NESS theory of random steady states

A theory is presented for the properties of random steady states based upon a generalization of existing theories of nonrandom steady states. A sample calculation is presented for the energy cascade in a weakly stirred system. The theory introduces multivariable time correlation functions, and a new method for evaluating such objects is also given.Research supported by NSF grant No. CHE78-09704.Dreyfus Teacher-Scholar.     

Explicit construction of steady state of a model of chemical turbulence

Using only the microscopic dynamics, the nonequilibrium steady state of a one-dimensional cellular automaton (CA) model of chemical turbulence is explicitly constructed. A coding is found which decomposes the CA into three interacting shift systems, each of which has an independent steady-state distribution. It was previously shown that the steady state of this model is a Gibbs state. Hence the steady state can be represented in the formZ ^–1 e ^–F , whereF is the conditional energy of the system such that all conditional probabilities are continuous. It is shown that the conditional energy of this model has an approximate expression in terms of familiar models from equilibrium statistical mechanics.     

Equilibrium state and non-equilibrium steady state in an isolated human system

The principle of increasing entropy （PIE） is commonly considered as a universal physical law tbr natural systems. It also means that a non-equilibrium steady state （NESS） must not appear in any isolated natural systems. Here we experimentally investigate an isolated human social system with a clustering effect. We report that the PIE cannot always hold, and that NESSs can come to appear. Our study highlights the role of human adaptability in the PIE, and makes it possible to study human social systems by using some laws originating from traditional physics.     

The steady state of two quantum dots in a cavity

The steady state of two quantum dots (QDs) resonantly coupled to a cavity mode is investigated under two pumping configurations: when the QDs are indistinguishable for the excitation, we find that as a result of the efficient singlet state population, the cavity emission is suppressed. On the other hand, the storage of photons is strongly enhanced when the dots are pumped independently. The system is found to be suitable for entanglement in the first case and for lasing in the second.     

基于统计物理的爆轰产物物态方程研究

用van der Waals等效单组分流体模型和Ross硬球微扰理论软球修正模型，计算爆轰气相产物的状态方程；用石墨相、金刚石相、类石墨液相和类金刚石液相４种相态描述凝聚成分，由Gibbs自由能最小确定不同状态下的凝聚产物相态.对爆轰产物混合系统采用Gibbs自由能最小原理，通过化学平衡方程组求解炸药爆轰产物系统的平衡组分，计算结果与Becker-Kistiakowsky-Wilson (BKW)和Lennard-Jones-Devonshire结果相近.使用该理论对炸药的爆轰参数做了预言，与BKW，Jo 关键词： 爆轰产物 物态方程 化学平衡方程组     

Solving nonlinear master equation describing quantum damping by virtue of the entangled state representation

This paper solves the newly constructed nonlinear master equation dρ/dt=κ[2f (N) aρ (1/f (N-1))a+-a+aρ-ρa+a],where f(N) is an operator-valued function of N=a+a,for describing amplitude damping channel,and derives the infinite operator sum representation of quasi-Kraus operators for the density operator.It also shows that in this nonlinear process the initial pure number state density operator will evolve into the binomial field (a mixed state) when f (N)=1/(N+1)～(1/2).     

Exact solutions to a class of nonlinear Schrödinger-type equations

A class of nonlinear Schrödinger-type equations, including the Rangwala-Rao equation, the Gerdjikov-Ivanov equation, the Chen-Lee-Lin equation and the Ablowitz-Ramani-Segur equation are investigated, and the exact solutions are derived with the aid of the homogeneous balance principle, and a set of subsidiary higher order ordinary differential equations (sub-ODEs for short).     

高温超导电缆层电流分布对电缆稳态运行特性的影响分析

为了分析冷绝缘高温超导电缆层电流分布对其稳态运行特性的影响,提出超导电缆的等效电路模型,给出求解各层电流的矩阵方程,应用超导电缆的温度分布计算模型和边界条件,获得不同均流效果下的超导电缆最大载流能力和稳态径向温升,并与有限元计算结果进行对比。结果比较表明,各层电流均衡分布不仅能提高电缆的载流能力,而且可以降低超导电缆的稳态运行温升,提高了超导电缆在稳态运行时的稳定性。     

An approximate analytic solution of the steady state Brillouin scattering in single mode optical fiber without neglecting the attenuation coefficient

The analysis of steady state Brillouin scattering in a long single mode optical fiber is presented. Meanwhile, an approximate analytical functions of distributed Brillouin scattering and pump wave along the fiber with the fiber attenuation coefficient are obtained for the first time. A comparison is made among the analytical solutions with the attenuation coefficient, the analytical solutions without the attenuation coefficient and the exact numerical solutions. The results show that the analytical solutions with fiber attenuation coefficient are more close to the numerical solutions, which can be used to describe the power distribution of the pump wave and the Stokes wave along the long distance single mode optical fiber accurately.     

单层石墨烯片的非线性板模型

基于实验得到的非线性本构关系和板理论,本文建立了包含三次及五次非线性项的单层石墨烯片的板动力学模型.针对四边简支矩形板,使用Ritz法研究了在板中点作用集中力时的静力弯曲,以及边界均匀受力时的静力屈曲问题.结果显示,基于非线性本构关系的板模型能很好的描述单层石墨烯片的力学行为,而且模型中的五次非线性项对结构的弯曲变形有显著影响.     

一类非线性相对转动周期系统的平衡稳定性分析

利用一类周期性变系数线性常微分方程解的基本矩阵的Jordan形，分析一类非线性相对转动系统扭转的运动稳定性，从而得到非线性相对转动周期系统的运动稳定准则. 运用Lyapunov函数法，对广泛存在的一类机械传动系统的相对转动运动的平衡稳定位置的稳定域进行研究，并给出数学解析表达式. 这为工程中广泛存在的这类机械传动系统稳定工作区间工作参数的选取和相似模拟提供了理论依据及方法，据此可进一步分析和评价大型复杂旋转机械主传动系统的扭振稳定性. 关键词： 相对转动 相似模拟 运动稳定 平衡稳定     

On the characterization of the stationary state of a class of dynamical semigroups

We consider a representation of the entropy production for a completely positive, trace-preserving dynamical semigroup satisfying detailed balance with respect to its faithful stationary state denned on aW*-algebra(): it is expressed as a positive Hermitian form on(), which is analogous to the quantum correlation functions used in the Kubo theory. By considering this Hermitian form as a variation function of a vector in(), an exact characterization of the stationary states of semigroups in a certain class is obtained. On this basis, the problem of characterizing the stationary states discussed by Spohn and Lebowitz for manyreservoir open systems is solved without the restriction to situations near thermal equilibrium.     

Statistical mechanics of a nonlinear stochastic model

A multivariable Fokker-Planck equation (FPE) is used to investigate the equilibrium and dynamical properties of a nonlinear stochastic model. The model displays a phase transition. The equilibrium distributions are found to be non-Gaussian; the deviation from Gaussian is especially significant near the transition point. To study the nonequilibrium behavior of the model, a self-consistent dynamic mean field (SCDMF) theory is derived and used to transform the FPE to a systematic hierarchy of equations for the cumulant moments of the time-dependent distribution function. These equations are numerically solved for a variety of initial conditions. During the time evolution of the system from an initial unstable equilibrium state to the final equilibrium state, three distinct time stages are found.Supported by a grant from the National Research Council of Canada (to RCD) and by the Sherman Fairchild Foundation (to RZ).Also Sherman Fairchild Distinguished Scholar, 1974–75, at the California Institute of Technology, where the early part of this research was done.     

Stochastic theory of nonlinear rate processes with multiple stationary states. II. Relaxation time from a metastable state

We have developed a methodology for obtaining a Fokker-Planck equation for nonlinear systems with multiple stationary states that yields the correct system size dependence, i.e., exponential growth with system size of the relaxation time from a metastable state. We show that this relaxation time depends strongly on the barrier heightU(x) between the metastable and stable states of the system. For a Fokker-Planck (FP) equation to yield the correct result for the relaxation time from a metastable state, it is therefore essential that the free energy functionU(x) of the FP equation not only correctly locate the extrema of U(x), but also have the correct magnitudeU at these extrema. This is accomplished by so choosing the coefficients of the FP equation that its stationary solution is identical to that of the master equation that defines the nonlinear system.This work was supported in part by the National Science Foundation under Grant CHE 75-20624.     

非线性增光子热态的非经典特性

本文从描述驻波激光场与囚禁离子相互作用的非线性Jaynes-Cummings模型出发,引入一种新的量子态,即非线性增光子热态.采用理论分析和数值计算相结合的方法,研究了Lamb-Dicke参数,温度和激光场的初相位等参数对这种量子态的非经典效应的影响.结果表明:非线性增光子热态的Mandel Q因子随温度的变化存在一个极小值.Lamb-Dicke参数越大,非线性增光子热态的非经典效应就越强.此外驻波场的初相位也对该态的非经典效应有明显的影响.     

The semiclassical modified nonlinear Schrödinger equation I: Modulation theory and spectral analysis

We study an integrable modification of the focusing nonlinear Schrödinger equation from the point of view of semiclassical asymptotics. In particular, (i) we establish several important consequences of the mixed-type limiting quasilinear system including the existence of maps that embed the limiting forms of both the focusing and defocusing nonlinear Schrödinger equations into the framework of a single limiting system for the modified equation, (ii) we obtain bounds for the location of the discrete spectrum for the associated spectral problem that are particularly suited to the semiclassical limit and that generalize known results for the spectrum of the nonselfadjoint Zakharov-Shabat spectral problem, and (iii) we present a multiparameter family of initial data for which we solve the associated spectral problem in terms of special functions for all values of the semiclassical scaling parameter. We view our results as part of a broader project to analyze the semiclassical limit of the modified nonlinear Schrödinger equation via the noncommutative steepest descent procedure of Deift and Zhou, and we also present a selfcontained development of a Riemann-Hilbert problem of inverse scattering that differs from those given in the literature and that is well adapted to semiclassical asymptotics.     

基于二阶离散变分方法的非线性映射参数估计

提出一种估计非线性映射未知参数的二阶离散变分方法.首先针对非线性离散混沌系统, 利用变分方法导出了伴随方程和目标泛函梯度, 以此为基础利用二阶离散变分方法给出了二阶伴随方程和精确计算Hessian矩阵-向量乘积的显式表达式; 其次设计了估计非线性映射未知参数的新算法, 并以此对Hyperhenón映射和二维抛物映射中的未知参数进行了精确的估计. 数值仿真结果表明了该方法的有效性和优点. 关键词： 非线性映射 参数估计 二阶离散变分方法 伴随方程     

Analysis of nonlinear steady state vibration of a multi-degree-of-freedom system using component mode synthesis method

In this paper, an analytical approach for nonlinear forced vibration of a multi-degree-of-freedom system is proposed using the component mode synthesis method. The whole system is divided into some components and a nonlinear modal equation of each component is derived using the free-interface vibration modes. The modal equations of all components and the conjunction conditions are solved simultaneously, and then the modal responses of components are derived. Finally, the dynamic responses of the whole system can be obtained. The degrees of freedom of modal equations can be reduced when the lower vibration modes are only adopted in each component. As a numerical example, a nine-degree-of-freedom system is considered, in which all spring have cubic type nonlinearity. As a result, it is shown that when there are no rigid modes in components, the compliance by the proposed method agrees very well with the exact one even if the lower vibration modes of components are only adopted. The other hand, in the case with rigid modes in components, the compliance has a little error compared with the exact result. It is recognized that the method proposed is very effective in the case without rigid modes in components for the actual application.     

一类非线性相对转动动力系统的平衡稳定性及组合谐波近似解

建立一类含广义非线性弹性力的两质量相对转动系统的非线性动力学方程. 应用变量梯度法构造李雅普诺夫函数,研究相对转动非线性自治系统的稳定性. 应用摄动法求得相对转动非线性非自治系统在两种不同频率谐波共同激励下的组合谐波响应的近似解. 关键词： 相对转动 非线性动力系统 稳定性 组合谐波响应     

A standard and direct method to obtain multiple soliton solutions of the nonlinear partial differential equation

In this paper, we improve some key steps in the homogeneous balance method (HBM), and propose a modified homogeneous balance method (MHBM) for constructing multiple soliton solutions of the nonlinear partial differential equation (PDE) in a unified way. The method is very direct and primary; furthermore, many steps of this method can be performed by computer. Some illustrative equations are investigated by this method and multiple soliton solutions are found.