Singularities and Transitions in Fluids

流体中的奇点和转变

• 批准号: 0652269
• 负责人: Sidney Nagel
• 金额: $ 52万
• 依托单位: University of Chicago
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2007
• 资助国家: 美国
• 起止时间: 2007-04-15 至 2011-03-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0652269&HistoricalAwards=false
• 关键词: Singularities; Transitions; Fluids

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.

非技术摘要流体是迷人的，因为它们的复杂运动出现在看似简单的过程中。 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物时留下的痕迹，或者在它们下落时破裂。流体在许多技术中都是必不可少的，在从大尺度天文物体到细胞内观察到的微观尺度的科学背景下都是至关重要的。 然而，流体是出了名的难以建模。 这个提议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，当液滴破裂成碎片时，会发生这种转变。 有人建议用实验来研究液滴破裂和液体被吸管吸入时的喷出现象。 这些研究对于基本了解这些过程和生物医学应用都很重要。 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。 因为这些现象在美学上是如此吸引人，这项研究的结果将以博物馆展览的形式被用于非常有效的公众宣传。 技术摘要流体在许多技术中是必不可少的，并且在从大尺度天文物体到细胞内观察到的微观尺度的科学背景中至关重要。 然而，流体是由非线性方程控制的，这在应用数学中是一个难题。 这个提议的中心主题是研究流体中发生的拓扑转变。 例如，当一滴流体破裂成几块时，就会发生这种转变。 提出了研究液滴破碎和选择性退出喷口的实验方法。这些研究对于如何处理奇点的基本理解非常重要，并且可以推广到许多不同科学领域中看到的类似行为。 提出了一种特定的生物医学应用，用于涂覆生物材料。由于许多拟议的研究涉及宏观现象，它提供了一个特殊的起点，使年轻的，没有经验的学生进入实验室。 因为这些现象是如此容易接近和美学吸引力，这项研究提供了很好的推广到公众。 博士后助理，研究生和本科生将通过在拟议的项目工作进行培训。