Singularities and Transitions in Fluids

非技术摘要流体之所以引人入胜，是因为它们的复杂运动从看似简单的过程中浮现出来。事实上，在所有科学中，一些最令人惊叹的图像是液体在流过障碍时留下的尾迹，或者在它们落下时分裂。流体在许多技术中是必不可少的，在科学背景下也是至关重要的，从大规模的天文物体到在细胞内观察到的微观尺度。然而，流体是出了名的难以建模。这一提议的中心主题是研究流体中令人惊叹的拓扑转变。例如，当液滴碎成碎片时，就会发生这样的转变。有人提议用实验来研究液滴的破碎和液体被吸进吸管时产生的喷口。这些研究对于对这些过程的基本理解和生物医学应用具有重要意义。拟议的研究为将年轻学生带入实验室提供了一个特殊的起点。因为这些现象是如此具有美学吸引力，而这项研究的结果将被用于以博物馆展品的形式非常有效地向公众宣传。技术摘要流体在许多技术中是必不可少的，在从大型天文物体到细胞内观察到的微尺度的科学背景下也是至关重要的。然而，流体是由非线性方程支配的，这是应用数学中的难题。这一提议的中心主题是研究流体中发生的拓扑转变。例如，当一滴液体分裂成几块时，就会发生这样的转变。提出了研究液滴破碎和选择性退出喷口的实验方法。这些研究对于基本理解如何处理奇点很重要，可以推广到在许多不同的科学领域中看到的类似行为。提出了涂层生物材料的一种特定的生物医学应用。由于许多拟议的研究涉及宏观现象，它为将年轻的、缺乏经验的学生带入实验室提供了一个特殊的起点。由于这些现象是如此容易理解和具有美学吸引力，这项研究为公众提供了极好的拓展。博士后助理、研究生和本科生将通过参与拟议的项目进行培训。

Non-Technical AbstractFluids are fascinating as their complex motion emerges out of seemingly simple processes. Indeed, some of the most stunning images in all of science are of liquids as they leave wakes upon flowing past barriers or break apart as they fall. Fluids are essential in many technologies and are crucial in scientific contexts ranging from the large scales of astronomical objects to the microscopic scales observed inside cells. However, fluids are notoriously difficult to model. The central theme of this proposal is to study the aesthetically stunning topological transitions in fluids. Such transitions occur, for example, when a liquid drop breaks into pieces. Experiments are proposed to study drop breakup and the spouts that occur as a fluid is sucked up into a straw. These studies are important for the basic understanding of these processes and, for biomedical application. The proposed studies provide an exceptional starting place for bringing young students into the laboratory. Because the phenomena are so aesthetically appealing, and the results of this research will be used in very effective outreach to the public in the form of museum exhibits. Technical Abstract Fluids are essential in many technologies and are crucial in scientific contexts ranging from the large scales of astronomical objects to the microscales observed inside cells. However, fluids are governed by non-linear equations that present difficult problems in applied mathematics. The central theme of this proposal is to study topological transitions that occur in fluids. Such transitions occur, for example, when a drop of fluid breaks into several pieces. Experiments are proposed to study drop breakup and selective withdrawal spouts. These studies are important for the basic understanding of how to handle singularities and can be generalized to similar behavior seen in many disparate areas of science. A specific biomedical application is proposed for coating biological material. Because much of the proposed research deals with macroscopic phenomena, it provides an exceptional starting place for bringing young, inexperienced students into the laboratory. Because the phenomena are so accessible and aesthetically appealing, this research affords excellent outreach to the public. Postdoctoral associates, graduate, and undergraduate students will be trained by working on the proposed projects.