Singularities and Transitions in Fluids

流体是迷人的，因为它们的复杂运动是从看似简单的过程中产生的。事实上，在所有科学中，一些最令人惊叹的图像是关于液体在流过屏障时留下尾迹或在落下时破裂的。流体在许多技术中都是必不可少的，在科学背景下，从天文物体的大尺度到细胞内观察的微观尺度，流体都是至关重要的。然而，流体是出了名的难以建模。本提案的中心主题是研究流体中美学上令人惊叹的拓扑转变。例如，当液滴破碎成碎片时，就会发生这种转变。提出了实验来研究液滴的破裂和液体被吸管吸入时发生的喷口。这些研究对这些过程的基本理解和生物医学应用都很重要。拟议的研究为年轻学生进入实验室提供了一个特殊的起点。因为这些现象在美学上非常吸引人，而这项研究的结果将以博物馆展览的形式非常有效地向公众推广。流体在许多技术中都是必不可少的，在科学背景下，从天文物体的大尺度到细胞内观察的微观尺度，流体都是至关重要的。然而，流体是由非线性方程控制的，这在应用数学中提出了难题。本提案的中心主题是研究发生在流体中的拓扑转换。例如，当一滴液体破碎成几块时，就会发生这种转变。提出了液滴破碎和选择性退出喷口的实验研究。这些研究对于如何处理奇点的基本理解很重要，并且可以推广到许多不同科学领域中看到的类似行为。提出了生物材料涂层的特定生物医学应用。由于许多拟议的研究涉及宏观现象，它为年轻的、没有经验的学生进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接近和美观，这项研究提供了良好的外联到公众。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.