'The Nonlinear Dynamical Foundations of Transition State Theory in Systems with Three or More Degrees-of-Freedom'

“三自由度或更多自由度系统中过渡态理论的非线性动力学基础”

• 批准号: 0071338
• 负责人: Stephen Wiggins
• 金额: $ 21万
• 依托单位: California Institute of Technology
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2000
• 资助国家: 美国
• 起止时间: 2000-08-01 至 2001-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0071338&HistoricalAwards=false
• 关键词: Nonlinear; Dynamical; Foundations; Transition; State

NSF Award Abstract - DMS-0071338Mathematical Sciences: The Nonlinear Dynamical Foundations of Transition State Theory in Systems with Three or More Degrees of FreedomAbstract0071338 WigginsThis research project is concerned with understanding the nonlinear dynamical foundations of transition state theory in systems with three or more degrees of freedom. While there has been much progress along these lines for two degree-of-freedom systems, there has been little progress of a similar nature for systems with three or more degrees-of-freedom. The geometrical point of view of dynamical systems theory offers a framework for discovering the types of higher dimensional phase space structures that govern reaction rates and energy flow in molecules. We will apply this approach to several problems: three dimensional Rydberg atoms in crossed electric and magnetic fields, the London-Eyring-Polanti-Sato potential, rotation-vibration interaction in formaldehyde, and a study of energy flow through resonances in carbonyl sulphide (OCS). In each case we will show that there are higher dimensional phase space structures that act as a "transition state." Indeed, it may even be possible to generalize the very useful idea of a periodic orbit dividing surface to systems with three or more degrees of freedom. Our research will also focus on developing computational approaches to realize these geometric structures in these specific problems. We will also develop a wavelet-based frequency map analysis tool for studying energy flow in resonances. This work will be carried out in collaboration with chemists and physicists, as well as computational scientists.This project investigates fundamental questions concerning chemical reactions. The underlying mathematical questions involve the nonlinear dynamical foundations of transition state theory in systems with three or more degrees of freedom. This is the fundamental theory that allows predictions concerning chemical reaction dynamics. While there is a fairly complete understanding of this theory for simple, low dimensional, systems, there is as yet no analogous theoretical framework for more physically realistic high dimensional systems. Such a theory will involve mathematical description of surfaces in dimensions larger than four and will require development of computational tools for realizing and visualizing such surfaces. This will result in a detailed understanding of the dynamics of how molecules break up and of how atoms combine to form molecules. The research is interdisciplinary, involving the collaboration of chemists, physicists, and computational scientists.

NSF 奖项摘要 - DMS-0071338数学科学：三自由度或更多自由度系统中过渡态理论的非线性动力学基础摘要0071338 Wiggins该研究项目旨在理解三自由度或更多自由度系统中过渡态理论的非线性动力学基础。 虽然二自由度系统在这些方面取得了很大进展，但三自由度或更多自由度系统却几乎没有类似性质的进展。 动力系统理论的几何观点提供了一个框架，用于发现控制分子中反应速率和能量流的高维相空间结构的类型。 我们将应用这种方法解决几个问题：交叉电场和磁场中的三维里德伯原子、伦敦-艾林-波兰蒂-佐藤势、甲醛中的旋转振动相互作用，以及通过羰基硫中的共振进行的能量流研究（OCS） ）。 在每种情况下，我们将证明存在充当“过渡态”的更高维相空间结构。 事实上，甚至可以将周期性轨道划分表面的非常有用的想法推广到具有三个或更多自由度的系统。我们的研究还将侧重于开发计算方法来实现这些特定问题中的这些几何结构。我们还将开发一种基于小波的频率图分析工具，用于研究共振中的能量流。这项工作将与化学家、物理学家以及计算科学家合作进行。该项目研究有关化学反应的基本问题。 潜在的数学问题涉及具有三个或更多自由度的系统中过渡态理论的非线性动力学基础。 这是允许预测化学反应动力学的基本理论。 虽然对于简单、低维系统的这一理论已经有了相当完整的理解，但对于更物理上真实的高维系统还没有类似的理论框架。 这样的理论将涉及对大于四维的表面的数学描述，并且需要开发计算工具来实现和可视化这些表面。 这将使我们详细了解分子如何分解以及原子如何结合形成分子的动力学。 该研究是跨学科的，涉及化学家、物理学家和计算科学家的合作。