一类二次曲面的位势函数

本文由Laplace方程出发,讨论由方程:x/(a~2+λ)+y/(b~2+λ)+z/(c~2+λ)=1所定义的一族二次曲面在一定的条件下((?)=(?)(λ))是等位面,并用直接积分的方法,求出电位表达式的通式,将这一结果用于具体的物理问题,可解决一类导体的电位分布、电荷分布等问题.     

一种C#中NURBS曲面建模方法

NURBS(Non-UniformRationalB-Splines)方法因其表示法的、形状控制灵活性,在曲面造型和曲面重构中具有重要作用。目前,还没有在C#中开发OpenGL(OpenGraphicsLibrary)的标准和规范的方法。研究了在C#中利用平台调结合OpenGL进行NURBS曲面快速建模的方法,获得了满意的结果,并给出了实例。     

Experimental measurements and theoretical calculations of the atomic structure of materials with subangstrom resolution and picometer precision

Lattice defects are unavoidable structural units in materials and play an important role in determining material properties. Compared with the periodic structure of crystals, the atomic configurations of the lattice defects are determined by the coordinates of a large number of atoms, making it difficult to experimentally investigate them. In computational materials science, multiparameter optimization is also a difficult problem and experimental verification is usually required to determine the possibility of obtaining the structure and properties predicted by cal- culations. Using our recent studies on oxide surfaces as examples, we introduce the method of integrated aberra- tion-corrected electron microscopy and the first-principles calculations to analyze the atomic structure of lattice defects. The atomic configurations of defects were mea- sured using quantitative high-resolution electron micros- copy at subangstrom resolution and picometer precision, and then the electronic structure and dynamic behavior of materials can be studied at the atomic scale using the first- principles calculations. The two methods complement each other and can be combined to increase the understanding of the atomic structure of materials in both the time and space dimensions, which will benefit materials design at the atomic scale.     

基于区域分割技术的等距天线曲面重构

针对逆向工程中空间坐标测量时仪器测头半径或靶标厚度的误差补偿问题,提出了对散乱点云数据进行自动区域分割的方法。快速搜索出子区域中测点的最近邻域,利用测点最近邻域构造一个有约束的最小二乘切平面,得到曲面在该测点处的法线矢量。基于Prim算法的优化算法对法线矢量方向进行调整,使各测点处的法线矢量都指向曲面同一侧,进而求取了实际曲面上的点。对于经过误差补偿后的点云数据,从空间任意二次曲面的一般方程出发,基于二次曲面的误差方程和法方程提出一种通用拟合算法,并借助二次型理论得到曲面的特征参数。实验结果证明：应用该区域分割算法能够提高最近邻域的搜索速度,且曲面拟合算法具有很好的鲁棒性和有效性。     

Symmetrical Fundamental Tensors, Differential Operators, and Integral Theorems in Differential Geometry

To make the geometrical basis for soft matters with curved surfaces such as biomembranes as simple as possible, a symmetrical analytical system was developed in conventional differential geometry. The conventional second fundamental tensor is replaced by the so-called conjugate fundamental tensor. Because the differential properties of the conjugate fundamental tensor and the first fundamental tensor are symmetrical, the symmetrical analytical system including the symmetrical differential operators, symmetrical differential characteristics, and symmetrical integral theorems for tensor fields defined on curved surfaces can be constructed. From the symmetrical analytical system, the symmetrical integral theorems for mean curvature and Gauss curvature, with which the symmetrical Minkowski integral formulas are easily deduced just as special cases, can be derived. The applications of this symmetrical analytical system to biology not only display its simplicity and beauty, but also show its powers in depicting the symmetrical patterns of networks of biomembrane nanotubes. All these symmetrical patterns in soft matters should be just the reasonable and natural results of the symmetrical analytical system.     

Ag在Si表面吸附的第一性原理研究

采用基于密度泛函理论的第一性原理平面波赝势方法计算优化了Ag原子在硅惯习面Si(111)和Si（220）晶面的最佳吸附位置,并计算了Ag/Si(111)和Ag/Si(220)体系的表面吸附能和表面态电子结构．研究表明:Si基表面Ag原子的最稳定吸附居于Si(220)晶面的穴位,此时的吸附能最低,其值为5.2569eV,属于强化学吸附;同时由于在Ag/Si(220)体系中,Ag-4d轨道和表面态Si-3s、3p轨道电子的强相互作用,以及Ag-4p轨道的电子云强偏向于Si-3s、3p轨道使得体系的能隙宽度变窄,导电性急剧增大．     

圆孔与三极子组合单元频率选择表面研究

应用谱域法分析了圆孔与三极子组合单元频率选择表面(FSS)的频率响应特性。分析了组合单元的结构参数、电磁波极化和入射角度对其稳定性的影响。研究结果表明,该组合单元的频率响应特性曲线具有明显的两个阻带和一个通带,且具有良好的极化稳定性和角度稳定性。在结构参数中,圆孔大小对频率响应特性曲线的位置影响较大,极子长度对传输带宽影响较大,而极子宽度影响较小。通过单元结构参数调整,可获得良好的宽带传输和陡峭下降边缘特性,实现相临波段信号分离和多波段通讯。该结构FSS可应用于卫星通讯、雷达罩及其他相关领域。     

类毛线团表面银微球的制备及其表面增强拉曼散射性能研究

以低分子量聚丙烯酰胺（PAM）为模板,通过液相化学还原法首次制备了类毛线团表面银微球,并采用扫描电子显微镜（SEM）、X射线衍射（XRD）及氮气吸附法对银微球形貌及分散性进行表征。结果表明,微球是由纳米片有序组装而成的介孔材料,表面遍布棱角和狭缝。考察了PAM分子量、硝酸银浓度及还原体系pH值变化对银球结构的影响,并对类毛线团表面的形成过程进行了阐述。将银球用作表面增强拉曼散射（SERS）检测基底,可显著地增强罗丹明B（Rh B）分子的拉曼信号强度,能够检测出浓度低至10^-16mol/L的Rh B。     

6种城市下垫面热环境效应对比研究

选择6种具有代表性的城市下垫面(沥青路面、水泥路面、荷兰砖地面、草地、嵌草砖地面、大理石地面)作为观测对象,基于热红外成像技术对其地表温度特征进行观测,系统分析不同城市下垫面地表温度的日变化以及季节变化特征,并利用不同下垫面温度的时间标准差、空间标准差及时空数据标准差定量揭示城市不同下垫面地表温度的时空变化特征,对比研究不同下垫面的热环境效应,结果如下。1)不同下垫面地表温度的日变化一般呈先上升后下降的单峰形态,草地地表温度在不同季节的日变化波动差异较大。沥青的地表温度在全年均为最高,对热环境的影响较大;嵌草砖和大理石在全年的温度均较低,对热环境具有较好的缓解作用,且缓解作用在夏季最显著。2)不同下垫面地表日均温度全年均高于大气温度,表明城市下垫面对大气在一年中都有加热作用。3)气温、太阳辐射以及空气相对湿度对下垫面地表温度的影响均较为显著;气温和太阳辐射与下垫面地表温度之间呈正相关关系,对下垫面以增温作用为主;空气相对湿度与下垫面地表温度之间呈负相关关系,对下垫面增温起抑制作用。4)嵌草砖的热环境稳定性较草地和大理石要好;沥青路面的温度变化特征最能代表本研究观测区域下垫面地表温度的时空变化特征。研究结果对了解城市不同下垫面热环境具有一定参考意义,可为缓解城市热环境提供科学依据。