吸收和色散混合受驱动光学系统多光子FPE和稳态方程

应用广义Wigner分布的Fokker-Planck方程的系统方法,研究了混合吸收和色散特征的受驱动光学系统的多光子跃迁过程。得到多光子、混合型Fokker-Plauck方程和稳态方程。并讨论了稳态方程的性质。 关键词：     

受驱动光学系统多光子量子统计理论(Ⅰ)——Fokker-Planck方程和良腔情况

我们应用广义Wigner分布的Fokker-Planck方程的系统方法,研究了受驱动光学系统的多光子跃迁过程。得到多光子过程普遍的Fokker-Planck方程、态方程以及良腔情况下透射光谱公式。计算了n光子双稳态的透射光谱并与单光子情况进行比较。还证明了在良腔情况,对于多光子过程,原子-原子关联也可以忽略。 关键词：     

KdV方程的直接微扰方法

系统地讨论了含修正项的KdV方程的直接微扰方法.从反散射变换所得的不含修正项方程的严格多孤子解出发,导出了线性化算子的零本征值的所有本征函数——平方Jost函数.引入了它们所对应的伴随函数和定义了内积.计算了应有的正交关系,并自然得到单位元的平方Jost函数的展开式.利用广义的Marchenko方程,证明了平方Jost函数的完备性.同时得到展开式中的积分是沿实轴从－∞到∞,但在原点附近将从上方绕过.这不同于过去所得的Cauchy主值积分.为最明确显示这一差别,在单孤子情况下又用平方Jost函数的显式,直接作了验证．同时指出,以前由于取Cauchy主值积分导出的KdV方程所特有的孤子尾,在采用从上方绕过原点的积分时,则事实上并不存在． 关键词：     

用赝角动量方法求解同调谐振子

采用赝角动量的方法研究了同调谐振子(带有附加有心势垒项的谐振子)的定态薛定谔方程的严格解.详细讨论了有心势垒项的参量对于形成体系束缚定态的有效取值区域,及该参量的不同取值区域对能谱的影响.给出了能谱的确切的全面表述和对应本征态的解析表达式.对于不同文献作者的不同处理予以分析和澄清 关键词： 同调谐振子 类角动量方法 广义湮没算符 广义产生算符 本征值谱 本征态     

CORRECTIONS TO THE COLLISION TERM IN THE BGK BOLTZMANN EQUATION

With the discrete method of the hexagonal cell and three different velocities of particle population in each cell, a two-dimensional lattice Boltzmann model is developed in this paper.^[1,2] The collision operator in the Boltzmann equation is expanded to fourth order using the Taylor expansion.^[3,4] With this model, good results have been obtained from the numerical simulation of the reflection phenomenon of the shock wave on the surface of an obstacle, and the numerical stability is also good. Thus the applicability of the D2Q 19 model is verified.     

湍流等离子体中的重整化色散方程

从速度v的傅里叶空间K的动力学方程出发,采用算子运算及变换方法,可较简便的算出静电湍流场中的重整化色散方程,在以有效关联时间代替湍流场的时、空关联的近似下,计算了有限关联时间效应的作用,表明它是削弱湍流场影响的。短关联时间极限可看成是湍流场影响的上限估计。讨论了湍流场对离声波、电子朗缪波和低频漂移波的影响。 关键词：     

THE GEOMETRIC MEANING OF THE RICCATI EQUATION RELATED TO SINE-GORDON EQUATION

The geometric meaning of the Riccati equation related to the structure of space is discussed. It is shown that the Riccati equation satisfied by the stereographic projection is essentially the structure equation of space.     

THE IMPROVED MURNAGHAN EQUATION

The improved Murnaghan equation is derived by integrating B(P)=-v(∂p/∂v)_T=B₀⁽¹⁾(P)·P and expanding B⁽¹⁾(P) and simllar function in series of (1-K) , where K is the compression ratio (K≡(v/v₀)^1/3. The new equation obtained is compared with Murnagnan equation, Keane equation and Birch equation.It is found that, the improved Murnaghan equation has better convergency in comparison with the Birch equation. The characteristics of the new equation and the reasons of its better convergency are discussed.     

共振辐射的理论研究——Holstein方程的解

解决介质中共振辐射的关键问题是求解Holstein方程。本文直接利用算符运算将方程积分,给出了激发态粒子集居数的含无限项的级数表达式。基于对这个级数高阶系数的极限行为的研究,成功地克服了无穷项求和的困难,整理出一个在任意给定精度下都只含有限项的解式,由它可以计算出任何时刻的结果。 关键词：     

Fick's law and Fokker-Planck equation in inhomogeneous environments

In inhomogeneous environments, the correct expression of the diffusive flux is not always given by the Fick's law Γ=−D∇n. The most general hydrodynamic equation modelling diffusion is indeed the Fokker-Planck equation (FPE). The microscopic dynamics of each specific system may affect the form of the FPE, either establishing connections between the diffusion and the convection term, as well as providing supplementary terms. In particular, the Fick's form for the diffusion equation may arise only in consequence of a specific kind of microscopic dynamics. It is also shown how, in the presence of sharp inhomogeneities, even the hydrodynamic FPE limit may becomes inaccurate and mask some features of the true solution, as computed from the Master equation.     

Relationship between a non-Markovian process and Fokker–Planck equation

We demonstrate the equivalence of a non-Markovian evolution equation with a linear memory-coupling and a Fokker–Planck equation (FPE). In case the feedback term offers a direct and permanent coupling of the current probability density to an initial distribution, the corresponding FPE offers a non-trivial drift term depending itself on the diffusion parameter. As the consequence the deterministic part of the underlying Langevin equation is likewise determined by the noise strength of the stochastic part. This memory induced stochastic behavior is discussed for different, but representative initial distributions. The analytical calculations are supported by numerical results.     

THE EXACT SOLUTIONS OF THE BURGERS EQUATION AND HIGHER-ORDER BURGERS EQUATION IN (2+1) DIMENSIONS

Some exact solutions of the Burgers equation and higher-order Burgers equation in (2+1) dimensions are obtained by using the extended homogeneous balance method. In these solutions there are solitary wave solutions, close formal solutions for the initial value problems of the Burgers equation and higher-order Burgers equation, and also infinitely many rational function solutions. All of the solutions contain some arbitrary functions that may be related to the symmetry properties of the Burgers equation and the higher-order Burgers equation in (2+1) dimensions.     

THE LINEAR ELIASHBERG EQUATION

Fn the present paper, the linear Eliashberg equation is converted into a new integral equation and from it, the following T_C formula is derived analytically in the weak coupling limit:T_c=28/πωlog·(πlog/π_c)μ^*/λ^*-μ^* exp{-1+λ/λ-μ^*}, where In γ=C=0.5772 is the Eater constant.     

ON THE PROLONGATION STRUCTURE OF ERNST EQUATION

An SL(2R) ×R¹(l) prolongation structure of Ernst equation with a real parameter l and the corresponding Riccati equation as well as a pair of linear equations which are in principle equivalent to the inverse scattering problem due to Belinsky and Zakharov are obtained by solving the fundamental equation for the prolongation structure. A necessary condition which should be satisfied by the Bäcklund transformations is pfesented in terms of prolongation structure. And it is indicated that in the, case of Ernst equation the Harrison transformation, Neugebauer transformations and other available Bäcklund transformations as well as Belinsky-Zakharov's Riemann transformation, i.e., the homogeneous Hilbertproblem (HHP), would be covered by this condition.     

对流方程的差分格式

用待定系数法构造了对流方程的一些新的差分格式.     

求解对流占优Burgers方程的随流格式

在用差分方法求解对流占优的Burgers方程时,许多常用的差分格式的计算精度会下降。为了提高对流占优问题的计算精度,本文提出非线性对流项的差分格式的设计要求,从而得到对流项的新的差分格式-随流格式。本文通过算例来表明随流格式的优点。     

System Driven by Correlated Gaussian Noises Related with Disorder

A system driven by correlated Gaussian noises related with disorder is investigated. The Fokker-Planck equation （FPE） for the system is derived. Using the FPE derived, some systems driven by correlated Gaussian noises related with disorder can be investigated for Brownian motors, nonequilibrium transition, resonant activation, stochastic resonance, and so on. We only give one example： i.e., using the FPE derived, we study the resonant activation for a single motor protein model with correlated noises related to disorder. Since the correlated noise related to disorder usually exists with the friction, for the temperature, and so on, our results have generic physical meanings for physics, chemistry, biology and other sciences.     

Analysis of price fluctuations in futures exchange markets

We show that the fluctuations of the tick-by-tick logarithmic price in a futures market can be described in terms of the Fokker-Planck equation (FPE). We calculate the corresponding drift and diffusion coefficients and argue that these values can contain some information pertaining to the market state. It is particularly showed that the Korean treasury bond (KTB) futures is well described by a FPE and has a similar structure to turbulence.     

相对运动的动力学方程

引入惯性力广义势的概念，推出非惯性系中的拉格朗日方程，并举例说明了其应用。     

基于小关联时间两相湍流色噪声的近似模型及数值模拟

从一般高斯型色噪声模型出发,通过泛函导数,应用小关联时间,近似计算多维色噪声,得到有效Fokker-Planck方程.将其应用到两相湍流中得到颗粒相的概率密度函数输运方程,从而得到颗粒相的二阶矩模型.将颗粒应力方程简化成代数方程,建立代数应力模型.将对流扩散方程的有限分析法运用到求解两相流模型中,对壁面两相射流进行数值模拟,并将求解结果与实验结果进行对比分析.