稳恒电路分析中的变分原理

变分原理告诉我们;满足一定约束条件的物理系统;在其所有的可能状态中;对应于作用量函数取极值的状态是真实存在的状态。     

基于变分原理的自适应方法在统一坐标系中的应用

在统一坐标系的基础上引入变分方法,并从自适应网格的正交性、光滑性、疏密程度等角度考虑,获取速度系数h的椭圆方程,从而在边界上可以自由控制h的取值,以适应不同物理问题的需要.算例证明,变分法在统一坐标系中的应用是可行的,在边界上可以满足物理要求.     

修正的变分迭代法在四阶Cahn-Hilliard方程和BBM-Burgers方程中的应用

变分迭代法是一种基于变分原理,具有高数值精度的数值格式,目前已广泛应用于各类强非线性孤立波方程的数值求解中.本文利用修正的变分迭代法对两类非线性方程进行研究.该格式是对原数值方法的一种改进,即在变分项前引入了参数h.通过定义误差函数的离散二范数并在定义域内绘出h-曲线,从而确定出使误差达到最小的h,再返回原迭代过程进行...     

梯度计算的集合变分方案及其在大气Ekman层湍流系数反演中的应用

大气Ekman层湍流系数的准确计算对数值天气预报和污染物扩散计算有着重要的意义. 将集合计算和变分法结合起来, 提出了目标泛函梯度计算的集合变分方案, 并根据正演模式的线性化情况提出了两种计算流程. 利用这种集合变分梯度算法及两种流程对Ekman层湍流系数进行了反演试验, 结果表明这种算法实施简单、方便, 根据观测资料能够比较准确地反演湍流系数值.关键词：梯度计算集合变分湍流系数反演     

有耗孤子的最小作用量原理及其在二维光子带隙结构中的应用

采用变分方法对于二维矩形光子带隙结构中X点孤子的耗散以及相干作用进行了动力学分析.通过对由作用量原理得到的孤子参量联立方程组的分析可知,除了耗散作用导致孤子的幅度衰减,并引起孤子横向的展宽以外,同向孤子的相互作用负势函数为耗散作用所减弱,从而使得孤子在x方向的束缚态被削弱.孤子中心间距随x的增加呈现出增幅变化且波动周期增大,当纵向距离增大到一定值后,孤子中心间距将一直增大下去.     

A novel variational principle in electrostatics and its consequences

We propose a novel variational principle in electrostatics and show that one can derive mirror equation in the context of image problem starting from this principle.     

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…     

Degenerate perturbation theory and its application to the Hubbard model

Projection operators are incorporated in the canonical transformation to derive an analytical infinite series of a degenerate perturbation expansion. The theory is used to calculate the ground state energy of a half-filled s-band Hubbard model to seventh order.     

Nonperturbative calculations in the framework of variational perturbation theory in QCD

Physics of Atomic Nuclei - We discuss applications of the method based on the variational perturbation theory to perform calculations down to the lowest energy scale. The variational series is...     

The bogolyubov variational principle in the theory of an anharmonic crystal

The Bogolyubov variational principle for classical systems is used to obtain the variation equation for a self-consistent field. With the help of this equation, various approximations of the self-consistent field method in the theory of a crystal with a multiparticle interaction are studied. The free energy of the crystal is calculated.     

Hamilton’s principle and associated variational principles in polar thermopiezoelectricity

We express Hamilton’s principle for a regular region of thermopiezoelectric polar materials. First, we obtain a four-field variational principle which leads, as its Euler-Lagrange equations, to the divergence equations and the associated natural boundary conditions only. Next, we adjoin the rest of the fundamental equations into the variational principle through an involutory transformation. Thus, we formulate a differential type of unified variational principles operating on all the field variables. The unified variational principle is extended for the region with a fixed internal surface of discontinuity and for a curvilinear laminated region as well. The principles derived in invariant form are expressible in a system of particular coordinate system most appropriate to the geometry of the regions. They are indicated to recover some of earlier principles as special cases.     

Unconventional Hamilton-type variational principle in phase space and symplectic algorithm

By a novel approach proposed by Luo, the unconventional Hamilton-type variational principle in phase space for elastodynamics of multidegree-of-freedom system is established in this paper. It not only can fully characterize the initial-value problem of this dynamic, but also has a natural symplectic structure. Based on this variational principle, a symplectic algorithm which is called a symplectic time-subdomain method is proposed. A non-difference scheme is constructed by applying Lagrange interpolation polynomial to the time subdomain. Furthermore, it is also proved that the presented symplectic algorithm is an unconditionally stable one. From the results of the two numerical examples of different types, it can be seen that the accuracy and the computational efficiency of the new method excel obviously those of widely used Wilson-θ and Newmark-β methods. Therefore, this new algorithm is a highly efficient one with better computational performance.     

A variational principle for boundary value problems in kinetic theory

A variational principle which applies directly to the integrodifferential form of the linearized Boltzmann equation is introduced. Extremely general boundary conditions and collision terms are allowed. For a class of interesting problems, the value of the functional to be varied is shown to be closely related to quantities of great physical interest. The formalism is applied to the treatment of plane Couette flow for different forms of the collision term (BGK model, rigid spheres, Maxwell's molecules).Research sponsored by the Air Force Office of Scientific Research under contract F 61(052)-68-C-0020, through the European Office of Aerospace Research, OAR, United States Air Force.