SGER: Nonstationary Time Series Analysis and Qualitative Nonlinear Dynamics of Nonequilibrium Nanoscale Processes

加州大学欧文分校的克雷格·马滕斯在理论和计算化学项目的探索研究小资助金(SGER)的支持下，启动了一个旨在开发非平衡纳米级过程的非平稳时间序列分析和定性非线性动力学的理论方法的项目。在这个项目中，PI正在使用新的计算方法来研究凝聚相系统中的超快动力学过程。这项工作的重点是多体系统中复杂的非平衡动力学的分析、可视化和理论建模。该项目的目的是弥合在模拟中产生的大量原子尺度信息与用简单的定性概念和定量分析理论描述这类系统之间的差距。正在开发的计算工具结合了大规模的经典分子动力学模拟，基于Wigner-Ville和小波表示的非平稳时间序列方法对微观轨迹数据的新颖分析，以及构建描述基本动力学特征的定性图像和定量模型，并可通过数值和实验室实验进行验证。计算和理论方法被应用于一系列超快多体物理和化学过程。其中包括振动弛豫以及纳米级激波和分子内自由度的相干非线性相互作用。这项工作将有助于对复杂系统中的非平衡和非线性动力学效应的一般理解，因为它既提供了模拟这类过程的工具，也为其解释和理论建模提供了一个直观的框架。

Craig Martens of the University of California, Irvine, is supported by a Small Grant for Exploratory Research (SGER) from the Theoretical and Computational Chemistry program to begin a project aimed at developing theoretical methods for nonstationary time series analysis and qualitative nonlinear dynamics of nonequilibrium nanoscale processes. In this project the PI is conducting investigations of ultrafast dynamical processes in condensed phase systems using novel computational methodology. The work is focusing on the analysis, visualization, and theoretical modeling of complex nonequilibrium dynamics in many-body systems. The aim of the project is to bridge the gap between the massive amounts of atomic-scale information generated in simulations and descriptions of such systems in terms of simple qualitative concepts and quantitative analytical theories. The computational tools that are being developed combine large-scale classical molecular dynamics simulation, novel analysis of microscopic trajectory data using nonstationary time series methodology based on Wigner-Ville and wavelet representations, and the construction of qualitative pictures and quantitative models that caricature the essential dynamical features and can be validated against numerical and laboratory experiments. The computational and theoretical approach is applied to a range of ultrafast many-body physical and chemical processes. These include vibrational relaxation and the coherent nonlinear interaction of nanoscale shock waves and intramolecular degrees of freedom. The proposed work will contribute to the general understanding of nonequilibrium and nonlinear dynamical effects in complex systems by providing both tools for simulation of such processes and an intuitive framework for their interpretation and theoretical modeling.