数值方程

In chapter three,we have derived a generalized dual London equation for the Abelian "electric" field A_μfrom the effective dual Abelian-Higgs model.The approximative result and the numerical simulation result as well as their figs were shown via solving the dual Abelian-Higgs model with different methods.Hereby the vortex solution of the chromo-electric field and the vortex energy density were also discussed.Finally,we have studied the dual Abelian-Higgs model with additional vacuum constant,and have unpuzzled the vacuum constant corresponding to the bag model.When the quark sources is introduced, the vacuum constant in the MIT bag model is proportional to the quartic of the monopole mass.

利用不同方法求解该方程，给出了该方程的近似结果和数值模拟结果，并分别对两种情形画出图像作了比较，据此还讨论了色电场的涡旋解及能量密度，最后讨论了含有附加真空常数的对偶阿贝尔-黑格斯模型并对应口袋模型给出了附加真空常数的物理解释，引入夸克源之后还预言麻省口袋模型中的真空常数正比于单极质量的四次方。

In this paper, on the base of paraxial approximations, we present a set of absorbing boundary conditions of 3D elastic wave equations and apply to the 3D elastic wave numerical modeling in isotropic medium.

本文基於傍轴近似法提出了计算三维弹性波方程的吸收边界条件公式，表示了各边界面、边棱和角点处波场所满足的单程波方程，并在三维弹性波数值模拟中进行了应用。

The new method is a combination of characteristic approximation to handle the convection part, to ensure the high stability of the method in approximating the sharp fronts and reduce the numerical diffusion, a smaller time truncation is gained at the same time, and a mixed finite elementspatial approximation to deal with the diffusion part, the sealer unknown and the adjoint vector function are approximated optimally and simultaneously.

此方法即为对方程的对流项沿流体流动的方向即特征方向进行离散，从而保证格式在流动锋线前沿逼近的高稳定性，消除了数值弥散现象，并得到了较小的时间截断误差；另一方面，对方程的扩散项采用混合元离散，可同时高精度逼近未知函数及其伴随向量函数，理论分析表明，此方法是稳定的，具有最优的L~2逼近精度。

The characteristic approximation is used to handle the convection part along the direc-tion of fluid namely characteristic direction to ensure the high stability of the method in approximating the sharp fronts and reduce the numerical diffusion; The mixed finite element spatial approximation is employed to deal with diffusion part and approximate the scalar unknown and the adjoint vector function optimally and simultaneously; In order to preserve the integral conservation of the method, we introduce the modified characteristic method.

该方法对方程的对流部分沿流体流动的方向即特征方向离散以保证格式在流动的锋线前沿逼近的高稳定性，消除数值弥散现象；对方程的扩散部分采用最低次混合有限元方法离散、同时以高精度逼近未知函数及未知函数的梯度；为保证方法的整体守恒性，在格式中引入修正项。

The calculation mechanics model is used for the curtain wall decussate rope net structure, including m horizontal ropes and n vertical ropes. The balance and displacement equations, alse the potential energy and kinetic energy equations, are constituted for the points with distributive loads and tensile force after the rope net distortion. Using the theory of finite analysis method, these groups of the n horizontal ropes' 2m+5 and m vertical ropes' 2n+5 equations are founded and the numerical solution is calculated.

建立幕墙由m根横向索、n根竖向索组成的正交索网结构的计算力学模型，在网点分配荷载及预张力作用下，列出钢索变形后的平衡方程、位移方程和弹性变形位能与外力作功方程，用有限分析方法将竖向索包含n个由2m+5变元组成的非线性方程组，将横向索包含m个由2n+5变元组成的非线性方程组寻求数值解。

Results show that the small vibration of this ideal model is non-simple harmonic,and the period of vibration in x direction and y direction are inverse ratio to the amplitude inverse ratio to the amplitude respectively,but influenced a little by them,and the waveform that coul.

本文应用拉格朗日方程方法研究了理想对称四弹性振子做二维运动的变化规律，得到其微小振动的控制方程，用数值解法求解出了振动方程，得到了振子运动的时程响应和轨迹图样。

In this dissertation the"Penalty"finite element method was employed to compute the velocity of the three-dimensional flow of power-law fluid in a profile die. In order to decrease the needed computer memory and raise the stability of numerical simulation, a set of decoupled methods such as PFEM, pseudo-body force method and transformation of momentum equation to the elliptic equation was developed to establish the general finite element equations to compute the distributions of velocity and viscoelastic stress of the three-dimensional viscoelastic flow of the Phan ThienTanner fluid in a profile die. During numerical simulation of the extrudate swell of the PTT fluid, the flow in the die and out of the die was analyzed separately, which demands less computer memory.

本文建立了求解挤出口模内幂律流体流动速度场的通用三维罚有限元模型；对于非线性粘弹性的Phan Thien-Tanner流体，为了降低模拟计算对计算机硬件的要求，并使模拟计算更加稳定，采用了一种去耦算法，包括罚有限元方法、拟体力方法和动量方程的椭圆类方程转化方法，并建立了求解速度场和粘弹性应力场的总体有限元方程；对于PTT流体的挤出胀大问题，提出了挤出胀大熔体口模内外分离模拟法，这样可以显著降低数值模拟对计算机硬件的要求。

In this dissertation the"Penalty"finite element method was employed to compute the velocity of the three-dimensional flow of power-law fluid in a profile die. In order to decrease the needed computer memory and raise the stability of numerical simulation, a set of decoupled methods such as PFEM, pseudo-body force method and transformation of momentum equation to the elliptic equation was developed to establish the general finite element equations to compute the distributions of velocity and viscoelastic stress of the three-dimensional viscoelastic flow of the Phan ThienTanner fluid in a profile die. During numerical simulation of the extrudate swell of the PTT fluid, the flow in the die and out of the die was analyzed separately, which demands less computer memory. The key techniques used in numerical simulation of the three-dimensional extrusion from dies such as decision of boundary conditions, creation of initial velocity field, selection of penalty factor, high Weissenberg number problem , regeneration of the free surface were studied in detail.

中文题名聚合物异型材口模挤出三维流动研究副题名外文题名 Study on three-dimensional flow of polymer melts during the process of profile extrusion from dies 论文作者涂志刚导师柳和生包忠诩教授学科专业材料加工工程研究领域\研究方向学位级别博士学位授予单位南昌大学学位授予日期2001 论文页码总数148页关键词挤出成型聚合物材料挤出口模聚合物异型材馆藏号BSLW /2003 /TQ320 /9 本文建立了求解挤出口模内幂律流体流动速度场的通用三维罚有限元模型；对于非线性粘弹性的Phan Thien-Tanner流体，为了降低模拟计算对计算机硬件的要求，并使模拟计算更加稳定，采用了一种去耦算法，包括罚有限元方法、拟体力方法和动量方程的椭圆类方程转化方法，并建立了求解速度场和粘弹性应力场的总体有限元方程；对于PTT流体的挤出胀大问题，提出了挤出胀大熔体口模内外分离模拟法，这样可以显著降低数值模拟对计算机硬件的要求。

According to the plastic equilibration equation and the theory of characteristic line, the stress equations of slip line in axial symmetry deformation on compressible materials were derived on basis of simplified yield criteria in this paper.

本文在可压缩材料简化屈服准则的基础上，根据塑性平衡方程和特征线理论推证出了可压缩材料轴对称问题的滑移线应力方程，提出了应力方程数值差分解

Considering of helical gear separate mesh and tooth-back shock, the non-linear vibration equitions of the system are also established, and the non-linear stable cycle solutions of the equitions are evaluated through dividing the timechanging stiffness matrics and dimension the equitions with selfadapt vary-step auto-RK4 numerical method.

考虑了斜齿轮传动的轮齿脱啮和齿后侧冲击，建立了系统的非线性振动方程，并通过对方程时变刚度阵的分块处理及无量刚化，用自适应变步长auto-RK4数值方法求出了系统非线性振动方程的稳态周期解。

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。