共查询到19条相似文献,搜索用时 281 毫秒
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研究了描述原子核裂变过程的Langevin方程和Fokker-Planck方程的协变性,给出了动力学参数的坐标交换规律. 相似文献
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通过引入变量,周期场中内部时间导数Ornstein-Uhlenbeck噪声驱动的布朗运动可用高维Fokker-Planck方程来描述. 上述系统不能直接应用通常的小参数展开和势谷中心展开近似求解. 用一种变通的小参数展开方法近似求解了系统的Fokker-Planck方程,结果适用于小势垒高度、中等关联时间和较大的相空间区域,近似解析解可获得系统的改进.
关键词:
Fokker-Planck方程
周期势
时间导数Ornstein-Uhlenbeck噪声
小参数展开 相似文献
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求解没有相对论效应的Fokker-Planck方程的程序包已于2002年完成。求解有相对论效应的Fokker-Planck方程的程序包,由意大利引进,该程序包是反跳平均的,考虑了捕获电子效应、各种不同加热模式下的准线性扩散系数。可用于描述托卡马克辅助加热情形的等离子体粒子的动力学过程,能够计算环形几何下电子和离子的分布函数,包含了波加热,中性束注入,粒子损失等效应。对HL-1M装置和HL-2A装置的实验数据分析非常有用。 相似文献
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按分布函数的定义不同,描述高能带电粒子在等离子体中输运的-Planck方程有不同的形式。从数值计算的观点出发对两种不同形式的Fokker-Planck方程作了比较和评价,并指出Fokker-Planck碰撞项可解释为速度空间的对流扩散项。在此基础上用有限差分方法求解二维(速度一维,几何一维)含时Fokker-Planck方程,编制了计算程序CAPT,并将其应用于α粒子的输运研究。最后计算了典型的Tokamak D-T聚变堆参数下α粒子的损失,并给出了堆内α粒子的分布及损失α粒子的速度分布。 相似文献
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Luis L. Bonilla 《Journal of statistical physics》1987,46(3-4):659-678
A nonlinear Fokker-Planck equation is derived to describe the cooperative behavior of general stochastic systems interacting via mean-field couplings, in the limit of an infinite number of such systems. Disordered systems are also considered. In the weak-noise limit; a general result yields the possibility of having bifurcations from stationary solutions of the nonlinear Fokker-Planck equation into stable time-dependent solutions. The latter are interpreted as non-equilibrium probability distributions (states), and the bifurcations to them as nonequilibrium phase transitions. In the thermodynamic limit, results for three models are given for illustrative purposes. A model of self-synchronization of nonlinear oscillators presents a Hopf bifurcation to a time-periodic probability density, which can be analyzed for any value of the noise. The effects of disorder are illustrated by a simplified version of the Sompolinsky-Zippelius model of spin-glasses. Finally, results for the Fukuyama-Lee-Fisher model of charge-density waves are given. A singular perturbation analysis shows that the depinning transition is a bifurcation problem modified by the disorder noise due to impurities. Far from the bifurcation point, the CDW is either pinned or free, obeying (to leading order) the Grüner-Zawadowki-Chaikin equation. Near the bifurcation, the disorder noise drastically modifies the pattern, giving a quenched average of the CDW current which is constant. Critical exponents are found to depend on the noise, and they are larger than Fisher's values for the two probability distributions considered. 相似文献
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B. H. Lavenda 《Foundations of Physics》1979,9(5-6):405-420
It is shown that: (i) the Onsager-Machlup postulate applies to nonlinear stochastic processes over a time scale that, while being much longer than the correlation times of the random forces, is still much shorter than the time it takes for the nonlinear distortion to become visible; (ii) these are also the conditions for the validity of the generalized Fokker-Planck equation; and (iii) when the fine details of the space-time structure of the stochastic processes are unimportant, the generalized Fokker-Planck equation can be replaced by the ordinary Fokker-Planck equation. 相似文献
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How to quantify deterministic and random influences on the statistics of the foreign exchange market
It is shown that price changes of the U.S. dollar-German mark exchange rates upon different delay times can be regarded as a stochastic Marcovian process. Furthermore, we show how Kramers-Moyal coefficients can be estimated from the empirical data. Finally, we present an explicit Fokker-Planck equation which models very precisely the empirical probability distributions, in particular, their non-Gaussian heavy tails. 相似文献
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The Fokker-Planck equation is useful to describe stochastic processes. Depending on the force acting in the system, the solution of this equation becomes complicated and approximate or numerical solutions are needed. The relation with the Schrödinger equation allows building a method to obtain solutions of the Fokker-Planck equation. However, this approach has been limited to the study of confined potentials, restricting its applicability. In this work, we suggest a general treatment for non-confining potentials through the use of series of functions based on the solution of the Schrödinger equation, with part of discrete spectrum and part of continuum spectrum. Two examples, the Rosen-Morse potential and a limited harmonic potential, are analyzed using the suggested approach. 相似文献
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We compute autocorrelation functions from nonlinear Fokker-Planck equations that describe nonlinear families of Markov diffusion processes and illustrate this approach for the Plastino-Plastino Fokker-Planck equation related to the Tsallis entropy.Received: 30 October 2003, Published online: 15 March 2004PACS:
05.20.-y Classical statistical mechanics - 05.40.-a Fluctuation phenomena, random processes, noise, and Brownian motion 相似文献
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An exact analogy is approached between systems in thermal equilibrium and those far from equilibrium which can be the cases without detailed balance. The analogy is based on the requirement that a given drift in the Fokker-Planck equation can be decomposed into two parts, one of which is divergence-free and the other can be derived from a potential which is invariant along the direction of the first part. If the conditions are fulfilled the Fokker-Planck equation changes in to a standard Poisson equation. The relations of this requirement to other conditions are diecussed. As a concrete example, the stationary Fokker-Planck equation for optical bistability is solved by using"this method. 相似文献
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A. Kossakowski 《Zeitschrift für Physik B Condensed Matter》1984,56(3):247-255
A method of studying the asymptotic properties of the Fokker-Planck equation near the Hopf bifurcation point is developed. The method consists in the construction of a nonlinear coordinate transformation which transforms the drift term into a canonical form. 相似文献
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The steady states and dynamics of the two Schlögl models on one- and two-dimensional lattices are studied using master equation techniques in tandem with simulations. It is found that the classic bistable behavior of model II is modified to monostable behavior at low dimension. An explanation of this modification is proposed in terms of the effective potential that appears in the dynamical equations on considering the significant effect of fluctuation correlations. The behavior can be modeled by replacing the transient average fluctuation correlation by its asymptotic value plus Gaussian white noise and analyzing the resulting effective potential obtained from the Fokker-Planck equation with multiplicative noise. For model I the transcritical bifurcation point is shifted to lower values of the forward ratek
2 of the second step of the reaction scheme and this shift can also be explained via an effective potential as a function of the average asymptotic fluctuation correlation. Further addition of noise to the asymptotic value is irrelevant for this model since the noise term in the corresponding Fokker-Planck equation turns out to be purely additive. 相似文献
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Joseph L. McCauley 《Physica A》2007,382(2):445-452
The purpose of this comment is to correct mistaken assumptions and claims made in the paper “Stochastic feedback, nonlinear families of Markov processes, and nonlinear Fokker-Planck equations” by T. D. Frank [T.D. Frank, Stochastic feedback, non-linear families of Markov processes, and nonlinear Fokker-Planck equations, Physica A 331 (2004) 391]. Our comment centers on the claims of a “non-linear Markov process” and a “non-linear Fokker-Planck equation.” First, memory in transition densities is misidentified as a Markov process. Second, the paper assumes that one can derive a Fokker-Planck equation from a Chapman-Kolmogorov equation, but no proof was offered that a Chapman-Kolmogorov equation exists for the memory-dependent processes considered. A “non-linear Markov process” is claimed on the basis of a non-linear diffusion pde for a 1-point probability density. We show that, regardless of which initial value problem one may solve for the 1-point density, the resulting stochastic process, defined necessarily by the conditional probabilities (the transition probabilities), is either an ordinary linearly generated Markovian one, or else is a linearly generated non-Markovian process with memory. We provide explicit examples of diffusion coefficients that reflect both the Markovian and the memory-dependent cases. So there is neither a “non-linear Markov process”, nor a “non-linear Fokker-Planck equation” for a conditional probability density. The confusion rampant in the literature arises in part from labeling a non-linear diffusion equation for a 1-point probability density as “non-linear Fokker-Planck,” whereas neither a 1-point density nor an equation of motion for a 1-point density can define a stochastic process. In a closely related context, we point out that Borland misidentified a translation invariant 1-point probability density derived from a non-linear diffusion equation as a conditional probability density. Finally, in the Appendix A we present the theory of Fokker-Planck pdes and Chapman-Kolmogorov equations for stochastic processes with finite memory. 相似文献