通过平均场处理的严格重正化群变换方法对Potts模型的应用

本文运用作者所发展的严格docimation- 平均场近似方法对Potts 模型的临界指数作了计算.所得结果与严格解符合得很好, 而与计算工作量相当的重正化群方法相比, 精确度大为提高。 关键词：     

e-A深度非弹性散射中胶子辐射振幅的新计算方法

在e-A深度非弹性散射过程中, 喷注穿过冷核介质时, 多重散射诱导胶子辐射会导致对碎裂函数的修正及喷注的能量损失.前期研究中关于计算e-A深度非弹性散射中胶子辐射振幅的两种方法: 螺旋振幅近似和微扰QCD严格计算都异常繁杂. 本文发展了一种新的方法, 可以方便计算出多重散射导致胶子辐射的振幅, 得到的碎裂函数的修正以及能量损失与严格计算的结果一致.     

用振幅矢量法计算光栅衍射的光强分布

本文介绍了一种在普通物理阶段严格计算光栅衍射光强分布的振幅矢量方法，此方法回避了困难的菲涅耳－基尔霍夫积分，这通常在普通物理中是不被采纳的，用振幅矢量法计算有两个显著的优点，一个是物理概念清楚，另一个是计算简单严格。     

有限温度真空极化与热背景介质的电磁性质

用有限温度场论方法,研究了真空极化的温度和密度效应及背景介质的电磁性质,严格计算了真空极化的有限温度、密度修正和热背景介质的介电常数与磁导率,给出了对任何温度和任何密度都适用的严格的解析表达式.     

用振幅矢量法计算光栅衍射的光强分布

本文介绍一种在普通物理阶段严格计算光栅衍射光强分布的振幅矢量方法，此方法回避了困难的菲涅耳－基尔霍夫积分，这通常在普通物理中是不被采纳的．用振幅矢量法计算有两个显著的优点，一个是物理概念清楚，另一个是计算简单严格     

运用严格耦合波理论计算平面电介质光栅的衍射效率

本文阐述了严格耦合波理论的基本思想。针对横电波的情况，详细分析了运用严格耦合波理论实现光栅衍射效率计算的方法，并且进一步给出了编制计算衍射效率程序的步骤。通过一个具体计算实例表明：各衍射级分布的光能量之和等于入射光的能量，满足能量守恒定律，从而证实了计算结果的正确性。     

平面光波导本征值的精确解法及光场分析

提出了一种严格且精确的基于传播矩阵方法计算光波导的算法,可计算出光波导的本征值,并画出场分布曲线。本方法物理意义清晰,计算方便,适用于计算机编程,并可推广用于波长量级光器件的计算。     

基于严格交换势的低能电子与H2分子碰撞振动激发散射截面的研究

严格交换势用于研究低能电子与H₂分子的弹性和非弹性散射截面,线性代数方法和R-矩阵传播子相结合求解基于振动密耦合方法的积分-微分耦合方程组,由此得到收敛的(0→0,0→1,0→2)散射微分截面和积分截面.理论计算结果与目前优秀的实验值和其他理论计算值进行了比较,表明基于振动密耦合方程的严格交换势在低能电子与H₂分子振动激发散射中有重要作用. 关键词： 严格交换势 2分子振动激发')" href="#">H₂分子振动激发 微分截面 积分截面     

二维伊辛模型相变临界点温度的模拟计算

用计算模拟方法计算了二维伊辛模型的相变临界点温度,其结果接近严格解,明显布喇格－威廉斯近似和贝特近似的结果。     

用超对称性和形不变性方法求解环形振子的能谱和波函数

运用超对称性和形不变性方法计算环形振子的能量本征值和本征波函数.所得到的能谱公式与用费曼路径积分方法得到的严格解完全一致.     

The auxiliary elliptic-like equation and the exp-function method

The auxiliary equation method is very useful for finding the exact solutions of the nonlinear evolution equations. In this paper, a new idea of finding the exact solutions of the nonlinear evolution equations is introduced. The idea is that the exact solutions of the auxiliary elliptic-like equation are derived using exp-function method, and then the exact solutions of the nonlinear evolution equations are derived with the aid of auxiliary elliptic-like equation. As examples, the RKL models, the high-order nonlinear Schrödinger equation, the Hamilton amplitude equation, the generalized Hirota-Satsuma coupled KdV system and the generalized ZK-BBM equation are investigated and the exact solutions are presented using this method.     

Dynamics of combined soliton solutions of unstable nonlinear Schrodinger equation with new version of the trial equation method

In this article, a new version of the trial equation method is suggested. With this method, it is possible to find the new exact solutions of the nonlinear partial differential equations. The developed method is applied to unstable nonlinear Schrödinger equation. New exact solutions are expressed with Jacobi elliptic function solutions, 1-soliton solutions and rational function solutions. When the obtained results are examined, we can say the unstable nonlinear Schrödinger equation shows different dynamic behaviors. In addition, the physical behaviors of these new exact solution are given with two and three dimensional graphs.     

A new exact substructure method using mixed modes

In this paper, the use of free- or fixed-interface modes in exact substructure displacement expansions is briefly summarized. Then the substructural displacements are expressed exactly in terms of mixed modes, i.e., the displacements consist of linear combinations of fixed- and free-interface modes. This yields a new exact mixed-mode substructure method. It is demonstrated that the exact substructure methods with fixed or free interfaces are two limiting cases of this new mixed-mode exact method. Thus, the exact substructure method variants with free-interface, fixed-interface or mixed modes form a systematic theory of substructure methods, which is unified by the new mixed-mode variant. This new exact variant not only has this important theoretical significance but also has great practical significance because it can lead to new approximate methods and to a deeper understanding of existing ones, e.g., quasi-comparison function methods, dynamic condensation methods or substructure modal synthesis methods.     

Group Analysis,Fractional Explicit Solutions and Conservation Laws of Time Fractional Generalized Burgers Equation

The generalized fractional Burgers equation is studied in this paper. Using the classical Lie symmetry method, all of the vector fields and symmetry reduction of the equation with nonlinearity are constructed. In particular,an exact solution is provided by using the ansatz method. In addition, other types of exact solution are obtained via the invariant subspace method. Finally, conservation laws for this equation are derived.     

Transformation from the nonautonomous to standard NLS equations

In this paper we show a systematical method to obtain exact solutions of the nonautonomous nonlinear Schrödinger (NLS) equation. An integrable condition is first obtained by the Painlevé analysis, which is shown to be consistent with that obtained by the Lax pair method. Under this condition, we present a general transformation, which can directly convert all allowed exact solutions of the standard NLS equation into the corresponding exact solutions of the nonautonomous NLS equation. The method is quite powerful since the standard NLS equation has been well studied in the past decades and its exact solutions are vast in the literature. The result provides an effective way to control the soliton dynamics. Finally, the fundamental bright and dark solitons are taken as examples to demonstrate its explicit applications.     

New exact solitary wave solutions to generalized mKdV equation and generalized Zakharov--Kuzentsov equation

In this paper, based on hyperbolic tanh-function method and homogeneous balance method, and auxiliary equation method, some new exact solitary solutions to the generalized mKdV equation and generalized Zakharov--Kuzentsov equation are constructed by the method of auxiliary equation with function transformation with aid of symbolic computation system Mathematica. The method is of important significance in seeking new exact solutions to the evolution equation with arbitrary nonlinear term.     

Diagonalizations on a correlated basis

Unsymmetrical quantum-dot systems are generally difficult to study using wave-function techniques, like quantum Monte Carlo (QMC) or exact diagonalization (ED) methods. The initial trial wave function for Monte Carlo methods is difficult to find, and the exact diagonalization method can only handle very few particles.In this article a two-dimensional semiconductor quantum dot containing a non-centered impurity ion is studied, using a new exact wave-function method. Results are analyzed and compared to density-functional-theory calculations. The computational method allows one to relax the commonly used lowest-Landau level (LLL) approximation, and it's effects are studied, e.g., on the charge and current density profiles.The method, which is a combination of QMC and ED methods, is described. It combines the scalability of Monte Carlo methods with the benefits of exact diagonalization, and allows one to accurately obtain the wave function for unsymmetrical quantum dots up to more than ten electrons. Also, excited states are accessible and are analyzed in this article.     

Numerical solution of 3D Green's function for the dynamic system of anisotropic elasticity

In this Letter, we used homotopy perturbation method to obtain numerical solution of the 3D Green's function for the dynamic system of anisotropic elasticity. Application of homotopy perturbation method to this problem shows the rapid convergence of the sequence constructed by this method to the exact solution. The numerical results obtained from convolution of Green's function and data of the Cauchy problem are compared with the exact solution for cubic media. The results reveal that the proposed method is very effective and simple.     

Calculation of the vortex pinning energy in a long periodically modulated Josephson contact

An analytical method for evaluating the Josephson and magnetic energies of a vortex, as well as the vortex pinning energy and its components, in a long periodically modulated Josephson contact is suggested. The method allows one to take into account the variation of the vortex shape with the position of the vortex. The results obtained with this method are much closer to those of exact computer analysis compared with results of the conventional techniques. The discrepancy between the exact shape of the vortex and a function obtained by solving a differential equation approximating the exact difference equation is studied.