模方程

词组短语

modular equation

与模方程相关的网络例句 [注：此内容来源于网络，仅供参考]

The coupling constants between the fundamental mode and the first-order cladding modes were determined by a mode-coupling equation.

通过耦合模方程确定了基模和一阶各次包层模之间的耦合常数。

Finally, in the third section, by constructing some functional which similar to the conservation law of evolution equation and the technical estimates, we prove that in the inviscid limit the solution of generalized derivative Ginzburg—Landau equation converges to the solution of derivative nonlinear Schrodinger equation correspondently in one-dimension; The existence of global smooth solution for a class of generalized derivative Ginzburg—Landau equation are proved in two-dimension, in some special case, we prove that the solution of GGL equation converges to the weak solution of derivative nonlinear Schr〓dinger equation; In general case, by using some integral identities of solution for generalized Ginzburg—Landau equations with inhomogeneous boundary condition and the estimates for the L〓 norm on boundary of normal derivative and H〓 norm of solution, we prove the existence of global weak solution of the inhomogeneous boundary value problem for generalized Ginzburg—Landau equations.

第三部分：在一维情形，我们考虑了一类带导数项的Ginzburg—Landau方程，通过构造一些类似于发展方程守恒律的泛函及巧妙的积分估计，证明了当粘性系数趋于零时，Ginzburg—Landau方程的解逼近相应的带导数项的Schr〓dinger方程的解，并给出了最优收敛速度估计；在二维情形，我们证明了一类带导数项的广义Ginzburg—Landau方程整体光滑解的存在性，以及在某种特殊情形下，GL方程的解趋近于相应的带导数项的Schr〓dinger方程的弱解；在一般情形下，我们讨论了一类Ginzburg—Landau方程的非齐次边值问题，通过几个积分恒等式，同时估计解的H〓模及法向导数在边界上的模，证明了整体弱解的存在性。

Based on the modem FEM with the dynamic substructure method, itd dynamic equation is established with almost no limits to DOFs of the system, in which the left side is the first approach of the nonlinear system and the right side is the excitation and coupling nonlinear pseudo forces. The modal analysis method is used to get the eigen solution to the reduced linear homogeneous dynamic differential equation. When the system is excited by the harmonic excitation at the right side of the equation, the nonlinear dynamic response can be calculated by the numerical method to give quantitative analysis.

基于近代有限元和子结构模态综合法的动力学建模方法，获得非线性系统动力学微分方程，其自由度几乎没有限制，对左端首次近似齐次方程进行模态分析，选取对响应有贡献的部分本征对，同样对右端激励和非线性伪力作模态变换，得到减缩后非线性系统耦合动力学微分方程。

The classical mode-locking equations shows to be coupling nonlinear second order partial difference equations.

4按照H.A.Haus等人所采取的方法，将量子锁模方程过渡为经典锁模方程。

In this topic, the dynamic analysis methods for piezoelectric vibrator are studied systematically based on the theoretical model, FEM numerical experimentation and FEM governing equation for given compound-mode vibrator, and some valuable conclusions are obtained. The main work accomplished is summarized as follows: 1.Elaborate the main modeling methods for piezoelectric vibrator and the significance and necessity to study the dynamic characteristics of piezoelectric vibrator which emphasize the urgency of this paper. 2.Take the bending deformation induced by piezoelectric ceramic as example, the energy transfer mechanism of electric energy to mechanical energy are analyzed; the motion and force transfer mechanism are analyzed for the longitudinal-bending vibrator. 3.Based on mode assumption and Hamilton principle, the coupling model of piezoelectric vibrator of linear USM is built; moreover, the equivalent circuit model is obtained and a coupling equation represents the relation between electric parameters and mechanical parameters is derived which provides foundation to match the vibrator and driving circuit. 4.Combine the constitutive equation of piezoelectric ceramic with elastic-dynamical equation, geometric equation in force field and the Maxwell equation in electric field and the corresponding boundary condition equation, the FEM control equation for piezoelectric vibrator of USM to solve dynamic electro-mechanical coupling field is established by employing the principle of virtual displacement. The equation lays the foundation to study the non-linear constitutive equation of piezoelectric ceramic driven by high-power. 5.Define the dynamic indexes of characteristic of vibrator and carry out variable parameters simulation by calculating the model parameters and the electric characteristics of vibrator are simulated according to the equivalent circuit model. By numerical experimentation, the working mode of vibration of vibrator and the shock excitation results of the working frequency band which provides the mode frequency to realize bimodal are analyzed. Detailed calculation of the electro-mechanical coupling field parameters is made by programming the FEM control equation.

本课题从理论模型、有限元数值试验、有限元控制模型等方面以复合振动模式振子为例对超声电机压电振子的动力学特性及其分析方法进行了全面系统地研究，得出了许多有价值的结论，主要概括如下： 1、阐述了目前针对超声电机压电振子的主要建模方法，对压电振子动态特性的研究意义和必要性进行了论述，突出了本文研究内容的迫切性； 2、以压电陶瓷诱发弹性体发生弯曲变形为例，分析了压电陶瓷通过诱发应变来实现机电能量转换的机理；对基于纵弯模式的压电振子的运动及动力传递机理进行了分析； 3、基于模态假定，利用分析动力学的Hamilton原理，建立了面向直线超声电机压电振子的机电耦合动力学模型，并据此建立了压电振子的等效电路模型，导出了电参量与动力学特性参量的耦合方程，为压电振子与驱动电路的匹配提供了依据； 4、从压电陶瓷的本构方程出发，综合力场的弹性动力学方程、几何方程、电场的麦克斯韦方程以及相应的边界条件方程，采用虚位移原理，建立了压电振子动态问题机电耦合场求解的有限元控制方程，为研究其大功率驱动下的非线性本构模型奠定了基础； 5、界定压电振子的动力学特性指标，对压电振子的机电耦合动力学模型参数进行计算及变参数仿真；依据等效电路模型，对压电振子的电学特性进行了仿真分析；通过有限元数值实验，对压电振子工作模态附近的模态振型及工作频率附近的频段进行了激振效果分析，找出了实现模态简并的激振频率；利用有限元控制方程，通过编程计算，对压电振子的力电耦合场参数进行了详细计算，得出了一些有价值的结论。

By comparison with theoretical K value to figure out variance and to find out the main soil character parameter. Using MATLAB software, theory of parameter modification is employed to modify parameters in Normal Equation. Eventually, the proper calculating model of K factor the same with the typical slope soil of highway in Hubei Province, is established.

比较理论土壤可蚀性因子K值及实测土壤可蚀性因子K值之间的差异，找出导致该差异的主要土壤性质参数，在此基础上运用MATLAB数学分析软件对诺模方程进行修正，以得到适用于湖北省孝襄高速公路边坡代表性土壤的土壤可蚀性因子K值的计算模型。

The Bragg wavelength of the fiber grating will shift when the uniform magnetic field in the solenoid changes.

2将正确的光纤中的正交关系应用于微扰理论得到了微扰形式的光纤耦合模方程。

The major research includes the following three points. First, using finite element method, the influence factors on propagation properties for PMF couplers are analyzed, including the shape of coupler cross-section, the taper of coupler bipyramidal and the angle deviation of the birefringent axes.

基于热-结构-电磁多物理场耦合有限元方法，分析了保偏光纤耦合器的传输特性和耦合系数在熔锥区的变化规律，从而求解耦合模方程，得到偏振光经过耦合器后的光功率分布，继而对保偏光纤耦合器的性能参数分光比、消光比及附加损耗进行理论分析。

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。

Eigenstates of laser system with negative GVD is constructed under the condition of steady state, and the expectation value of variables that describe optical field are obtained as well.

利用算符的海森堡运动方程以及算符之间的对易关系分别在频域和时域中导出了双波长飞秒激光器的量子锁模方程。

与模方程相关的网络解释 [注：此内容来源于网络，仅供参考]

analog to digital conversion：模数转换

9 Amplifier 放大器 | 10 Analog-to-Digital Conversion 模数转换 | 11 Analysis equation 分析方程

associated graded ring：形式环

associated graded module 相伴分次模 | associated graded ring 形式环 | associated homogeneous equation 相伴齐次方程

Bernoulli equation：白努利方程[式] = 伯努利方程

bent bond 彎鍵 | Bernoulli equation 白努利方程[式] = 伯努利方程 | Bernstein Greene Kruskal mode BGK模

Fuchs：富克斯

.克罗内克(Kronecker)的算术方向.但黎曼的原始思想--亏格、双有理变换、参模等概念以及黎曼-洛赫定理始终是指导其发展的一条主线.(3)微分方程.1865年,L.富克斯(Fuchs)在黎曼思想基础上创立了复域的常微分方程论.在他的影响下,

hilbert modular form：希尔伯特模形式

希尔伯特流形|Hilbert manifold | 希尔伯特模形式|Hilbert modular form | 希尔微分方程|Hill differential equation

hill differential equation：希尔微分方程

希尔伯特模形式|Hilbert modular form | 希尔微分方程|Hill differential equation | 希尔行列式|Hill determinant

normal hyperbolic equation：模双曲方程

normal hydrostatic pressure 正常静水压力 | normal hyperbolic equation 模双曲方程 | normal identifier 正常标识符

modular character：模特征

modular category 模范畴 | modular character 模特征 | modular equation 模方程

modular equation：模方程

modular character 模特征 | modular equation 模方程 | modular figure 模图

modular figure：模图

modular equation 模方程 | modular figure 模图 | modular form 模形式