数值方程

The control principle of electrostatic shaping was introduced according to the balance between electrostatic force and resulting force formed by membrane deformation and the complex shaping process of SMEC. Then, taking the trisection circularity electrode for an example, the distribution characteristic of electric potential in the electrostatic field was analyzed, namely, the expression of potential function in the electrostatic field was deduced by Laplacian equation. And then, by combining the difference equation with electric potential expression, the numerical solutions of electrostatic force in single electrode mode and trisection circularity electrode mode were disposed. Finally, the calculated figure was compared with the ideal paraboloid and comparison shows that more accuracy would be achieved by multi-electrode control.

根据静电力与薄膜变形载荷作用力之间的平衡关系和静电拉伸薄膜反射镜成形的复杂过程，介绍了薄膜反射镜静电成形的控制原理；以三等分环状电极为例，分析了静电场中空间电势分布特性，即从拉普拉斯方程推导出静态场势函数的表达式；然后，利用差分与电势方程结合的方法，对单电极电场力和三等分环状电极电场力进行了数值求解；最后，将计算面形与理想抛物面进行了比较，结果显示，单电极情况下得到的薄膜反射镜面形不是理想抛物面，若采用多电极控制可获得更高的控制精度。

The control principle of electrostatic shaping was introduced according to the balance between electrostatic force and resulting force formed by membrane deformation and the complex shaping process of SMEC. Then, taking the trisection circularity electrode for an example, the distribution characteristic of electric potential in the electrostatic field was analyzed, namely, the expression of potential function in the electrostatic field was deduced by Laplacian equation. And then, by combining the difference equation with electric potential expression, the numerical solutions of electrostatic force in single electrode mode and trisection circularity electrode mode were disposed.

根据静电力与薄膜变形载荷作用力之间的平衡关系和静电拉伸薄膜反射镜成形的复杂过程，介绍了薄膜反射镜静电成形的控制原理；以三等分环状电极为例，分析了静电场中空间电势分布特性，即从拉普拉斯方程推导出静态场势函数的表达式；然后，利用差分与电势方程结合的方法，对单电极电场力和三等分环状电极电场力进行了数值求解；最后，将计算面形与理想抛物面进行了比较，结果显示，单电极情况下得到的薄膜反射镜面形不是理想抛物面，若采用多电极控制可获得更高的控制精度。

Using numerical analysis and visual technology, the parameters of the known Rayleigh van der pol equation are discussed in detail The relation between the limit circle and chaos strange attractors is foun

通过数值分析及科学可视化技术，对著名的 Rayleigh Van Der Pol方程的参数进行较详细的讨论，获得该方程的混沌吸引子与极限环的关系

Based on the experiences in Computational Fluid Dynamics, the linear equation solver takes more than 60% CPU time of the whole process, therefore acceleration of the linear equation solver is a key element in enhancing the whole performance of CFD.

研究了基于非结构化网格通用输运方程的数值求解方法，包括输运方程的离散格式，边界条件处理方法，压力速度耦合SIMPLE求解方法，详细讨论了影响界面流量计算的重要因素。

In this paper, applying an integral expression of linear viscoelastic theory, several integral equation expressions for obtaining shear modulus G from stress relaxation modulus E{t and bulk modulus K are acquired by using inversion of the Laplace Transform.

本文应用线粘弹性理论的一种粘弹性积分变换式，采用拉氏逆变换，导出了由拉伸松弛模量E和体积松弛模量K求解剪切模量G的几种积分方程，并给出了由已知试验数据E和K通过迭代和数值积分求G的数值积分算法。

In order to improve the capability of Hooke's universal joints, the effects of structural parameters on the contact pressure distribution are analyzed based on Lundberg's logarithmic equation and the numerical calculation of three-dimension elastic contact problems in finite length.

为改善万向节的性能，文中基于Lundberg对数凸型方程和三维有限长弹性接触问题的数值计算，分析了轴承结构参数对接触压力分布的影响，提出滚针凸度量设计时必须考虑滚针倒角半径和越程槽宽度的影响，并给出了相应的数值计算方法。

First of all, in the study from magnetohydrodynamics equilibrium equations describe the plasma derived from the balance of the Grad-Shafranov equation of the theory of expression, and to analyze its borders in a fixed way to solve the region;then we solved the equation with Variational method in given pressure, and the exact numerical value of poloidal magnetic flux and the profile of the magnetic flux surfaces contours in the definite error range are given.At last, the poloidal and toroidal magnetic field with D-shaped is obtained.

在研究中首先从磁流体力学平衡方程出发推导出描述等离子体平衡问题的Grad-Shafranov方程的理论表达式，并分析其在固定边界区域内的求解途径；然后在给定的压强分布情况下采用基于能量形式的变分法对其进行了数值计算，并在一定的误差范围内得到了极向磁通的大致图像以及等离子体的平衡位形分布；最后求出了D-型截面下的极向磁场以及环向磁场分布。

A deformable model is used to reconstruct the shape of the LV: first, the dynamic equation governing the surface deformation is deduced; secondly the image planes are mapped to the reconstruction coordinate system. From the slices data, the external force exerted on the surface is defined and the elastic force of the surface is constructed by mean curvature of the deformation surface. Finally, a level set method is applied to solve the dynamic equation for LV shape.

为了重建左心室的形状，使用基於形变模型的方法：首先建立变形曲面的动力学方程；再将成像坐标系中的图像平面映射到重建坐标系，根据图像数据构造外力，使用平均曲率构造变形曲面的弹性力，然后用水平集数值解法求解动力学方程以重建左心室的表面。

The mixed boundary problem was reduced to a system of singular integral equations by means of Fourier transform.

利用Fourier积分变换技术将混合边值问题转化为一对奇异积分方程，通过数值求解奇异积分方程获得含裂纹功能梯度板条分别在剪切和法向载荷作用下的I型和Ⅱ型应力强度因子，并讨论了材料的非均匀性和裂纹相对尺寸对裂纹尖端应力强度因子的影响。

A numerical method for solution of multigroup neutron integral transport equation in two-dimensional hexagonal geometry has been s...

本文首先研究了在二维六角形几何情况下，多群中子积分输运方程的数值解法，建立了完整的理论模型及数值方法。

But we don't care about Battlegrounds.

但我们并不在乎沙场中的显露。

Ah! don't mention it, the butcher's shop is a horror.

啊！不用提了。提到肉，真是糟透了。