Institute of Physical Chemistry, Polish Academy of Sciences, Kasprzaka 44/52, 01-224 Warsaw, Poland.
J Chem Phys. 2011 Aug 28;135(8):084123. doi: 10.1063/1.3626520.
In order to develop a stochastic description of gaseous reaction-diffusion systems, which includes a reaction-induced departure from local equilibrium, we derive a modified expression of the master equation from analytical calculations based on the Boltzmann equation. We apply the method to a chemical wave front of Fisher-Kolmogorov-Petrovsky-Piskunov type, whose propagation speed is known to be sensitive to small perturbations. The results of the modified master equation are compared successfully with microscopic simulations of the particle dynamics using the direct simulation Monte Carlo method. The modified master equation constitutes an efficient tool at the mesoscopic scale, which incorporates the nonequilibrium effect without need of determining the particle velocity distribution function.
为了开发一种能够描述包含反应诱导非局部平衡的气态反应-扩散系统的随机模型，我们从基于玻尔兹曼方程的解析计算出发，推导出了主方程的修正表达式。我们将该方法应用于费希尔-科尔莫戈罗夫-彼得罗夫斯基-皮斯昆诺夫（Fisher-Kolmogorov-Petrovsky-Piskunov）型化学波前，已知其传播速度对小扰动非常敏感。修正后的主方程的结果与使用直接模拟蒙特卡罗方法的粒子动力学微观模拟成功进行了比较。修正后的主方程在介观尺度上构成了一种有效的工具，它无需确定粒子速度分布函数即可纳入非平衡效应。
