刚性化学Langevin方程的随机分裂模拟  

Stochastic Splitting Simulation of Stiff Chemical Langevin Equation

作　　者：左路[1] 胡玮[1] ZUO Lu;HU Wei(College of Chemistry and Chemical Engineering,Hubei University,Wuhan 430062,China)

机构地区：[1]湖北大学化学化工学院,湖北武汉430062

出　　处：《数学的实践与认识》2022年第5期150-158,共9页Mathematics in Practice and Theory

基　　金：国家自然科学基金(21606075);湖北大学教研项目(202005)。

摘　　要：对于反应动力学而言,尽管常微分方程已经成为了基本的研究工具,仍然无法精确描述离散分子的随机演变规律.化学Langevin方程的出现则打破了这个困境,使得研究者从随机角度进行动力学数值模拟成为可能.这种模拟可以为研究提供基本的动力学信息.建立了探测刚性并剖分系统为不同时间尺度子系统的自适应策略,并构建了基于算子分裂的多时间尺度反应体系的随机模拟方法.方法运用于两种基本的酶动力反应体系的模拟实验结果表明,随机分裂方法对于具有清晰时间差异的刚性系统能够实现高效且精确模拟,并且保持了反应体系的动力特性.Although ordinary differential equation(ODE) provides a mathematical basis for the fundamental of thermodynamics and kinetics,the random evolution of discrete molecules in a reaction system cannot be described with ODE precisely.This mismatch is overcome by chemical Langevin equation(CLE),which opens up a stochastic approach to numerical simulation.Stochastic simulation by CLE can provide essential information for thermodynamics and kinetics of reactions.In this paper,a new stochastic splitting simulation scheme is proposed,which focuses on the multiscales nature of reaction systems.This scheme deals with partitioned system,and simulates subsystems with different time scales separately.However,the first step of simulation is to detect the existence of stiffness,which is achieved by a new adaptive partitioning strategy.Performance of this splitting simulation scheme is investigated with two elementary reaction systems.According to our results,this scheme can perform well on accuracy and efficiency of stiff systems,and keep dynamics in the meantime.

关 键 词：化学动力学 刚性化学Langevin方程 随机模拟算法 随机龙格库塔法 

分 类 号：O643.1[理学—物理化学] O175[理学—化学]