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decimation-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：     

三维晶格统计模型的一种封闭的近似解

引用四元数(或转动群的双值表示)推广处理二维晶格统计模型的无规行走法,为三维简立方晶格求得了统计配分函数的一个封闭的近似解析表达式。它在从零到无限大的温度区间内都成立,可以过渡到正确的二维结果,具有一个温度奇点、非对数型的比热奇异性和较好的高温展开系数。     

三维Ising模型的封闭近似解(Ⅲ)——用高阶超复数改进数值结果的可能性

在分析Ising模型二维严格解和三维Q近似的基础上,讨论统计配分函数解析表达式应当具备的各种性质。在此基础上探讨引用高阶超复数从数值上改进Q近似所得结果的可能性,为构造高低温之间的配分函数的内插公式作好准备。 关键词：     

RING APPROXIMATION FOR A SYSTEM WITH S-D INTERACTION

The ring approximation for a system with s-d interaction is studied by the Abrikosovfs pseudofermion method. It is shown that the RKKY interaction should be included in the expression of the thermodynamic potential. .Some implications are noted.     

THE CRITICAL DYNAMICS OF THE KINETIC ISING MODELS ON THE SYSTEMS WITH Rmin> 2

We perform the exact TDRG transformations on the kinetic Ising model of the braced ladder whose R_min is 5. Within our knowledge, this is the only example that the exact TDRG transformations have been performed on a system with R_min >2. We show that under Achiam's linear response theory there must be important excitations of the multi-spin operators in the kinetic Ising models of the systems with R_min > 2, the dynamic critical behaviours of the systems are greatly affected by these excitations. Moreover, we get the conclusion that for the kinetic Ising models of the systems with R_min=∞ exact TDRG calculationa are impossible. The complete new and interesting results are given.     

三维Ising模型的封闭近似解(Ⅳ)——配分函数的近似内插公式

根据对二维严格解和三维Q近似的分析,为三维Ising模型的配分函数提出一类近似的内插公式。只要付出足够的计算量,它原则上可以尽量多地反映目前已有的关于奇异点位置和高低温展开系数的知识,由一个封闭的解析表达式同时给出较好的高温和低温行为,但不能更好地反映比热奇异性。 关键词：     

THE CRITICAL DYNAMICS OF THE KINETIC ISING MODELS ON THE SYSTEMS WITH Rmin> 2

We perform the exact TDRG transformations on the kinetic Ising model of the braced ladder whose R_min is 5. Within our knowledge, this is the only example that the exact TDRG transformations have been performed on a system with R_min >2. We show that under Achiam's linear response theory there must be important excitations of the multi-spin operators in the kinetic Ising models of the systems with R_min > 2, the dynamic critical behaviours of the systems are greatly affected by these excitations. Moreover, we get the conclusion that for the kinetic Ising models of the systems with R_min=∞ exact TDRG calculationa are impossible. The complete new and interesting results are given.     

EXACT SOLUTION FOR EXTENDED ESSLER-KOREPIN-SCHOUTENS MODEL WITH OPEN BOUNDARY CONDITIONS

The eigenvalue of the transfer matrix is obtained for the extended Essler-Korepin-Schoutens model with open boundary conditions. The energy of the system and the Bethe equations of the model are given also.     

AN INTEGRAL EXPRESSION OF EXACT SOLUTION FOR HARMONIC OSCILLATOR WITH TIME-VARYING FREQUENCY

Using Feynman's method of disentangling operators, an exact expression of evolution operator of harmonic oscillator with time-varying frequency is obtained. The parameters in this expression are related to the time-varying frequency directly. Some implications are further investigated, including general form of linear and quadratic invariants and evolution of Wigner function.     

非线性浅水长波近似方程组的显式精确解

利用两种不同的方法考虑非线性浅水长波近似方程组.用sine-cosine方法并借助Mathematica软件和吴文俊消元法,获得三组孤子解.通过引入新的变换,又获得若干有理形式的解.这两种方法也适合于其他非线性方程(组).     

AN EXACT METHOD FOR THE FREE VIBRATION ANALYSIS OF TIMOSHENKO-KELVIN BEAMS WITH OSCILLATORS

In this paper, a modern exact method is proposed for solving the problem of free vibrations of a Timoshenko-type viscoelastic beam with discrete rigid bodies, connected to the beam by means of viscoelastic constraints. The phenomenon of free vibrations of this discrete-continuous system is described by a set of three partial and two subsystem ordinary differential equations with generalized boundary conditions and initial conditions. Vector notation of the equations allows one to identify the self-adjoint linear operators of inertia, stiffness and damping. In this case, these operators are not homothetic hence a separation of variables in this set of equations is possible only in a complex Hilbert space. Such separation of variables leads to ordinary differential equations of motion with respect to time as well as to a set of three ordinary differential equations with respect to a spatial variable and two subsystem algebraical equations. Solution of the boundary-value problem was carried out in the classical way, but its results are complex conjugated. Using these results and the fundamental principle, describing the orthogonality property of complex eigenvectors, the problem of free vibrations of the system with arbitrary initial conditions has been finally solved exactly.     

无反射势的Schr?dinger方程严格解的三维推广

文献[1]给出无反射势V(x)=-N(N+1)sech²x当N为任意正整数时Schr?dinger方程束缚态和散射态的严格解。本文推广文献[1]的工作,继续给出三维情况下无反射势Schr?dinger方程束缚态和散射态的严格解,并得到了与一维情况不同的一些物理结果。 关键词：     

Coulomb－Born近似下的He基态（e，2e）三重微分散射截面

在Ｃｏｕｌｏｍｂ－Ｂｏｒｎ近似下，利用满足一定边界条件且包括电子动量相关的库仑波近似描述ｅ－＋Ｈｅ（１ｓ２）→Ｈｅ＋（１ｓ１）＋２ｅ－两出射电子，得出了三重微分散射截面（ＴＤＣＳ）的明晰表达式，计算了入射能为６００ｅＶ和４００ｅＶ、散射角为４°和１０°条件下的ＴＤＣＳ，并与实验值和Ｂｒａｕｎｅｒ理论结果进行了比较。结果发现，电子动量相关效应对解释ｂｉｎａｒｙ峰和ｒｅｃｏｉｌ峰的大小和位置起重要作用。     

RITZ VECTOR APPROACH FOR STATIC AND DYNAMIC ANALYSIS OF PLATES WITH EDGE BEAMS

A Ritz vector approach is used to develop new formulations for evaluating the static and the dynamic characteristics of rectangular plates with edge beams. Unlike previous studies in which stiffness coefficients with specified distributions along the plate edges are used to represent the effect of edge restraints, the effect of elastic edge restraints is accounted for by including appropriate integrals for edge beams in the expressions for total kinetic and potential energies in a Rayleigh-Ritz approach. The effect of various types of boundary conditions at the beam ends is accounted for by considering the corresponding Ritz vectors. The contribution of beam mass to the total kinetic energy is also considered in the proposed approach. This effect has often been neglected in the previous studies but can be significant in some applications. The results obtained from the application of the proposed approach to a variety of examples are compared with the corresponding results obtained from the finite element analysis.     

修正的Thomas-Fermi模型及惰性气体原子抗磁磁化率的计算（Ⅰ）

 在本文中，我们在Thomas-Fermi（TF）及Thomas-Fermi-Amadi（TFA）模型下，选用Jensen的试验密度函数，在考虑到TF模型所确定的密度渐近行为情况下，计算了惰性气体原子Ne、Ar、Kr、Xe、Rn的抗磁磁化率。计算表明，考虑密度渐近行为式是必要的，并给出了较以往的同类计算更好的结果。     

三维流动传热空隙率计算程序FASTOR—3D开发研究

1引言大粘度（大r）和大系数（ss和sc）法是处理流动区域中障碍物的常用方法山。但当流动区域中障碍物数量较多时，宜采用空隙率来模拟障碍物，如模拟反应堆流动传热的商用程序COMMIX［’］。我们根据空隙率模拟的基本概念，针对采用交错网格的压力校正法，自行编制了多障碍物流动传热三维计算的全部源程序代码，应用于某核反应堆钠池流动传热的数值模拟，获得了比较合理的结果。2数学模型和数值方法2．1控制方程空隙率修整的质量、动量、能量及湍流动能与耗散率的守恒方程通式的三维柱坐标形式为其中中一1，。，。，。，T，k，。分别表…     

腔内填充低Z物质对腔内壁运动的影响

 为创造腔内均匀、干净的辐射场,用解析方法研究了腔内填充低Z介质的方法防止腔壁重元素喷射到腔内的设计思想。简化模型给出的物理图象清楚显示,该方法是一种好的设计思想。给出了在腔内填充0.1、1和10个大气压的氦气和各种温度状态下,腔壁内界面的运动速度。     

计算波状表面半透明流体层光谱反射特性的光线分裂跟踪法

提出一种计算具有波状表面的半透明流体层光谱反射特性的光线分裂跟踪法.对平行入射和漫入射光谱分别采用正向和反向跟踪计算,实现了对光线的分裂跟踪.该方法计算思路简捷、速度快、需用内存小,对此类问题的求解有良好的适应性.算例结果表明,表面的波状弯曲降低了流体层对漫入射光谱的反射能力;但对平行入射光谱,呈现出两种相反的影响.