Carpenter Barry K, Ezra Gregory S, Farantos Stavros C, Kramer Zeb C, Wiggins Stephen
School of Chemistry , Cardiff University , Cardiff CF10 3AT , United Kingdom.
Department of Chemistry and Chemical Biology , Cornell University , Ithaca , New York 14853-1301 , United States.
J Phys Chem B. 2018 Apr 5;122(13):3230-3241. doi: 10.1021/acs.jpcb.7b08707. Epub 2017 Oct 12.
Classical Hamiltonian trajectories are initiated at random points in phase space on a fixed energy shell of a model two degrees of freedom potential, consisting of two interacting minima in an otherwise flat energy plane of infinite extent. Below the energy of the plane, the dynamics are demonstrably chaotic. However, most of the work in this paper involves trajectories at a fixed energy that is 1% above that of the plane, in which regime the dynamics exhibit behavior characteristic of chaotic scattering. The trajectories are analyzed without reference to the potential, as if they had been generated in a typical direct molecular dynamics simulation. The questions addressed are whether one can recover useful information about the structures controlling the dynamics in phase space from the trajectory data alone, and whether, despite the at least partially chaotic nature of the dynamics, one can make statistically meaningful predictions of trajectory outcomes from initial conditions. It is found that key unstable periodic orbits, which can be identified on the analytical potential, appear by simple classification of the trajectories, and that the specific roles of these periodic orbits in controlling the dynamics are also readily discerned from the trajectory data alone. Two different approaches to predicting trajectory outcomes from initial conditions are evaluated, and it is shown that the more successful of them has ∼90% success. The results are compared with those from a simple neural network, which has higher predictive success (97%) but requires the information obtained from the "by-hand" analysis to achieve that level. Finally, the dynamics, which occur partly on the very flat region of the potential, show characteristics of the much-studied phenomenon called "roaming." On this potential, it is found that roaming trajectories are effectively "failed" periodic orbits and that angular momentum can be identified as a key controlling factor, despite the fact that it is not a strictly conserved quantity. It is also noteworthy that roaming on this potential occurs in the absence of a "roaming saddle," which has previously been hypothesized to be a necessary feature for roaming to occur.
经典哈密顿轨迹在一个具有两个自由度的模型势的固定能量壳层的相空间中的随机点处起始，该模型势由在无限延伸的平坦能量平面中的两个相互作用的极小值组成。在平面能量以下，动力学明显是混沌的。然而，本文的大部分工作涉及在比平面能量高1%的固定能量处的轨迹，在该能量区域，动力学表现出混沌散射的特征行为。对轨迹进行分析时不考虑势，就好像它们是在典型的直接分子动力学模拟中生成的一样。所解决的问题是，仅从轨迹数据中能否恢复关于控制相空间动力学的结构的有用信息，以及尽管动力学至少部分具有混沌性质，能否从初始条件对轨迹结果进行具有统计意义的预测。结果发现，可以通过对轨迹进行简单分类来识别在解析势上可确定的关键不稳定周期轨道，并且仅从轨迹数据中也能轻易辨别出这些周期轨道在控制动力学中的具体作用。评估了两种从初始条件预测轨迹结果的不同方法，结果表明其中更成功的方法成功率约为90%。将结果与一个简单神经网络的结果进行了比较，该神经网络具有更高的预测成功率（97%），但需要从“手工”分析中获得的信息才能达到该水平。最后，部分发生在势的非常平坦区域的动力学表现出被广泛研究的“漫游”现象的特征。在这个势上，发现漫游轨迹实际上是“失败”的周期轨道，并且角动量可被识别为一个关键控制因素，尽管它不是一个严格守恒的量。同样值得注意的是，在这个势上的漫游发生时不存在“漫游鞍点”，而之前曾假设漫游鞍点是漫游发生的必要特征。
