压电体的几个变分原理

本文首先讨论了压电体态变量的协调性。接着系统地提出了压电体的四个变分原理。这四个变分原理的泛函是压电体不同的热力学函数与动能的差,它们反映不同的物理条件,有不同的应用范围。本文讨论了它们的应用。     

基于等几何分析的边界元法求解Helmholtz问题

将基于一类局部双变量B样条函数的等几何分析方法和Burton-Miller方法相结合,分析三维Helmholtz问题.对于某些从二维参数域映射到三维空间具有奇异点的参数曲面,该方法可以有效地避免奇异点处大量奇异与近奇异积分的计算.数值算例表明该方法具有较好的计算精度和计算效率.复杂问题的分析表明,该方法具有良好的工程应用前景.     

样条函数在光学器件设计和优化中的建模与应用

讨论了样条函数在光学器件设计和优化过程中的建模方法与应用。提出了用样条函数进行太阳能会聚器的优化设计。根据太阳能会聚器曲面的设计要求,首先讨论了抛物面与高次非球曲面的光学性能,然后给出了样条函数的数学模型和优化设计过程。基于光学设计软件CODE V的计算机仿真结果表明,它与通常的抛物面会聚器相比,样条函数方法具有太阳能转换效率高、系统可实现间断跟踪太阳和成本低等优点。     

用样条函数表示非球面方程式的光线追迹

提出用样条函数来表示非球面方程式,它优于一般的非球面方程式表示法,便于计算。     

啁啾微波场中里德伯钠原子高激发态的布居跃迁

采用含时多态展开方法, 结合B样条函数和单电子原子模型势研究微波场中钠原子里德伯高激发态的性质, 得到钠原子的能级结构及在微波场中的布居数迁移, 实现对量子态的操纵与控制. 结果表明: 含时多态展开方法结合B样条函数和单电子原子模型势是有效研究微波场中碱金属原子性质的一种方法; 选择合适的啁啾率、振幅等参数, 可以实现布居数在量子态之间的完全迁移和量子态囚禁.     

Boussinesq方程组的广义变分原理

半反推法是何吉欢为了寻求物理问题的变分原理而提出的,可避免由拉氏乘子法引起的临界变分现象. 应用半反推法分别获得了描述水波运动的两类Boussinesq方程组的一族广义变分原理,并验证了它们的正确性. 关键词： 半反推法 广义变分原理 Boussinesq方程组     

广义Duffing扰动振子随机共振机理的渐近解

利用非线性方法研究了一类广义Duffing扰动方程.首先求得了典型的Duffing方程的解.然后利用泛函广义变分迭代原理得到了广义Duffing扰动振子随机共振机理的近似解,并论述了解的一致有效性.     

凑合反推法──流体力学变分原理建立的一条新途径

凑合反推法是刘商联系统方法[1]的进一步发展，应用这种方法可以方便地构造各种亚广义变分原理及广义变分原理，并可以消除临界变分现象．对于任何二维守恒型流体力学方程，作者推导得到了其广义变分通用公式．几个实例证明这种方法是有效的、简单的，并具有普遍的意义．     

用广义变分迭代理论求一类相对转动动力学方程的解

研究了一类具有非线性阻尼力和强迫周期力项的相对转动扰动动力学方程. 首先利用变分原理构造了广义变分迭代, 其次决定方程的初始近似, 最后通过迭代表示式得到了对应方程的任意次近似解. 关键词： 相对转动 动力系统 变分迭代     

传质势容耗散极值原理及通风排污过程的优化

为了获得排污效率较高的室内通风方式,本文将传热势容耗散极值原理应用到对流传质过程分析,定义了传质势容耗散函数,并利用变分原理在给定条件下对耗散函数求极值,获得了场协同方程,求解场协同方程获得了最佳流场,使传质势容耗散取得极小值,室内污染物浓度最低.这些结论对通风排污过程的分析与优化设计有重要指导意义.     

A variational formulation for the finite element analysis of the vibratory and acoustical response of high speed machinery

The principle of virtual velocities is employed herein to develop a variational theorem for determining the vibratory and acoustical response of high speed mechanisms immersed in a perfect fluid (air). Both the solid and fluid media are modeled as continua and the basic functional expression is generalized by using Lagrange multipliers to incorporate field equations, boundary conditions and a kinematic constraint on the intetface region between the two types of continua. The resulting mixed variational equation of motion then provides the basis for finite element analyses of these acousto-mechanical systems by mixed and displacement (velocity) formulations.     

A new orthogonality relationship for orthotropic thin plate theory and its variational principle

While Hamiltonian system was led to solution of elastic theory a symplectic system-atic methodology for theory of elasticity was established and a symplectic orthogonality relationship was presented[1,2]. For two-dimensional theory of elasticity a new dual vec-tor and a new dual differential matrix were presented by putting the old dual vector[1] in a new order. It was discovered for isotropic materials that the symplectic orthogonality relationship may be decomposed into two independent and s…     

Three-dimensional electromagnetic articulography: a measurement principle

A measurement principle of the three-dimensional electromagnetic articulographic device is presented. The state of the miniature receiver coil is described by five variables representing the position in the three-dimensional coordinate system and the rotation angles relative to it. When the receiver coil is placed in the magnetic field produced from the distributed transmitter coils, its state can be optimally estimated by minimizing the difference between the measured strength of the received signal and the predicted one using the known spatial pattern of the magnetic field. Therefore, the design and calibration of the field function inherently determine the accuracy in estimating the state of the receiver coil. The field function in our method is expressed in the form of a multivariate B spline as a function of position in the three-dimensional space. Because of the piecewise property of the basis function and the freedom in the selection of the rank and the number of basis functions, the spline field function has a superior ability to flexibly and accurately represent the actual magnetic field. Given a set of calibration data, the spline function is designed to form a smooth curved surface interpolating all of these data samples. Then, an iterative procedure is employed to solve the nonlinear estimation problem of the receiver state variables. Because the spline basis function is a polynomial, it is also shown that the calculation of the Jacobian or Hessian required to obtain updated quantities for the state variables can be efficiently performed. Finally, experimental results reveal that the measurement accuracy is about 0.2 mm for a preliminary condition, indicating that the method can achieve the degree of precision required for observing articulatory movements in a three-dimensional space. It is also experimentally shown that the Marquardt method is a better nonlinear programming technique than the Gauss-Newton or Newton-Raphson method for solving the receiver state problem.     

小波抽样与气象要素场插值

首先用6种插值方法对一个带限与非带限一维信号分别进行等距插值计算检验.6种方法是基于Shannon抽样定理的插值法、两种基于小波抽样的插值法、三次样条插值法、三次卷积插值法和快速Fourier变换插值法.结果显示小波和三次样条插值法最好,其中小波插值误差的局域性最好.最差的是快速Fourier变换法.其次,剔除快速Fourier变换插值法,将其它5种插值公式推广到二维的情形,对大气层中层500hPa高度场、海平面气压场和降水量场也进行了插值计算.误差分析表明对于降水量场三次样条小波插值最好,对高度场和海平面气压场三次样条插值法仍然是最好的.在此基础上,提出了既保证降水量场插值精度又能避免插出"负降水"的插值处理方法并进行了计算检验.最后指出了小波插值法有待改进的问题.     

Binding energies of impurity states in strained wurtzite GaN/Al_xGa_(1-x)N heterojunctions with finitely thick potential barriers

Ground state binding energies of donor impurities in a strained wurtzite GaN/AlxGal_xN heterojunction with a po- tential barrier of finite thickness are investigated using a variational approach combined with a numerical computation. The built-in electric field due to the spontaneous and piezoelectric polarization, the strain modification due to the lattice mismatch near the interfaces, and the effects of ternary mixed crystals are all taken into account. It is found that the binding energies by using numerical wave functions are obviously greater than those by using variational wave functions when impurities are located in the channel near the interface of a heterojunction. Nevertheless, the binding energies using the former functions are obviously less than using the later functions when impurities are located in the channel far from an interface. The difference between our numerical method and the previous variational method is huge, showing that the former should be adopted in further work for the relevant problems. The binding energies each as a function of hydrostatic pressure are also calculated. But the change is unobvious in comparison with that obtained by the variational method.     

The generalized quasi-variational principles of non-conservative systems with two kinds of variables

Many investigators have paid much attention to the generalized variational principles in mechanics of deformable bodies. Ref. [1] laid a foundation for the generalized varia-tional principles by studying the principle of complementary energy, from both theoreti-cal and practical points of view. Ref. [2] established the generalized variational princi-ples of elasticity and plasticity and provided the theoretical foundation for the mixed finite element method, which was widely used in the field.…     

A variational principle for the scattered wave

A Schwinger-type variational principle is presented for the scattered field in the case of scalar wave scattering with an arbitrary field incident on an object of arbitrary shape with homogeneous Dirichlet boundary conditions. The result is variationally invariant at field points ranging from the surface of the scatterer to the farfield and is an important extension of the usual Schwinger variational principle for the scattering amplitude, which is a farfield quantity. Also, a generic procedure, physically motivated by the general principles of boundary conditions and shadowing, is presented for constructing simple trial functions to approximate the fields. The variational principle and the trial function design are tested for the special case of a spherical scatterer and accurate answers are found over the entire frequency range.     

Natural vibration of circular and annular thin plates by Hamiltonian approach

The present paper deals with the natural vibration of thin circular and annular plates using Hamiltonian approach. It is based on the conservation principle of mixed energy and is constructed in a new symplectic space. A set of Hamiltonian dual equations with derivatives with respect to the radial coordinate on one side of the equations and to the angular coordinate on the other side are obtained by using the variational principle of mixed energy. The separation of variables is employed to solve Hamiltonian dual equations of eigenvalue problem. Analytical frequency equations are obtained based on different cases of boundary conditions. The natural frequencies are the roots of the frequency equations and corresponding mode functions are in terms of the dual variables q₁(r, θ). Three basic edge-constraint cases for circular plates and nine edge-constraint cases for annular plates are calculated and the results are compared well with existing ones.     

Solving optimization problems with mean field methods

A brief review is given for the use of feed-back artificial neural networks (ANN) to obtain good approximate solutions to combinatorial optimization problems. The key element is the mean field approximation (MFT), which differs from conventional methods and “feels” its ways towards good solutions rather than fully or partly exploring different possible solutions. The methodology, which is illustrated for the graphs bisection and knapsack problems, is easily generalized to Potts systems. The latter is related to the deformable templates method, which is illustrated with the track finding problem.

The mean field approximation is based on a variational principle, which also turns out to be very profitable when computing correlations in polymers.