化学反应体系中涨落的时间空间关联(Ⅰ)——涨落、扩散和波

本文着重分析了如何描述化学反应体系中密度涨落的空间关联,对照反应扩散方程,我们在密度涨落分布函数所满足的Master方程中引入了扩散项或压力项,对无限介质,解Master方程,得到了一系列波,第一支波是与反应扩散方程的解一致,描述了平均密度起伏在空间的传播,在气体中就是声波,其它各支波,则描述了局部密度涨落高阶矩的变化在空间的传播(平均密度不改变),其实就是局部机率分布函数畸变后的传播过程,我们称之为涨落波,文中还讨论了如何求解线性初值问题。 关键词：

THE SPACE-TIME CORRELATION OF THE FLUCTUATION IN A CHEMICAL REACTION SYSTEM (I)——FLUCTUATION, DIFFUSION AND WARES

In this article, the question about how to describe the space correlation of the fluctuation in a chemical reaction system has been analysed. Eeferring to the reaction-diffusion equation., we have successfully introduced the diffusion or pressure terms into master equation of the probability distribution function of density. Solving this master equation for infinite medium, a series of waves have been obtained. The first branch is the average density wave which has already been obtained from the reaction-diffusion equation. It is just the acoustic wave in gases. Other branches decribe the propagation of the fluctuation moments of the local density. They present the propagation processes of the local distortion of the probability distribution function. The method to solve the initial problem of the master equation have also been discussed.