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首页> 外文期刊>The journal of physical chemistry, A. Molecules, spectroscopy, kinetics, environment, & general theory >Sampling Phase Space Dividing Surfaces Constructed from Normally Hyperbolic Invariant Manifolds (NHIMs)
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Sampling Phase Space Dividing Surfaces Constructed from Normally Hyperbolic Invariant Manifolds (NHIMs)

机译：从正常双曲不变歧管（NHIMS）构建的采样相空间分割表面

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In this paper, we further investigate the construction of a phase space dividing surface (DS) from a normally hyperbolic invariant manifold (NHIM) and the sampling procedure for the resulting dividing surface described in earlier work (Wiggins, S.; et al. J. Chem. Phys. 2016, 144, 054107). Our discussion centers on the relationship between geometrical structures and dynamics for 2 and 3 degree of freedom (DoF) systems, specifically, the construction of a DS from a NHIM. We show that if the equation for the NHIM and associated DS is known (e.g., as obtained from Poincare-Birkhoff normal form theory), then the numerical procedure described in Wiggins et al. (J. Chem. Phys. 2016, 144, 054107) gives the same result as a sampling method based upon the explicit form of the NHIM. After describing the sampling procedure in a general context, it is applied to a quadratic Hamiltonian normal form near an index- one saddle where explicit formulas exist for both the NHIM and the DS. It is shown for both 2 and 3 DoF systems that a version of the general sampling procedure provides points on the analytically defined DS with the correct microcanonical density on the constant-energy DS. Excellent agreement is obtained between analytical and numerical averages of quadratic energy terms over the DS for a range of energies.
机译：在本文中，我们进一步研究了从正常的双曲线不变歧管（NHIM）的相位空间分割表面（DS）的构造以及前面工作中所述的所得分割表面的采样过程（Wiggins，S.等。j 。化学。物理。2016,144,054107）。我们的讨论中心对几何结构与动力学之间的关系2和3自由度（DOF）系统，具体地，从NHIM构建DS的结构。我们表明，如果已知NHIM和相关的DS的等式（例如，从Poincare-Birkhoff正常形式理论中获得），那么Wiggins等人中描述的数值程序。 （J.Chem. Phys。2016,144,054107）基于NHIM的明确形式提供与采样方法相同的结果。在将采样过程描述在一般背景中之后，它应用于索引 - 一个鞍座附近的二次哈密顿正常形式，其中NHIM和DS都存在显式公式。它显示为2和3 DOF系统，即一般采样过程的版本在分析定义的DS上提供具有正确的微常DS上的分析定义的DS的点。在DS的二次能量术语的分析和数值平均值之间获得了优秀的一致性，用于一系列能量。

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