Presidential Young Investigators Award

这个多方面的研究项目涉及流体动力学、非线性光学、耦合刚体动力学和无限维动力学。流体动力学工作与由于混沌平流引起的流体流动中的输送和混合现象有关。这项工作将集中在两个不同的主题，具体地说，传输和混合的反馈控制，以及具有更一般的时间相关性的流动。光学研究主要研究光脉冲在非线性介质中传输的偏振动力学。这项工作可应用于光纤器件。刚体动力学作用研究具有粘性阻尼和外力的耦合刚体动力学系统的全局动力学问题。最后一个研究课题的目的是将动力系统的几何理论应用于无限维中的问题。

This multifaceted research project addresses issues in fluid dynamics, nonlinear optics, coupled rigid body dynamics, and infinite dimensional dynamics. The fluid dynamics work is related to transport and mixing phenomena which arise in fluid flows due to chaotic advection. This effort will focus on two distinct topics, specifically, feedback control of transport and mixing, and flows with more general time dependence. The optics research deals with the polarization dynamics of optical pulses propagating in nonlinear media. This work has applications to fiber optical devices. The rigid body dynamics effort studies the global dynamics of coupled rigid body dynamics systems with viscous damping and external forcing. The intent of the final research topic is to bring the geometrical theory of dynamical systems to bear on problems in infinite dimensions.