CAREER: Nonlinear Dynamics and Control from Microscale to Macroscale

主要研究者姓名，机构：Igor Mezic，加州大学圣巴巴拉分校提案编号：9875933提案标题：“非线性动力学和控制从微观到宏观到课堂”项目摘要：我们建议开发数学方法来研究与工程相关的问题，在微观的设备，如微尺度混合器，和动态和宏观尺度的设备，如压缩系统的控制。 我们将开发的新方法是建立在动力系统和遍历理论，控制理论和微尺度物理学的跨学科思想的基础上。 在1微米尺度的几何形状中。 这里提出的工作包括混合的主动控制的研究，以及新的物理效应，如稀疏和双电层的治疗，介绍了小规模的设备。 我们将提供一个基本的理论控制的混合在这方面使用的方法，鲁棒控制理论和遍历理论。本论文的研究将为微流体系统控制领域的快速发展提供理论基础，同时也将为宏观和微观压缩系统的动力学和控制研究提供理论基础。最近，我们开发了一个数学模型的轴向压缩系统的动力学平均和缩放的Navier-Stokes方程。 将对解决方案进行严格的研究，并开发相关的应用数学方法。 将研究使用所谓的微型襟翼主动控制边界层不稳定性的可能性。 目前正在开发用于微型喷气发动机的微型压缩机。本课程将研究微型压缩机的建模和控制问题，让学生熟悉应用数学和工程学之间的接口的最新发展。我们建议教授一门非线性现象课，使用上述研究中的例子作为背景动机和问题生成器。在我们的研究小组的学生将接触到一个真正的跨学科的主题，从动力系统，控制理论，数学，微尺度物理和工程。

PI's Name, Institution: Igor Mezic, University of California at Santa Barbara Proposal Number: 9875933 Proposal Title: "Nonlinear Dynamics and Control from Microscale to Macroscale to Classroom" Project Abstract:We propose to develop mathematical methods to study problems related to engineering of devices at the microscale, such as microscale mixers, and dynamics and control of macroscale devices such as compression systems. The new methods that we will develop are built on an interdisciplinary mix of ideas from dynamical systems and ergodic theory, control theory and microscale physics.We will study mixing of fluids in geometries of the scale of 1 micron. The work proposed here includes the study of active control of mixing as well as treatment of new physical effects such as rarefaction and electric double layer, introduced by the small scale of the devices. We will provide a fundamental theory for control of mixing in this context using methods of robust control theory and ergodic theory. This study will provide theoretical backbone for the rapidly evolving field of control in microfluid systems.We also propose to study the dynamics and control of macroscopic and microscopic compression systems. We have recently developed a mathematical model for axial compression system dynamics by averaging and scaling of the Navier-Stokes equations. A rigorous study of the solutions will be pursued and the relevant applied mathematics methods developed. Possibilities of active control of boundary layer instabilities using the so-called microflaps will be studied. Microcompressors for the use in micro jet engines are currently being developed. Modelling and control issues in microcompressors will be studied.We will familiarize students with the current developments on the interface between applied mathematics and engineering. We propose to teach a Nonlinear Phenomena class that uses examples from the research described above as the background motivation and problem generator. The students in our research group will be exposed to a truly interdisciplinary set of topics from dynamical systems, control theory, mathematics, microscale physics and engineering.