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

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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.