CAREER: Nonlinear Dynamics and Control from Microscale to Macroscale

职业：从微观到宏观的非线性动力学和控制

• 批准号: 9875933
• 负责人: Igor Mezic
• 金额: $ 20万
• 依托单位: University of California-Santa Barbara
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1999
• 资助国家: 美国
• 起止时间: 1999-07-01 至 2003-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9875933&HistoricalAwards=false
• 关键词: CAREER; Nonlinear; Dynamics; Control; Microscale

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.

项目负责人姓名，机构：Igor Mezic，加州大学圣巴巴拉分校提案号：9875933提案题目：“从微观尺度到宏观尺度到课堂的非线性动力学与控制”项目摘要：我们建议发展数学方法来研究与微观尺度设备工程相关的问题，如微尺度混合器，以及宏观尺度设备的动力学和控制问题，如压缩系统。我们将开发的新方法是建立在动力系统和遍历理论、控制理论和微观物理学的跨学科混合思想之上的。我们将研究1微米尺度的几何流体混合。本文提出的工作包括研究混合的主动控制，以及由于装置的小规模而引入的新的物理效应，如稀薄和双电层的处理。我们将利用鲁棒控制理论和遍历理论的方法，为这种情况下的混合控制提供一个基本理论。本研究将为快速发展的微流体系统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。我们最近通过对Navier-Stokes方程进行平均和缩放，建立了轴向压缩系统动力学的数学模型。将对这些问题的解决方案进行严格的研究，并开发相关的应用数学方法。利用所谓的微襟翼主动控制边界层不稳定性的可能性将被研究。目前正在开发用于微型喷气发动机的微型压缩机。将研究微型压缩机的建模和控制问题。我们将使学生熟悉应用数学和工程之间的界面的最新发展。我们建议教授一门非线性现象课程，使用上述研究中的例子作为背景动机和问题生成器。我们的研究小组的学生将接触到一个真正跨学科的主题，从动力系统，控制理论，数学，微观物理和工程。