Theory of external two-state Markov noise in the presence of internal fluctuations

A theory is presented to take into account internal fluctuations in the study of stochastically driven systems. Internal fluctuations are modeled by a master equation in which external noise is introduced. External noise is modeled by a two-state Markov process. A unified theory of internal and external fluctuations is described in terms of an effective integrodifferential master equation or its equivalent generating function representation. Two examples for which exact analytical results can be obtained are presented. A discussion of the white noise limit of the theory is also given.     

外力作用下反馈耦合布朗棘轮的定向输运

本文研究了处于外力作用下双阱棘轮势中两个反馈耦合布朗粒子的定向输运性能. 通过对过阻尼朗之万方程的数值求解, 详细讨论了外力、热噪声与势阱的不对称参数等对耦合布朗粒子的平均速度、 有效扩散系数及Pe数的影响. 研究发现, 平均速度随外力呈周期性的变化规律. 同时耦合系统存在最优噪声强度会使定向输运达到最强. 值得指出的是棘轮系统可通过改变双阱势的结构来获得较强的定向流. 关键词： 耦合布朗棘轮 外力 双阱棘轮势 平均速度     

正压流体中具有β效应与地形效应的强迫Rossby孤立波

正压流体中,从有外源的准地转位涡方程出发采用摄动方法和时空伸长变换推导了具有β效应、地形效应和外源的强迫Rossby孤立波方程,得到孤立Rossby波振幅的演变满足带有地形与外源强迫的非齐次 Boussinesq方程的结论. 通过分析孤立Rossby波振幅的演变,指出β效应、地形效应以及外源都是诱导Rossby孤立波产生的重要因素,说明在地形强迫效应和非线性作用相平衡的假定下,Rossby孤立波振幅的演变满足非齐次Boussinesq方程,给出在切变基本气流下地形和正压流体中R     

层结流体中在热外源和β效应地形效应作用下的非线性Rossby孤立波和非齐次Schrödinger方程

在层结流体中, 从带有地形、热外源耗散的下边界条件以及带有热外源的准地转位涡方程开始, 使用小参数展开方法和多尺度时空伸长变换推导出了具有热外源、β效应和地形效应的强迫Rossby孤立波方程, 得到孤立Rossby振幅满足的带有地形与热外源的非齐次非线性的Schrödinger方程. 通过分析Rossby孤立波振幅的变化, 指出了热外源、β效应和地形效应都是诱导Rossby孤立波产生的重要因素, 给出了切变基本流下地形、热外源和层结流体中Rossby的相互作用.     

The influence of noise on the logistic model

The behavior of the logistic system which is generated by the functionf(x =ax (1–x) changes in an interesting way if it is perturbed by external noise. It turns out that the chaotic behavior which was predicted by Li and Yorke for orbits of period 3, becomes visible and that a sequence of mergence transitions occurs at the critical parameter. The change of the invariant probability density and the Lyapunov exponents are examined numerically. The power spectrum for the period 3 orbit for different fluctuations is calculated and a recursion formula for the time evolution of the probability density is presented as a discrete-time analog of a Chapman-Kolmogorov equation.     

The effects of colored quadratic noise on a turbulent transition in liquid4He

Liquid⁴He presents an important physical system for the experimental study of noise-induced dynamical transitions. At temperatures belowT in the He II phase, the flow of heat in the liquid helium is limited by a kind of superfluid turbulence. The steady-state properties of this turbulence are adequately described by a dense tangle of quantized vortex lines in the superfluid component of the He II. The turbulence undergoes a continuous transition as the heat current is increased. At this transition the intrinsic fluctuations in the dissipation and the relaxation time both become large [D. Griswold, C. P. Lorenson, and J. T. Tough,Phys. Rev. B 35:3149 (1987)]. These observations are consistent with a model of the transition as an imperfect pitchfork bifurcation [M. Schumaker and W. Horsthemke,Phys. Rev. A 36:354 (1987)]. External noise can be easily added to the driving heat current. Small-amplitude noise simply causes the system to fluctuate about the deterministic steady states. Large-amplitude noise causes dramatic changes. The stochastic steady states of the turbulence show noise-induced bistability [D. Grisowld and J. T. Tough,Phys. Rev. A 36:1360 (1987)]. Comparison with the imperfect pitchfork model is difficult because the noise is colored, quadratic, and large. Nevertheless, an approximate result obtained by Schumaker and Horsthemke is in good qualitative agreement with the data.This paper will appear in a forthcoming issue of theJournal of Statistical Physics.     

Effect of external fluctuations on the Fréedericksz transition in an analogue simulator

The influence of multiplicative external fluctuations (noise) on the phenomenological equation describing the Fréedericksz transition has been studied by means of an electronic analogue simulator. Measurements were made of the stationary probability density for a wide range of fluctuation intensities and correlation times, for both dichotomous and Gaussianly distributed noise. For dichotomous forcing, the resultant phase diagrams at particular values of the field intensity parameter were found to be in satisfactory agreement with exact theoretical predictions by Horsthemkeet al. In the (physically more realistic) case of Gaussian fluctuations, for which no theory is currently available, the results obtained were distinctively different. A physically motivated discussion is given to account for the interesting differences and similarities of behavior found for the two types of external noise.     

Augmented Langevin approach to fluctuations in nonlinear irreversible processes

A Fokker-Planck equation derived from statistical mechanics by M. S. Green [J. Chem. Phys. 20:1281 (1952)] has been used by Grabertet al. [Phys. Rev. A 21:2136 (1980)] to study fluctuations in nonlinear irreversible processes. These authors remarked that a phenomenological Langevin approach would not have given the correct reversible part of the Fokker-Planck drift flux, from which they concluded that the Langevin approach is untrustworthy for systems with partly reversible fluxes. Here it is shown that a simple modification of the Langevin approach leads to precisely the same covariant Fokker-Planck equation as that of Grabertet al., including the reversible drift terms. The modification consists of augmenting the usual nonlinear Langevin equation by adding to the deterministic flow a correction term which vanishes in the limit of zero fluctuations, and which is self-consistently determined from the assumed form of the equilibrium distribution by imposing the usual potential conditions. This development provides a simple phenomenological route to the Fokker-Planck equation of Green, which has previously appeared to require a more microscopic treatment. It also extends the applicability of the Langevin approach to fluctuations in a wider class of nonlinear systems.     

Gaussian,non-Gaussian critical fluctuations in the Curie-Weiss model

It is known that at the critical temperature the Curie-Weiss mean-field model has non-Gaussian fluctuations and that internal fluctuations can be Gaussian. Here we compute the distribution of theq-mode magnetization fluctuations as a function of the temperature, the wave vectorq, and a fading out external field. We obtain new classes of probability distributions generated by this external field as well as new critical behavior in terms of its rate of fading out. We discuss also the susceptibility as the limitq tending to zero.     

简谐速度噪声与简谐噪声环境中谐振子的动力学共振

通过求解简谐势场中的广义量子朗之万方程，得到平均能量的精确表达式.由于简谐速度噪声与简谐噪声功率谱的不同特点，两种内部噪声驱动的谐振子在简谐外力的作用下具有不同的共振特征.这些特征可用来检验两种噪声.