Thurston-Nielsen Theory and Fluid Mixing

瑟斯顿-尼尔森理论和流体混合菲利普·博伊兰瑟斯顿-尼尔森理论为分析和理解二维动力系统提供了一套强大的工具。这一理论有可能在物理意义上的二维系统的研究中取得重大进展。其中最有趣和最重要的是来自流体力学。博伊兰博士将使用瑟斯顿-尼尔森理论和其他动力学工具，对二维流体混合有更深入的了解。我们将得到瑟斯顿-尼尔森理论的各种数学扩展。这些扩展将增强该理论的适用性以及内在的数学兴趣。此外，还提出了数值和实验室实验，目的是设计有效的混合器，并将许多旋涡作为二维湍流的模型。不同种类的材料的混合在自然系统和工业应用中是非常常见的。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，材料的高粘度、敏感性、避免发泡的需要以及其他限制因素使得湍流混合变得不可行和不可取。因此，在大多数情况下，设计有用的混合程序需要密切注意效率。这个项目带来的额外的数学理解应该有助于这个设计过程，为有效的混合过程提供新的想法，并帮助在昂贵的实验之前消除效率低下的想法。此外，这个项目将使一个强大的纯数学体系更容易应用于具有物理和工业重要性的问题。

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.