随机模拟化学反应系统的加速L-leap算法

提出了随机模拟化学反应系统的加速L-leap算法,该算法根据leap条件确定具有最大倾向函数的反应通道的反应次数,并利用二项分布随机数生成其它反应通道在当前leap时间区间内的反应次数．L-leap算法可更好地满足leap条件．数值模拟实验表明该算法能取得更好的模拟性能．     

Implicit Simulation Methods for Stochastic Chemical Kinetics

In biochemical systems some of the chemical species are present with only small numbers of molecules. In this situation discrete and stochasticsimulation approaches are more relevant than continuous and deterministic ones. The fundamental Gillespie’s stochastic simulation algorithm (SSA) accounts for every reaction event, which occurs with a probability determined by the configuration of the system. This approach requires a considerable computational effort for models with many reaction channels and chemical species.In order to improve efficiency, tau-leaping methods represent multiple firings of each reaction during a simulation step by Poisson random variables. For stiff systems the mean of this variable is treated implicitly in order to ensure numerical stability. This paper develops fully implicit tau-leaping-like algorithms that treat implicitly both the mean and the variance of the Poisson variables. The construction is based on adapting weakly convergent discretizations of stochastic differential equations to stochastic chemical kinetic systems. Theoretical analyses of accuracy and stability of the new methods are performed on a standard test problem. Numerical results demonstrate the performance of the proposed tau-leaping methods.     

Adjoint Error Estimation for a Pseudo-Spectral Approach to Stochastic Field-Circuit Coupled Problems

This work is concerned with the numerical approximation of random differential-algebraic equations (DAE), arising from electric field-circuit coupled problems. Using the adjoint DAE, the stochastic collation error is analyzed. The error can be evaluated using a collocation method of the same polynomial degree for the adjoint DAE. In particular, there is no need for constructing a solution of higher polynomial degree. The accuracy of the estimator is illustrated by a numerical example. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A Possible Homogenization Approach for the Numerical Simulation of Periodic Microstructures with Defects

We present a general strategy, adapted from classical homogenization theory, to approximate at the fine scale the solution to an elliptic equation with oscillatory coefficient when this coefficient is a locally perturbed periodic function. We illustrate numerically the efficiency of the approach. The setting considered is a particular case of a more general method which is developed in works in preparation [6].     

Uncertainty Quantification of Stochastic Simulation for Black-box Computer Experiments

Stochastic simulations applied to black-box computer experiments are becoming more widely used to evaluate the reliability of systems. Yet, the reliability evaluation or computer experiments involving many replications of simulations can take significant computational resources as simulators become more realistic. To speed up, importance sampling coupled with near-optimal sampling allocation for these experiments is recently proposed to efficiently estimate the probability associated with the stochastic system output. In this study, we establish the central limit theorem for the probability estimator from such procedure and construct an asymptotically valid confidence interval to quantify estimation uncertainty. We apply the proposed approach to a numerical example and present a case study for evaluating the structural reliability of a wind turbine.     

非平稳随机过程模拟的一个谱表示方法

本文由Priestley渐进谱理论导出了非平稳随机过程蒙特卡罗模拟的一个谱表示方法.按照该方法,样本过程可直接由一余弦级数公式计算产生.可以证明,当级数项数足够大时,模拟的样本过程可准确地反映非平稳随机过程规定的性质;当产生的样本过程足够多时,其总体均值和总体自相关函数均趋于相应目标函数;样本过程随着级数项数趋于无穷而渐近呈正态分布.本文方法最显著的特点在于可以借助随机相位角产生具有某些预期特征的样本过程.     

渗流耦合系统动边值问题特征分数步差分方法

对多层渗流方程耦合系统动边值问题,提出适合并行计算的一类特征分数步差分格式,利用区域变换、变分形式、粗细网格配套、乘积型叁二次插值、差分算子乘积交换性、高阶差分算子的分解、先验估计的理论和技巧,得到收敛性的最佳阶l2误差估计．该方法已成功地应用到多层油资源运移聚集的资源评估生产实际中,得到了很好的数值模拟结果．     

水滴清除气溶胶过程的随机算法和数值模拟

气溶胶尺度分布的时间演变可量化气溶胶的湿沉降过程,它在数学上可由考虑湿沉降的通用动力学方程来描述．该方程为一典型的部分积分微分方程,与气溶胶尺度分布和雨滴尺度分布均相关,且由于需要考虑Brown扩散、拦截和惯性碰撞等湿沉降机制而使得清除系数模型非常复杂,普通的数值方法难以求解．为此发展了一种新的多重Monte Carlo算法,以求解考虑湿沉降的通用动力学方程,并用于模拟实际环境中气溶胶的湿沉降．对于对数正态分布的气溶胶尺度分布和雨滴尺度分布, 多重Monte Carlo算法进行的数值模拟表明, 雨滴几何平均尺度越小, 雨滴几何标准偏差越小,越有利于小尺度和中等尺度气溶胶的湿去除,而稍微不利于大尺度气溶胶的湿去除．     

一类具耦合的化学反应扩散系统的奇摄动

本文研究一类带耦合项的化学反应扩散方程组解的性态,利用上下解理论证得解的存在性,然后在一定的参数环境下考虑了相应的奇摄动问题,并给出一致有效的渐近解.     

Stability Analysis for the Numerical Simulation of Hybrid Stochastic Differential Equations

This paper is mainly concerned with the exponential stability of a class of hybrid stochastic differential equations–stochastic differential equations with Markovian switching (SDEwMSs). It first devotes to reveal that under the global Lipschitz condition, a SDEwMS is pth (p ∈ (0,1)) moment exponentially stable if and only if its corresponding improved Euler-Maruyama(IEM) method is pth moment exponentially stable for a suitable step size. It then shows that the SDEwMS is pth(p ∈ (0,1)) moment exponentially stable or its corresponding IEM method with small enough step sizes implies the equation is almost surely exponentially stable or the corresponding IEM method, respectively. In that sense, one can infer that the SDEwMS is almost surely exponentially stable and the IEM method, no matter whether the SDEwMS is pth moment exponentially stable or the IEM method. An example is demonstrated to illustrate the obtained results.