Thurston-Nielsen Theory and Fluid Mixing

瑟斯顿-尼尔森理论和流体混合

• 批准号: 9870323
• 负责人: Philip Boyland
• 金额: $ 7.8万
• 依托单位: University of Florida
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1998
• 资助国家: 美国
• 起止时间: 1998-07-15 至 2002-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9870323&HistoricalAwards=false
• 关键词: Thurston; Nielsen; Theory; Fluid; Mixing

DMS-9870323Thurston-Nielsen theory and Fluid MixingPhilip BoylandThe Thurston-Nielsen theory provides a powerful collection of tools toanalyze and understand two-dimensional dynamical systems. The theoryhas potential for significant advances in the study of two-dimensionalsystems of physical interest. Among the most interesting and importantcome from fluid mechanics. Dr. Boyland will use Thurston-Nielsentheory in conjunction with other dynamical tools to obtain a deeperunderstanding of two-dimensional fluid mixing. Various mathematicalextensions of the Thurston-Nielsen theory will be obtained. Theseextensions would enhance the applicability of the theory as well asbeing of intrinsic mathematical interest. In addition, numerical andlaboratory experiments are proposed with the goal of designingeffective mixers and understanding many vortices as a model fortwo-dimensional turbulence.The mixing of different species of materials is extremely common innatural systems and industrial applications. The main scientificquestion is to understand how the mixing takes place, while inindustrial applications the focus is usually on the development ofschemes for effective mixing. In many applications high viscosity,sensitivity of materials, the need to avoid foaming, and otherconstraints make turbulence mixing infeasible and undesirable. Thus inmost instances the design of useful mixing procedures requires closeattention to efficiency. The added mathematical understanding madepossible by this project should help in this design process, providingnovel ideas for efficient mixing procedures and helping to eliminateinefficient ones prior to expensive experimentation. In addition, thisproject will make a powerful body of pure mathematics more accessiblefor application to problems of physical and industrial importance.

DMS-9870323 Thurston-Nielsen理论和流体混合Philip Boyland Thurston-Nielsen理论提供了分析和理解二维动力系统的强大工具集。 这一理论在二维物理系统的研究中具有潜在的重大进展。 其中最有趣和最重要的来自流体力学。 Boyland博士将使用Thurston-Nielsen理论与其他动力学工具相结合，以深入了解二维流体混合。 将得到Thurston-Nielsen理论的各种几何扩展。 这些扩展将增强理论的适用性以及内在的数学兴趣。 此外，为了设计有效的混合器和理解作为二维湍流模型的许多涡旋，提出了数值和实验室实验。不同种类材料的混合在自然系统和工业应用中非常常见。 主要的科学问题是了解混合是如何发生的，而在工业应用中，重点通常是开发有效混合的方案。 在许多应用中，高粘度、材料的敏感性、避免起泡的需要以及其他限制使得湍流混合不可行且不受欢迎。 因此，在大多数情况下，设计有用的混合程序需要密切关注效率。 这个项目所增加的数学理解应该有助于这个设计过程，为有效的混合程序提供新的想法，并有助于在昂贵的实验之前消除低效的混合程序。此外，这个项目将使一个强大的纯数学机构更容易应用于物理和工业重要性的问题。