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1.
ISSDE: A Monte Carlo implicit simulation code based on Stratonovich SDE approach of Coulomb collision 下载免费PDF全文
《中国物理 B》2021,30(9):95201-095201
A Monte Carlo implicit simulation program, Implicit Stratonovich Stochastic Differential Equations(ISSDE), is developed for solving stochastic differential equations(SDEs) that describe plasmas with Coulomb collision. The basic idea of the program is the stochastic equivalence between the Fokker–Planck equation and the Stratonovich SDEs. The splitting method is used to increase the numerical stability of the algorithm for dynamics of charged particles with Coulomb collision. The cases of Lorentzian plasma, Maxwellian plasma and arbitrary distribution function of background plasma have been considered. The adoption of the implicit midpoint method guarantees exactly the energy conservation for the diffusion term and thus improves the numerical stability compared with conventional Runge–Kutta methods. ISSDE is built with C++ and has standard interfaces and extensible modules. The slowing down processes of electron beams in unmagnetized plasma and relaxation process in magnetized plasma are studied using the ISSDE, which shows its correctness and reliability. 相似文献
2.
开发一种适用于求解含库仑碰撞等离子体随机微分方程(SDE)的第一性原理隐式模拟程序——Implicit Stratonovich Stochastic Differential Equations (ISSDE).该程序基于Fokker-Planck (FP)方程与Stratonovich SDE的等价性理论,通过精确求解Stratonovich SDE达到对FP方程的高效第一性原理计算的目标.ISSDE采用隐式格式保证求解的数值稳定性,同时可以保证粒子碰撞过程的能量守恒.ISSDE基于C++语言开发,具有标准接口和灵活的可扩展模组.通过模拟电子束在非磁化和磁化致密等离子体中的慢化过程验证ISSDE的正确性,并展示该程序在碰撞等离子体模拟中的应用. 相似文献
3.
Using the general theory of numerical integration of stochastic differential equations, a constructive approach to numerical methods for a system with colored noise is proposed. Efficient methods up to the 5/2 strong order and up to the third weak order, including Runge-Kutta and implicit schemes, are presented. The algorithms are tested on the Kubo oscillator. 相似文献
4.
Impulsive control of stochastic system under the sense of stochastic asymptotical stability 总被引:2,自引:0,他引:2 下载免费PDF全文
This paper studies the stochastic asymptotical stability of stochastic impulsive differential equations,and estab-lishes a comparison theory to ensure the trivial solution’s stochastic asymptotical stability.From the comparison theory,it can find out whether the stochastic impulsive differential system is stable just by studying the stability of a deter-ministic comparison system.As a general application of this theory,it controls the chaos of stochastic L system using impulsive control method,and numerical simulations are employed to verify the feasibility of this method. 相似文献
5.
A stochastic version of Lotka-Volterra model subjected to real noises is proposed and investigated. The approximate stationary probability densities for both predator and prey are obtained analytically. The original system is firstly transformed to a pair of It o stochastic differential equations. The Ito formula is then carried out to obtain the It o stochastic differential equation for the period orbit function. The orbit function is considered as slowly varying process under reasonable assumptions. By applying the stochastic averaging method to the orbit function in one period, the averaged Ito stochastic differential equation of the motion orbit and the corresponding Fokker-Planck equation are derived. The probability density functions of the two species are thus formulated. Finally, a classical real noise model is given as an example to show the proposed approximate method. The accuracy of the proposed procedure is verified by Monte Carlo simulation. 相似文献
6.
随机微分方程计算方法及其应用 总被引:1,自引:0,他引:1
介绍随机微分方程离散化格式的构造、收敛性法则、强收敛格式、弱收敛格式、带跳跃的随机微分方程的计算方法,偏微分方程的概率求解以及它们在物理、工程和金融等领域中的一些应用. 相似文献
7.
We use path integral methods to obtain expansions for the correlation functions of the non-Markovian stochastic processes generated by stochastic differential equations with colored noise. 相似文献
8.
We construct a stochastic mechanics by replacing Bohm‧s first-order ordinary differential equation of motion with a stochastic
differential equation where the stochastic process is defined by the set of Bohmian momentum time histories from an ensemble
of particles. We show that, if the stochastic process is a purely random process with n-th order joint probability density in the form of products of delta functions, then the stochastic mechanics is equivalent
to quantum mechanics in the sense that the former yields the same position probability density as the latter. However, for
a particular non-purely random process, we show that the stochastic mechanics is not equivalent to quantum mechanics. Whether
the equivalence between the stochastic mechanics and quantum mechanics holds for all purely random processes but breaks down for all non-purely random processes remains an open question. 相似文献
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10.
将基于参数展开的同伦分析法(PE-HAM)进行了推广,使之适用于谐和激励与随机噪声联合作用下的强非线性随机动力系统. 通过构造合适的同伦映射,将对强非线性随机动力系统响应的求解转化为对一组线性随机微分方程的求解. 进一步研究了受到谐和与Gauss白噪声激励的强非线性Duffing振子,由PE-HAM得到了该系统的解过程和稳态概率密度的解析表达式. 数值模拟的结果说明了PE-HAM方法的精确性.
关键词:
PE-HAM方法
强非线性随机动力系统
稳态概率密度
解过程
随机激励 相似文献
11.
In information theory, lossless compression of general data is based on an explicit assumption of a stochastic generative model on target data. However, in lossless image compression, researchers have mainly focused on the coding procedure that outputs the coded sequence from the input image, and the assumption of the stochastic generative model is implicit. In these studies, there is a difficulty in discussing the difference between the expected code length and the entropy of the stochastic generative model. We solve this difficulty for a class of images, in which they have non-stationarity among segments. In this paper, we propose a novel stochastic generative model of images by redefining the implicit stochastic generative model in a previous coding procedure. Our model is based on the quadtree so that it effectively represents the variable block size segmentation of images. Then, we construct the Bayes code optimal for the proposed stochastic generative model. It requires the summation of all possible quadtrees weighted by their posterior. In general, its computational cost increases exponentially for the image size. However, we introduce an efficient algorithm to calculate it in the polynomial order of the image size without loss of optimality. As a result, the derived algorithm has a better average coding rate than that of JBIG. 相似文献
12.
Aaron B. Budgor 《Journal of statistical physics》1977,17(1):21-44
A fusion of the highly successful methods of harmonic and statistical linearization is used as a first approximation in determining, either iteratively or via a nonlinear integral equation, the effects of higher harmonics and non-Gaussian distortion terms on the second-order statistics of a wide variety of nonlinear stochastic differential equations perturbed by some linear combination of Gaussian noise and a periodic deterministic/stochastic excitation. Physical a posteriori applicability criteria are presented which justify when these higher order effects may be neglected. A simple modification of this statistical-harmonic linearization procedure based upon the Fokker-Planck variance is proposed.This work was supported in part by the National Science Foundation under grant CHE75-20624. 相似文献
13.
A. Careta F. Sagués L. Ramirez-Piscina J. M. Sancho 《Journal of statistical physics》1993,71(1-2):235-242
Analytical results are derived for the effective dispersion of a passive scalar in a stochastic velocity field evolving in a fast time scale. These results are favorably compared with direct computer simulation of stochastic differential equations containing multiplicative space-time correlated noise. 相似文献
14.
《Journal of Nonlinear Mathematical Physics》2013,20(3):427-441
Necessary and sufficient conditions which allow a second-order stochastic ordinary differential equation to be transformed to linear form are presented. The transformation can be chosen in a way so that all but one of the coefficients in the stochastic integral part vanish. The linearization criteria thus obtained are used to determine the general form of a linearizable Langevin equation. 相似文献
15.
Simulations of Two-Step Maruyama Methods for Nonlinear Stochastic Delay Differential Equations 下载免费PDF全文
In this paper, we investigate the numerical performance of a family of
P-stable two-step Maruyama schemes in mean-square sense for stochastic differential
equations with time delay proposed in [8, 10] for a certain
class of nonlinear stochastic delay differential equations
with multiplicative white noises.
We also test the convergence of one of the schemes for
a time-delayed Burgers' equation with an additive white noise. Numerical results show that
this family of two-step Maruyama methods exhibit similar stability for nonlinear equations
as that for linear equations. 相似文献
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From Random Matrices to Stochastic Operators 总被引:3,自引:0,他引:3
We propose that classical random matrix models are properly viewed as finite difference schemes for stochastic differential
operators. Three particular stochastic operators commonly arise, each associated with a familiar class of local eigenvalue
behavior. The stochastic Airy operator displays soft edge behavior, associated with the Airy kernel. The stochastic Bessel operator displays hard edge behavior, associated with the Bessel kernel. The article concludes with suggestions for a stochastic sine operator, which would display bulk behavior, associated with the sine kernel. 相似文献
19.
Analysis of stochastic bifurcation and chaos in stochastic Duffing--van der Pol system via Chebyshev polynomial approximation 下载免费PDF全文
The Chebyshev polynomial approximation is applied to investigate the stochastic
period-doubling bifurcation and chaos problems of a stochastic Duffing--van
der Pol system with bounded random parameter of exponential probability
density function subjected to a harmonic excitation. Firstly the stochastic
system is reduced into its equivalent deterministic one, and then the
responses of stochastic system can be obtained by numerical methods.
Nonlinear dynamical behaviour related to stochastic period-doubling
bifurcation and chaos in the stochastic system is explored. Numerical
simulations show that similar to its counterpart in deterministic nonlinear
system of stochastic period-doubling bifurcation and chaos may occur in the
stochastic Duffing--van der Pol system even for weak intensity of random
parameter. Simply increasing the intensity of the random parameter may
result in the period-doubling bifurcation which is absent from the
deterministic system. 相似文献
20.
GEAR算法在随机轨道模型计算中的应用 总被引:3,自引:0,他引:3
本文对随机轨道模型中颗粒相常微分方程组的刚性问题进行了分析,结果表明:当采用常规算法如四阶Runge-kutta法求解方程组时,方程组的刚性是导致某些情况下计算发散或计算时间过长的原因。为此,本文将适用于求解刚性方程组的Gear算法应用于随机轨道模型的计算中,取得了良好的效果. 相似文献