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regular perturbation
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  正则摄动
     for one-dimension nonlinear oscillation with resistance f(x) =-kx-vx-βx~3,a regular perturbation solution is demonstrated
     本文详细讨论了一维含阻尼非线性振动f(x)=-kx-vx-βx~3的摄动解。 计算结果表明此解是长期有效的正则摄动解。
短句来源
     Regular Perturbation Theory for Application in Electromagnetic Scattering
     正则摄动理论在电磁散射中的应用
短句来源
     The muti-scale method and regular perturbation method are used for solving governed equations of nonlinear thermoelastically coupled vibrations of the plate which are derived in [2,3,4].
     本文以文[2,3,4]为基础,导出了板的热弹耦合非线性振动控制方程,在采用Galerkin法离散化以后,按各个变量性质分别用多尺度法或正则摄动法求得近似解析解。
短句来源
     This article brings forth the variational perturbation method—the known variational function J=J(y,a) is expanded into a series of the small parameter a by using the regular perturbation method and then turned into the linear function to be solved.
     本文所提出的变分泛函摄动法是对已知的变分泛函数J=J(y,a),用正则摄动法对小参数a展开,然后化为线性泛函求解。
短句来源
     A REGULAR PERTURBATION SOLUTION TO ONE—DIMENSION NONLINEAR OSCILLATION WITH RESISTANCE
     一维含阻尼非线性振动的正则摄动
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  “regular perturbation”译为未确定词的双语例句
     Regular Perturbation Method for Studying the Subthreshold Characteristics of Nano-Scaled MOSFETs
     摄动法研究纳米MOSFETs亚阈值特性
短句来源
     Regular perturbation analysis of cable withstanding twodi mersional loods
     二维载荷索道摄动法计算
短句来源
     With the permeability modulus assumed to be constant and Pedrosa transformation introduced, the nonlinearity of the governing equation for the pressure becomes weaker and the first-order perturbation solution is obtained for a radial reservoir with infinite boundary condition by use of the regular perturbation method.
     假设渗透率模量为常数,通过引入Pedrosa变换,使得压力控制方程的非线性弱化,并利用正规摄动法获得在无穷大边界条件下的一阶摄动解;
短句来源
     Introducing Pedrosa transform to weaken the non-linear item in the percolation diffusion equation when the model is solved, and using the regular perturbation equation to accurately derive the zero-order and first-order solutions of the percolation model, the inflow performance equation is established for the wells of stress-sensitive gas reservoirs with high pressure.
     在求解模型时,引入Pedrosa变换将渗流扩散方程中的非线性项弱化,用正规摄动技术精确地求解出渗流模型的零阶和一阶解,得到应力敏感性高压气藏井流入动态方程。
短句来源
  相似匹配句对
     The regular perturbation method is described.
     简要介绍了正则摄动法 .
短句来源
     Perturbation of Regular Spectral Operators
     正则谱算子的微扰
短句来源
     S-REGULAR SEMIGROUPS
     S-正则半群
短句来源
     On P~s-Regular Groups
     关于P~S—正则群
短句来源
     ON THE PERTURBATION OF MATRIX EIGENVALUES
     关于矩阵特征值的扰动
短句来源
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  regular perturbation
An approximate solution for the complete differential equation is given using a regular perturbation technique.
      
A regular perturbation approach to the problem of diffusion towards a growing mercury drop electrode
      
The convergence of the results obtained by this approximate technique is checked by comparing the results with those of exact solutions obtained using a regular perturbation technique.
      
Analytical expressions for the velocity and the angular velocity fields have been obtained, using the regular perturbation technique.
      
A solution of the Navier-Stokes equations is obtained by employing a regular perturbation technique.
      
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Using regular perturbation method, a series of asymptotic equations and corresponding boundary condtiions of those problems, in which the geometric forms of the boundary surfaces are characterized by small asymmetry, have been established. For every order of the asymptotic solution, the dimensionality of the problem has been decreased by one. Thus the analytic solutions of some two-dimensional problems may be obtained, and some complex three-dimensional problems can be transformed into two-dimensional...

Using regular perturbation method, a series of asymptotic equations and corresponding boundary condtiions of those problems, in which the geometric forms of the boundary surfaces are characterized by small asymmetry, have been established. For every order of the asymptotic solution, the dimensionality of the problem has been decreased by one. Thus the analytic solutions of some two-dimensional problems may be obtained, and some complex three-dimensional problems can be transformed into two-dimensional problems so that the quantity of numerical computation could be much decreased. At the same time, it is bellieved that a theoritical basis and a method of modification have been given to the usually used "revolution-profile-method".

利用正则摄动法建立了边界几何形状具有微小非轴对称性问题的渐近方程组及其相应的边界条件。使问题的维数,对各级渐近解而言,降低了一维。从而可能得到一些二维问题的解析解,或者可将复杂的三维问题变为二维问题,大大减少了计算工作量。同时,对工程上惯用的“旋转剖面法”提供了理论依据及修正的方法。 作为例子,给出了具有偏心内园孔的厚壁筒温度场及应力场的解析解,绘出了剖面上温度及应力的分布曲线。结果表明,该方法是可行的。

The Lighthill's technique is applied to the solution of heat conduction in a cylindrical body undergoing solidification. The boundary conditions of the first kind and the third kind are considered. The Ste-number, the ratio of the sensible heat to the latent heat, is chosen as small parameter s. The temperature U, the freezing depth S and the time r are expanted as powers in terms of e. The first order term of r is chosen so that the solution is still applicable as the freezing front approaches the center where...

The Lighthill's technique is applied to the solution of heat conduction in a cylindrical body undergoing solidification. The boundary conditions of the first kind and the third kind are considered. The Ste-number, the ratio of the sensible heat to the latent heat, is chosen as small parameter s. The temperature U, the freezing depth S and the time r are expanted as powers in terms of e. The first order term of r is chosen so that the solution is still applicable as the freezing front approaches the center where the regular perturbation solution is found to diverge. The correlation of the entire solidification period with Ste-number and Bi-number is given. The solution obtained is compared with both experimental results and numerical results using the enthalpy model, the agreement is reasonable good.

在求解伴随凝固和熔融的热传导问题时,本文试用一种奇异摄动方法,选择显热与潜热之比—Ste数为摄动参数,将温度、移动的固液界面位置以及时间按摄动参数的幂级数展开,求得了初态在熔点,表面因对流冷却而凝固的热传导问题的一阶近似解;给出了凝固总时间与Ste数以及Bi数之间的良好近似公式.所得结果与基用于焓模型求得的数值解和实验结果相符得很好.

The purpose of this paper is to develop a regular perturbation method for solving the problem of one dimensional elastic/visco-plastic wave propagation in materials of Malvern's type. Firstly, non-dimensionalized linear multiplication coefficient and damping coefficient of dislocation are introduced as two independent small parameters into the perturbation expansion of solution. Thus, the problem of solving the non-linear wave equations is transformed into finding the solution of homogeneous/nonhomoge-neous...

The purpose of this paper is to develop a regular perturbation method for solving the problem of one dimensional elastic/visco-plastic wave propagation in materials of Malvern's type. Firstly, non-dimensionalized linear multiplication coefficient and damping coefficient of dislocation are introduced as two independent small parameters into the perturbation expansion of solution. Thus, the problem of solving the non-linear wave equations is transformed into finding the solution of homogeneous/nonhomoge-neous telegraph equations. Secondly, an analytical zeroth order approximate solution can be obtained by means of Laplace transform or series expansion technique. Then the first order and higher order approximate solutions are derived from the zeroth order approximate solution based on the method of finding the Riemann function.Through the comparison of the first order approximate solution with the numerical solution of the corresponding non-linear governing equations under the boundary condition of constant stress aσ|x=0= const, it is seen that the first order approximate solution is quite good. Lastly, it appears that, from the results given in this paper, the perturbation method is quite powerful in the study of elastic/visco-plastic wave propagation theory.

采用控制金属材料宏观塑性流动的两个无量纲物理参数作为小参数,将一维弹/粘-塑性问题的解摄动展开,从而,求解非线性波动方程的问题可以转化成求解相应的齐次或非齐次电报方程的问题,用Laplace积分变换或级数展开技术首先得到零次精确解。然后,用Riemann函数方法可获得一次和高次摄动解。与非线性问题的数值解比较,在恒应力或恒速度边界条件下,一次摄动解给出了波动问题的良好近似。这就表明,摄动技术在研究一类广泛的弹/粘-塑波问题中是有效的。

 
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