Theoretical Chemistry, Dynamical Systems, and the Geometry of Global Phase Space Dynamics

理论化学、动力系统和全局相空间动力学几何

• 批准号: 9704759
• 负责人: Stephen Wiggins
• 金额: $ 19.5万
• 依托单位: California Institute of Technology
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1997
• 资助国家: 美国
• 起止时间: 1997-08-01 至 2001-01-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9704759&HistoricalAwards=false
• 关键词: Theoretical; Chemistry; Dynamical; Systems; Geometry

9704759 Wiggins This research project is concerned with developing analytical and computational tools for studying the global dynamics of semiclassical models of molecules. The emphasis will be on molecular models with three or more degrees-of-freedom and the analytical approach is that of the geometric theory of nonlinear dynamical systems. In particular, we will investigate how geometrical structures in phase space are manifested in experimental spectra, the local to normal mode transition in molecules with three or more degrees-of-freedom, energy transport and the role of invariant manifolds in determining this, and the dynamics of rotational-vibrational interaction in molecules with three or more degrees-of-freedom. In addition, we will investigate mechanism for global instabilities in Hamiltonian systems with three or more degrees of freedom; in particular, the Arnold mechanism. The research is concerned with the development of techniques to study classical and semiclassical dynamics of molecules with three or more degrees-of-freedom, as well as a fundamental study of mechanisms for instability in Hamiltonian systems with three or more degrees-of-freedom. Over the past 10 years experimental techniques have been developed in chemistry to the point where real time dynamical data related to molecular interactions and dynamics can be obtained, which has resulted in the area of research known as "femtochemistry". In some ways the experimental situation in chemistry today bears a strong resemblance to the experimental situation in fluid mechanics in the late 1970`s. At that time new laser based experimental techniques were developed that resulted in global, real time dynamical data from fluid flows. Such data played a key role in the dynamical systems analyses of fluid flows. In fact, one could make the case that these experimental advances were the reason that fluid mechanics became (probably) the main application area for dynamical sy stems theory throughout the 1980`s. Today we are in an analogous situation for theoretical chemistry vis- -vis the relation of experimental advances in fluid mechanics and dynamical systems theory in the late 1970`s. Consequently, a focused, interdisciplinary research effort in dynamical systems and theoretical chemistry could play an important role in the interpretation of this new experimental data, as well as the further development of the field of theoretical chemistry. This award will be supported by the Division of Mathematical Sciences, the Division of Chemistry, and the Office of Multidisciplinary Activities of the Directorate for Mathematical and Physical Sciences.

9704759 Wiggins该研究项目与开发用于研究分子半经典模型的全球动态的分析和计算工具有关。重点将放在具有三个或多个自由度的分子模型上，分析方法是非线性动力学系统的几何理论。特别是，我们将研究相位空间中的几何结构如何在实验光谱中表现出来，在具有三个或以上的自由度，能量传输的分子中，局部至正常模式转变，以及不变歧管在确定这一点中的作用，以及三个或以上自由度的分子中旋转振动相互作用的动力学。此外，我们将调查具有三个或以上自由度的哈密顿体系中全球不稳定性的机制；特别是阿诺德机制。 这项研究涉及研究具有三个或以上自由度的分子的经典和半经典动力学技术的发展，以及对三个或多个自由度的汉密尔顿系统中不稳定性机制的基本研究。 在过去的10年中，实验技术是在化学中开发的，即可以获得与分子相互作用和动力学有关的实时动力学数据，这导致了称为“ FEM化学”的研究领域。在某些方面，当今化学的实验状况与1970年代后期流体力学的实验状况非常相似。当时，开发了新的基于激光的实验技术，从而从流体流中产生了全局的实时动力学数据。这样的数据在流体流的动态系统分析中起关键作用。实际上，可以证明这些实验进步是流体力学成为整个1980年代动力学理论的主要应用领域的原因。今天，我们正处于理论化学相似的情况下，相对于1970年代后期流体力学和动力学系统理论的实验进步的关系。 因此，在动态系统和理论化学方面进行的重点，跨学科的研究工作可能在解释这一新实验数据以及理论化学领域的进一步发展中起着重要作用。 该奖项将得到数学科学，化学划分和数学和物理科学局多学科活动办公室的支持。