Connecting Dynamical Structure and Statistical Analysis in Quasi-2D Fluid Flow

连接准二维流体流动中的动力结构和统计分析

• 批准号: 0906245
• 负责人: Nicholas Ouellette
• 金额: $ 32万
• 依托单位: Yale University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2009
• 资助国家: 美国
• 起止时间: 2009-08-01 至 2012-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0906245&HistoricalAwards=false
• 关键词: Connecting; Dynamical; Structure; Statistical; Analysis

****NON-TECHNICAL ABSTRACT****This award is funded under the American Recovery and Reinvestment Act of 2009 (Public Law 111-5). Complex systems that are far from equilibrium are ubiquitous in nature; common examples include fluid flows, weather systems, and many biological systems. Developing accurate and efficient models for these types of systems is very important, but has proved to be tremendously challenging. One of the central problems in modeling complex systems is how to identify the salient features that produce the majority of the observed phenomena. Statistical tools, which have proven very valuable in treating equilibrium systems, have often been applied to complex systems as a way to capture the average properties, with varying degrees of success. Models have also been proposed that rest on the tendency of nonequilibrium systems to self-organize spontaneously into dramatic structures, such as long-lived vortices in fluid flows. This project seeks to bring these two approaches together by conducting laboratory experiments in a two-dimensional fluid flow, a flexible model system that both forms coherent structures and has well characterized statistics. This project will provide concrete tools for determining accurate simplifications of complex systems, and will lay the groundwork for the next generation of models that combine structure and statistics. The project will support the training of a Ph.D. student in both nonlinear physics and in modern, high-precision fluid measurement techniques. Undergraduates will also be involved in the research, both giving them research experience in an interdisciplinary field and helping the Ph.D. student acquire mentoring skills.****TECHNICAL ABSTRACT****This award is funded under the American Recovery and Reinvestment Act of 2009 (Public Law 111-5). This project seeks to find a link between two common descriptions of complex, nonlinear systems: one based on specification of the statistical properties, and one based on self-organized dynamical structures. Both approaches have been studied previously, but little progress has been made on joining the two. This project will address the connection between statistics and structures using a model experimental system: a quasi-two-dimensional fluid flow (generated by electromagnetic forcing of stably stratified thin layers) that can be operated in the laminar, spatiotemporally chaotic, or turbulent regimes. Several types of self-organized structures will be studied, including dynamic topological singularities, spatially extended structure such as vortices, and clusters of fluid elements that move and deform with the flow. The system will be characterized by powerful particle-tracking techniques, which will be released to other researchers as a part of this project. Additionally, a database of the raw particle trajectories will be made available. The award will support a Ph.D. student, who will carry out the experiments and thereby be trained in the high- precision, flexible particle-tracking techniques employed in the research. Undergraduates will also be involved in the project, giving them strong research experience in an interdisciplinary field.

****非技术摘要****该奖项是根据2009年美国复苏和再投资法案（公法111-5）资助的。远离平衡的复杂系统在自然界中无处不在；常见的例子包括流体流动、天气系统和许多生物系统。为这些类型的系统开发准确有效的模型非常重要，但事实证明这是非常具有挑战性的。复杂系统建模的核心问题之一是如何识别产生大多数观测现象的显著特征。统计工具在处理平衡系统方面已经被证明是非常有价值的，它经常被应用于复杂系统，作为捕获平均特性的一种方式，并取得了不同程度的成功。也有人提出了一些模型，这些模型依赖于非平衡系统自发地自组织成戏剧性结构的趋势，例如流体流动中的长寿命漩涡。该项目旨在通过在二维流体流动中进行实验室实验，将这两种方法结合起来，这是一种既形成连贯结构又具有良好特征统计的灵活模型系统。该项目将为确定复杂系统的精确简化提供具体的工具，并将为结合结构和统计的下一代模型奠定基础。该项目将支持培养一名非线性物理和现代高精度流体测量技术的博士生。本科生也将参与研究，既给他们跨学科领域的研究经验，又帮助博士生获得指导技能。****技术摘要****该奖项是根据2009年美国复苏和再投资法案（公法111-5）资助的。该项目旨在找到复杂非线性系统的两种常见描述之间的联系：一种基于统计特性的规范，另一种基于自组织的动态结构。这两种方法以前都有过研究，但在将两者结合起来方面进展甚微。该项目将使用一个模型实验系统来解决统计学和结构之间的联系：一个准二维流体流动（由稳定分层薄层的电磁力产生），可以在层流、时空混沌或湍流状态下运行。将研究几种类型的自组织结构，包括动态拓扑奇点，空间扩展结构，如漩涡，以及随流动移动和变形的流体元素簇。该系统将以强大的粒子跟踪技术为特征，该技术将作为该项目的一部分发布给其他研究人员。此外，将提供原始粒子轨迹的数据库。该奖项将支持一名博士生，他将进行实验，从而在研究中使用的高精度，灵活的粒子跟踪技术方面进行培训。本科生也将参与该项目，为他们提供跨学科领域的丰富研究经验。