Nowakowski B, Lemarchand A
Institute of Physical Chemistry, Polish Academy of Sciences, Kasprzaka 44/52, 01-224 Warsaw, Poland.
Phys Rev E Stat Nonlin Soft Matter Phys. 2003 Sep;68(3 Pt 1):031105. doi: 10.1103/PhysRevE.68.031105. Epub 2003 Sep 22.
We study a thermochemical gaseous system in the vicinity of the bifurcation related to the emergence of bistability. Corrections to the standard deterministic dynamics induced by the perturbation of the particle velocity distribution are obtained from the solution of the Boltzmann equation. Using these results, analytical expressions including the nonequilibrium effects are derived for the ignition time in the explosive regime and mean first passage time in the bistable regime. It is demonstrated that a departure from partial equilibrium can shift the bifurcation point. The system which was bistable according to the standard deterministic approach, can become monostable and explosive in the presence of nonequilibrium effects. Even when the system remains in the bistable regime, the mean first passage time can be changed by several orders of magnitude. In the monostable domain, the ignition time can be about ten times smaller than the unperturbed value. These analytical predictions agree well with the results of the microscopic simulations of the dilute gas system.
我们研究了一个与双稳态出现相关的分岔附近的热化学气体系统。由粒子速度分布扰动引起的对标准确定性动力学的修正，是从玻尔兹曼方程的解中获得的。利用这些结果，推导了包括非平衡效应在内的爆炸 regime 下点火时间和双稳态 regime 下平均首次通过时间的解析表达式。结果表明，偏离局部平衡会使分岔点发生移动。根据标准确定性方法双稳态的系统，在存在非平衡效应时可能变为单稳态并发生爆炸。即使系统仍处于双稳态 regime，平均首次通过时间也可能改变几个数量级。在单稳态区域，点火时间可比未受扰动的值小约十倍。这些解析预测与稀薄气体系统微观模拟的结果吻合良好。
