deformation of a workpiece was estimated in the second step using the ANSYS. The deformation was analyzed for a 150 mm-long workpiece at three different measuring points, such as 10, 70 and 130 mm from a reference point, and the amounts of the deformation were compared through experiments. /n the results of the comparison and analysis, the values obtained from these comparison and analysis represent similar tendencies. Also, it is verified that their geometric errors increase with the increase in temperature. In addition, regarding the factors that affect the deformation of a workpiecc, it can be seen that the geometric error in the lathe is about 15%, the error caused by the cutting force is about 10%, and the deformation caused by the heat is about 75%.

Advances in Studies and Applications of Centroidal Voronoi Tessellations

Centroidal Voronoi tessellations(CVTs) have become a useful tool in many applications ranging from geometric modeling,image and data analysis,and numerical partial differential equations,to problems in physics,astrophysics,chemistry,and biology. In this paper,we briefly review the CVT concept and a few of its generalizations and well-known properties.We then present an overview of recent advances in both mathematical and computational studies and in practical applications of CVTs.Whenever possible,we point out some outstanding issues that still need investigating.

Finite element analysis and simulation for cold precision forging of a helical gear

To investigate the effects of billet geometry on the cold precision forging process of a helical gear, six different billet geometries were designed utilizing the relief-hole principle. And the influences of the billet geometry on the forming load and the deformation uniformity were analyzed by three-dimensional （3D） finite element method （FEM） under the commercial software DEFORM 3D. The billet geometry was optimized to meet lower forming load and better deformation uniformity requirement. Deformation mechanism was studied through the distribution of flow velocity field and effective strain field. The forging experiments of the helical gear were successfully performed using lead material as a model material under the same process conditions used in the FE simulations. The results show that the forming load decreases as the diameter of relief-hole do increases, but the effect of do on the deformation uniformity is very complicated. The forming load is lower and the deformation is more uniform when do is 10 mm.

Some Transformation of a Multiple Hypergeometric Series of Lauricella Function of n Variables

This paper deals with an integral transformation involving Whittaker function Mk,m（X） into a multiple hypergeometric series of Lauricella function FA（n） of n variables. A number of known and new transformation and reduction formulae for a hypergeometric function 2F1, Appell function F2, Lauricella function FA（3） and a hypergeometric function of four variables Fp（4） are derived as special cases.

High-Resolution Seismic Reflection Profiling of the Fenhe Fault in Taiyuan City

In this paper, we demonstrate the high resolution seismic reflection data for a depth range of several hundred meters across the Fenhe fault in Taiyuan city, China. In combination with the relevant borehole logs, these data provide useful constraints on the accurate position, geometry and deformation rate of the fault, as well as the kinematics of recent fault motion. The high resolution seismic reflection profiling revealed that the western branch of the Fenhe fault is a high angle, eastward dipping, oblique normal fault, and cutting up to the lower part of the Quaternary system. It was revealed that the top breaking point of this fault is at a depth of ～70m below the ground surface. A borehole log across the Fenhe fault permitted us to infer that there are two high angle, oppositely dipping, oblique normal faults. The eastem branch lies beneath the eastern embankment of the Fenhe river, dipping to the west and cutting into the Holocene late Pleistocene strata with a maximum vertical offset of ～8m. Another borehole log across the northern segment of the Fenhe fault indicates that the western branch of this fault has cut into the Holocene late Pleistocene strata with a maximum vertical offset of ～6m. The above mentioned data provide a minimum average Pleistocene Holocene vertical slip rate of 0 06～0 08mm/a and a maximum average large earthquake recurrence interval of 5 0～6 7ka for the Fenhe fault.

A new look on wetting models:continuum analysis

In this study,we considered the wetting phenomenon on a general substrate from a new viewpoint of continuum mechanics.The analyses first show how the Wenzel and the Cassie models deviate the practical results in some special substrates,and then elucidate the mechanism of the triple contact line(TCL) moving.Based upon variational theory of the total free functional dealing with the movable boundary condition,we show that the macroscopic contact angle(MCA) expression is the corresponding transversality condition.It manifests that the MCA depends only on the chemical and geometric property at the TCL,and is not affected by the gravity of the droplet and the contact area beneath the liquid.Our continuum model also shows the exploration of the pinning effect on a sharp wedge or the interface between two different phases.This investigation will help designing super-hydrophobic materials for novel micro-fluidic devices.

EXPLICIT CONSTRUCTION OFHARMONIC MAPS FROM R^2 TO U(N)

Darboux transformation method is used for constructing harmonic maps from R2 to U(N).The explicit expressions for Darboux matrices are used to obtain new harmonic maps from aknown one.The algorithm is purely algebraic and can be repeated successively to obtain aninfinite sequence of harmonic maps. Single and multiple solitons are obtained with geometriccharacterizations and it is proved that the interaction between solitons is elastic. By introducingthe singlllar Darboux transformations, an explicit method to construct new unitons is presented.

LOOP GROUP ACTIONS AND THE RIBAUCOUR TRANSFORMATIONS FOR FLAT LAGRANGIAN SUBMANIFOLDS

The Ribaucour transformations for flat Lagrangian submanifolds in Cn and CPn via loop group actions are given. As a consequence, the authors obtain a family of new flat Lagrangian submanifolds from a given one via a purely algebraic algorithm. At the same time, it is shown that such Ribaucour transformation always comes with a permutability formula.

Orlicz mixed affine quermassintegrals

A class of geometric quantities for convex bodies is introduced iu the framework of Orlicz Brunn- Minkowski theory. It is shown that these new geometric quantities are affine invariant and precisely the generalizations of classical affine quermassintegrals.