CAREER: Nonlinear Dynamics and Control from Microscale to Macroscale

派的名字，机构：伊戈尔·梅齐克，加州大学圣巴巴拉分校提案编号：9875933提案标题：从微观到宏观再到课堂的非线性动力学和控制项目摘要：我们建议开发数学方法来研究与微观设备工程相关的问题，如微型混合器，以及宏观设备的动力学和控制，如压缩系统。我们将开发的新方法建立在动力系统和遍历理论、控制理论和微观物理的跨学科混合的基础上。我们将在1微米的几何尺度上研究流体的混合。本文提出的工作包括对混合的主动控制研究，以及对设备小型化带来的稀薄和双电层等新物理效应的处理。在这一背景下，我们将利用鲁棒控制理论和遍历理论的方法，为混合控制提供基础理论。这项研究将为微流体系统中快速发展的控制领域提供理论基础。我们还建议研究宏观和微观压缩系统的动力学和控制。最近，我们通过对Navier-Stokes方程进行平均和定标，建立了轴向压缩系统动力学的数学模型。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襟翼主动控制边界层不稳定性的可能性。用于微型喷气发动机的微型压缩机目前正在开发中。我们将研究微型压缩机中的建模和控制问题。我们将使学生熟悉应用数学和工程之间的接口的最新发展。我们建议教授一门使用上述研究中的例子作为背景、动机和问题生成器的非线性现象课程。我们研究组的学生将接触到来自动力系统、控制理论、数学、微尺度物理和工程学的真正跨学科的主题。

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.