CAREER: Spatiotemporal Chaos in Fluid Convection: New Physical Insights from Numerics

尽管非平衡系统在许多工程领域都很重要，但由于时空模式影响能量和物质传输的非线性方式，它们仍然难以分析、控制、设计或预测，而能量和物质的传输反过来又改变了时空模式。例子包括天气和气候，燃烧和化学反应的效率，海洋中生物有机体的对流，心脏动力学，熔体晶体生长和流体湍流。一个特别的挑战是理解时空混沌，这是一种通常观察到的非平衡系统的行为，其中系统的性质在时间和空间上是非周期性地演变。通过对瑞利-贝纳德对流（一种从下面均匀加热的薄薄的水平层流体）的详细数值研究，将获得对空间扩展非平衡系统的时空混沌的新的基本见解。PI开发了并行数值方法，为精确的实验条件提供了精确的模拟。本研究在这些成功的基础上探索大纵横比对流域中的时空混沌，并做出可以通过实验验证的预测。这些预测只有在最近计算能力的提高和数值算法的改进下才有可能实现，包括PI的持续研究进展。该研究将探索时空混沌的起源和基本组成部分，以量化个体混沌自由度的数量、大小和动态。数值模拟也将对混沌流场中的输运提供新的认识。例如，利用复杂流体速度场提高预混气体燃烧效率的探索将直接影响能源的生产和消耗；对悬浮在海洋中的生物有机体活动所驱动的流体对流的理解，将改善气候模型。教育计划与这项研究紧密结合，为各级学生提供广泛的机会，参与最先进的工程研究。PI的大学前拓展计划的重点是让大批学生（特别强调代表性不足的群体）了解当今工程面临的挑战，目标是吸引、留住并最终毕业一批更多样化的世界级工程师。PI正在与弗吉尼亚理工大学工程多样性增强中心密切合作，开发和实施每年将惠及400多名大学预科学生的项目。PI将开发，组织，并领导问题解决会议，由动手互动数值实验指导。数值实验将与这项研究直接相关，并将激发年轻学生的兴趣，例如天气预报的难度和流行短语“蝴蝶效应”的科学含义。交互程序将用Java编写，并在为此目的而建立的计算科学和工程网站上公开提供。PI将在每个学年和每个夏季指导本科生进行与本研究相关的项目。学生将从多元文化学术机会计划（MAOP）和NSF资助的暑期本科生研究计划（SURP）中选择。将开设一门新的多学科研究生课程，名为“时空混沌”。本课程的一个主要主题将是本研究的计算所提供的理论与实验之间的定量联系。教育计划将通过与弗吉尼亚理工大学工程教育部的密切合作进行仔细评估和改进。

CBET-0747727PaulDespite their importance in many areas of engineering, nonequilibrium systems remain difficult to analyze, to control, to design, or to predict because of the nonlinear way that spatiotemporal patterns affect the transport of energy and matter, which in turn modifies the spatiotemporal patterns. Examples include the weather and climate, the efficiency of combustion and chemical reactions, the convection of biological organisms in the oceans, heart dynamics, crystal growth from a melt, and fluid turbulence. A particular challenge is to understand spatiotemporal chaos, a commonly observed behavior of nonequilibrium systems where properties of the system evolve aperiodically in time and space. New fundamental insights into the spatiotemporal chaos of spatially-extended nonequilibrium systems will be obtained through a detailed numerical investigation of Rayleigh-Benard convection (a thin horizontal layer of fluid heated uniformly from below). The PI has developed parallel numerical methods providing accurate simulations for the precise conditions of experiment. This research builds upon these successes to explore spatiotemporal chaos in large-aspect-ratio convective domains to make predictions that can be verified by experiment. These predictions are only possible by the recent convergence of increased computing power and improved numerical algorithms, including the continuing research progress of the PI. The research will probe the origins and basic building blocks of spatiotemporal chaos to quantify the number, size, and dynamics of the individual chaotic degrees of freedom. Numerical simulations will also shed new insight upon transport in a chaotic flow field. As examples, an exploration of the enhancement of combustion efficiency in premixed gases by complex fluid velocity fields will directly affect energy production and consumption; and an understanding of the fluid convection driven by the activity of biological organisms suspended in oceans will improve models of the climate. The education program is tightly coupled with this research to provide extensive opportunities for students at all levels to participate in state-of-the-art engineering research. The PI's pre-college outreach program is focused upon exposing a large group of students, with special emphasis on under-represented groups, to challenges facing engineering today with the goal of attracting, retaining, and eventually graduating a more diverse group of world-class engineers. The PI is working closely with the Virginia Tech Center for the Enhancement of Engineering Diversity to develop and implement programs that will reach over 400 pre-college students each year. The PI will develop, organize, and lead problem solving sessions that are guided by hands-on interactive numerical experiments. The numerical experiments will be directly related to this research and will spark the interests of young students with such subjects as the difficulty of weather prediction and the scientific meaning of the popular phrase "the Butterfly Effect." The interactive programs will be written in Java and publicly available on a computational science and engineering web site established for this purpose. The PI will mentor undergraduate students each academic year and each summer on projects related to this research. Students will be selected from the Multicultural Academic Opportunities Program (MAOP) and a NSF funded Summer Undergraduate Research Program (SURP). A new multidisciplinary graduate course will be developed entitled "Spatiotemporal Chaos." A major theme of the course will be the quantitative link between theory and experiment provided by the computations of this research. The education program will be carefully assessed and improved through a close collaboration with the Virginia Tech Engineering Education Department.