The dynamic phase transition in the spin-1/2 Ising system within the path probability method

We study the dynamic phase transitions and present the dynamic phase diagrams of the spin-1/2 Ising system under the presence of a time-varying (sinusoidal) external magnetic field within the path probability method (PPM) of Kikuchi and we observe that the PPM gives exactly the same result as with the Glauber-type stochastic dynamics based on the mean-field theory (DMFT). We also investigate the influence of the rate constant on the dynamic phase diagrams in detail and five new and interesting dynamic phase diagrams are found. We notice that the derivation of the dynamic equations by using the PPM is more clear and easier than within the DMFT and the Glauber-type stochastic dynamics based on the effective-field theory (DEFT). The advantages and disadvantages of the PPM over the DMFT and DEFT are also discussed.     

A stochastic approach to the kinetic theory of gases

A theory of fluctuations in non-equilibrium diluted gases is presented. The velocity distribution function is treated as a stochastic variable and a master equation for its probability is derived. This evolution equation is based on two processes: binary hard sphere collisions and free flow. A mean-field approximation leads to a non-linear master equation containing explicitly a parameter which represents the spatial correlation length of the fluctuations. An infinite hierarchy of equations for the successive moments is found. If the correlation length is sufficiently short a truncation after the first equation is possible and this leads to the Boltzmann kinetic equation. The associated probability distribution is Poissonian. As to the fluctuation of the macroscopic quantities, an approximation scheme permits to recover the Langevin approach of fluctuating hydrodynamics near equilibrium and its fluctuation-dissipation relations.     

Remarks concerning the derivation and the expansion of the master equation

The present work consist of two parts: In the first part we apply the method of quasilinearization to the differential equation describing the time development of the quantum-mechanical probability density. In this way we derive the master equation without resorting to perturbation theory. In the second part of the paper, for a general form of the master equation which is an integro-differential equation, we test the accuracy of the Fokker-Planck approximation with the help of a solvable model. Then we study an alternative way of reducing the integro-differential equation to a partial differential equation. By expanding the transition probability W(q, q′), and the distribution function in terms of a complete set of functions, we show that for certain forms of W(q, q′), the master equation can be transformed exactly to partial differential equations of finite order.     

Mixed ion effects in Na/Cu-NaZr2(PO4)3

The mixed ion effect by which the conductivity minimum of a crystal with three dimensional diffusion path is observed is firstly reported for Na/Cu-NaZr₂(PO₄)₃. The phase diagram is also obtained by estimating the frequency dependence of ionic conductivity. The behavior is in agreement with the conductivity result. NMR spectra (²³Na MAS) showed the formation of an ordered distribution among different kinds of ions. The ionic conductivity of the mixed ion system Na/Cu was calculated for a two dimensional honeycomb lattice by means of the path probability method (PPM). It suggested that the mixture of two ions led to the conductivity minimum. Paper presented at the 5th Euroconference on Solid State Ionics, Benalmádena, Spain, Sept. 13–20, 1998.     

Time-dependent probability density of statistical mechanics

We study fluctuations around nonequilibrium steady states of some model nonlinear chemical systems. A previous result of Nicolis and Prigogine states that the mean square fluctuation computed from a master equation in the space of internal states of the reacting species is identical to that calculated from Einstein's fluctuation formula. Our analysis of fluctuations based on that master equation leads with the assumption of local equilibrium to a result identical to that obtained from a master equation for the total concentration of the reacting species, which is different from the equilibrium (Einstein relation) result. Nicolis and Prigogine approximated one term in their master equation, and a discussion of this approximation is presented. The master equation without this approximation yields at equilibrium the result expected on the basis of Einstein's formula.Work supported in part by the National Science Foundation and Project SQUID, Office of Naval Research.     

On the relationship between continuous time random walks and the non-equilibrium Ornstein-Zernike equation

An exact non-equilibrium Ornstein-Zernike (OZ) equation is derived for lattice fluid systems whose time development is given by a generalized master equation. The derivation is based on a generalization of the Montroll-Weiss continuous-time random walk on a lattice, and on their relationship with master equation solutions. Time dependent direct and total correlation functions are defined in terms of the generating functions for the probability densities of the random walker, such that, in the infinite time limit the equilibrium OZ equation is recovered. A perturbative analysis of the time dependent OZ equation is shown to be formally analogous to the perturbation of the Bloch equation in quantum field theory. Analytic results are obtained, under the mean spherical approximation, for the time dependent total correlation function for a one-dimensional lattice fluid with exponential attraction.     

应用多介质PPM方法计算斜激波与物质交界面的相互作用

利用多介质PPM方法研究斜激波与物质交界面的相互作用.采用与体积分数耦合的Euler方程组作为计算模型,用双波近似来求解一般刚性气体状态方程Riemann问题.通过体积分数的计算来获得界面的位置,在整个流场采用统一的高阶PPM格式进行计算.文中对斜激波与不同物质界面相互作用进行了数值模拟,并给出了交界面上由于斜压效应产生的涡列的演化过程,特别是强斜激波与不同物质界面的相互作用的情况.     

A stochastic master equation representation of statistical mechanics

A functional master equation for a probability density of the velocity distribution function is presented. This constitutes a representation of statistical mechanics which is equivalent to the BBGKY hierarchy but makes alternative approximation schemes available.     

用类O原子波函数对H+9团簇的体心立方结构与能量的研究

在单中心球模型近似下,选用类O原子解析函数,用变分法计算了H+9团簇体心立方结构与能量。结果表明当中心氢原子核到顶角氢原子核之间的距离R=1.97a0时,体系能量有一极小值E=-4.376h0(a0=0.529177×10-10m,h0=27.2eV)。这表明H+9团簇的体心立方结构是稳定的结构,H+9团簇是存在的。     

H_5~-团簇正四面体中心结构与能量的变分计算

选用类Ｃ原子波函数,在单中心球模型近似下,利用变分法计算了Ｈ－５团簇正四面体中心结构与能量。结果表明当中心Ｈ原子核到顶角Ｈ原子核之间的距离Ｒ＝１．５８ａ０时,体系能量有一极小值－２．８０３６ｈ．ａ．ｕ．。这表明Ｈ－５的正四面体中心结构是可能稳定存在的。计算结果与用ＭＡＣＱＭ法计算的结果基本相符,表明采用的物理模型及其计算方法是合理可靠的。     

Kinetics of monolayer growth

The kinetics of a monolayer growth is studied using the two-dimensional lattice gas model by means of the path-probability method (PPM) for nonequilibrium phenomena. Kinetic equations for the combined processes of relaxation (adsorption and desorption) and diffusion are derived analytically and solved for the first time in the square approximation of the PPM. Comparison of the square approximation with the point and pair approximations along with Monte Carlo simulation shows the effect of using a larger basic cluster than in the previous studies. When the square approximation is used, the growth rate results are much improved in both cases with and without diffusion and agree well with the Monte Carlo simulations results, except for very small values of the driving forceL=/k _b T where is the chemical potential difference between the vapor and the solid phase. In the range where the agreement is good, there exists a region where the growth rateR is proportional to exp(–c/L with a constantc. This is the feature which is characteristic of two-dimensional nucleation-limited growth.     

Master equation with two times: Diffusion in external field

The master equation for diffusion involving two times applies to the problem of diffusion in a time-dependent (in general inhomogeneous) external field. We consider the case of the quasi Fokker-Planck approximation, when the probability transition function for diffusion (PTD-function) does not possess a long tail in coordinate space and can be expanded as the function of instantaneous displacements. For relatively weak external field the linear expansion of the PTD function leads to a simple generalization of diffusion equation, containing the retardation factors.     

一维多介质可压缩流动数值方法

应用高精度界面追踪方法计算一般状态方程的多介质可压缩流动问题;应用LevelSet技术捕捉界面位置,在界面附近采用守恒数值离散,用双波近似求解一般状态方程Riemann问题,并采用统一高阶PPM格式进行内点和交界面点的计算.一维算例表明,该方法对于光滑区域以及多介质交界面具有二阶精度,能准确地模拟交界面的位置,交界面计算无数值振荡和数值耗散,并能处理一般状态方程的多介质可压缩流动问题.     

Theoretical prediction and experimental validation of the angle-of-arrival probability density of a laser beam in a strong plane-flame turbulence

The propagation of a laser beam through a plane turbulent flame is studied using geometrical optics approximation. The random fluctuations of the refractive index caused by a strong thermal turbulence in the flame create random perturbations of the laser beam direction. From the Markovian process model applied along the whole random path of the beam, the theoretical probability density of the laser beam angle-of-arrival is derived from the analytical solution of the Einstein-Fokker-Kolmogorov equation, which we have determined in terms of a series expansion of spherical harmonics. An experimental setup and a method for measuring this probability density are described. The experimental results obtained are shown to agree with the theoretical predictions.     

Van der Waals状态方程可压缩多流体流动的PPM方法

基于流体体积分数的混合型多流体数值模型,将Piecewise Parabolic Method（PPM）方法应用于可压缩多流体流动的数值模拟,采用双波近似求解多流体van der Waals状态方程的Riemann问题．模拟高密度比且含有激波的可压缩多流体流动,典型的纯界面平移问题模拟结果表明,在接触间断的界面附近,压力和速度没有任何的振荡且界面数值耗散都被控制在2—3个网格之内;一维和二维算例表明,该数值方法可以有效地处理接触间断、激波和多维滑移线等物理问题,并能够比其它多流体数值方法更精细地模拟多流体交界面．     

RANDOM RESPONSE OF PREISACH HYSTERETIC SYSTEMS

An approximate method for analyzing the response of Preisach hysteretic systems with non-local memory under stationary Gaussian excitation is proposed. The covariance matrix equation of system response is derived. The cross correlation function of Preisach hysteretic force and response in the covariance equation is evaluated based on the switching probability analysis and the Gaussian approximation of response process and an explicit expression for the cross correlation function is given for the case of symmetric Preisach weighting function. It is shown that the numerical result obtained by using the proposed method is in good agreement with that from digital simulation.     

化学反应体系中涨落的时间空间关联(Ⅰ)——涨落、扩散和波

本文着重分析了如何描述化学反应体系中密度涨落的空间关联,对照反应扩散方程,我们在密度涨落分布函数所满足的Master方程中引入了扩散项或压力项,对无限介质,解Master方程,得到了一系列波,第一支波是与反应扩散方程的解一致,描述了平均密度起伏在空间的传播,在气体中就是声波,其它各支波,则描述了局部密度涨落高阶矩的变化在空间的传播(平均密度不改变),其实就是局部机率分布函数畸变后的传播过程,我们称之为涨落波,文中还讨论了如何求解线性初值问题。 关键词：     

A self-consistent master equation and a new kind of cumulants

Generalized master equations correspond to different kinds of cumulants. Here, we discuss the recently introduced non-crossing cumulants from a physical point of view and propose the corresponding integro-differential master equation as a new type of equation for a self-consistent treatment of memory effects. We prove the cluster property of the non-crossing cumulants, and show that the Gaussian approximation of our equation is given by a random matrix process. As an instructive example for our expansion formula we treat the random frequency-modulated oscillator.     

On the Gaussian Approximation for Master Equations

We analyze the Gaussian approximation as a method to obtain the first and second moments of a stochastic process described by a master equation. We justify the use of this approximation with ideas coming from van Kampen’s expansion approach (the fact that the probability distribution is Gaussian at first order). We analyze the scaling of the error with a large parameter of the system and compare it with van Kampen’s method. Our theoretical analysis and the study of several examples shows that the Gaussian approximation turns out to be more accurate than van Kampen’s expansion at first order. This could be specially important for problems involving stochastic processes in systems with a small number of particles.     

周期永磁磁场导引环形强流电子束研究

 利用磁场有限元法，计算了周期性布置的永磁铁内的磁场；利用流体模型分析了作用在束电子上的力并导出了改进Matheiu函数形式的径向力方程；利用2.5维PIC程序研究了束传输的物理过程。计算发现强流相对论电子束的稳定传输与束等离子体密度、束平衡位置、磁场的强度、磁场周期长度等有关。研究认为利用周期性永磁场导引数kA的环形电子束，使之稳定传输是可能的。