Collaborative Research: Capillary Interfaces

合作研究：毛细管接口

• 批准号: 0103954
• 负责人: Robert Finn
• 金额: $ 11.9万
• 依托单位: Stanford University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2001
• 资助国家: 美国
• 起止时间: 2001-08-15 至 2005-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0103954&HistoricalAwards=false
• 关键词: Collaborative; Research; Capillary; Interfaces

NSF Award Abstract - DMS-0103954Mathematical Sciences: Collaborative Research: Capillary InterfacesDMS-0103954FinnThis research addresses behavior of solutions to the mathematical equations of capillarity theory. The equations will be studied in their full nonlinear generality, using procedures deriving from the intrinsic structure of the physical problems. These procedures have turned out to interact in a natural way with newly developed methods of geometric measure theory, which were developed initially for the special case of minimal surfaces in other contexts. In a number of cases of interest, striking and unusual behavior of solutions was uncovered in this way. Our investigations will continue in directions that have already led to discoveries of discontinuous dependence on boundary data, symmetry breaking, failure of existence under physical conditions, failure of uniqueness under conditions for which solutions exist, and discontinuous reversal of comparison relations.Capillary interfaces play an important role in many practical situations, notably in reduced gravity or in configurations for which physical length scales are very small. Capillarity is an essential concept for describing situations in which substances are in contact at surface interfaces and do not mix. A precise understanding of the mathematical properties of solutions of the capillarity equations will provide valuable insight for resolving such matters as how to design fuel tanks on an orbiting spacecraft so that the fuel will be accessibly located, predicting where oil or water resides in underground pore spaces of rocks, or determining the manner in which the faces of microelectronic components will become partially covered when they are dipped in a coating bath. The work under consideration is of particular relevance for predicting unexpected behavior of liquids in these and in other applications.

NSF 奖项摘要 - DMS-0103954 数学科学：协作研究：毛细管界面 DMS-0103954Finn 这项研究解决了毛细管理论数学方程的解的行为。 将使用从物理问题的内在结构导出的程序，以完全非线性的一般性来研究这些方程。 事实证明，这些过程与新开发的几何测量理论方法以自然的方式相互作用，这些方法最初是针对其他情况下最小曲面的特殊情况而开发的。 在许多有趣的案例中，解决方案的惊人且不寻常的行为都是通过这种方式发现的。 我们的研究将继续朝着已经导致发现边界数据的不连续依赖性、对称性破缺、物理条件下存在性失败、解存在条件下唯一性失败以及比较关系的不连续反转的方向继续。毛细管界面起着重要的作用。在许多实际情况中发挥着重要作用，特别是在重力减小或物理长度尺度非常小的配置中。 毛细现象是描述物质在表面界面接触且不混合的情况的基本概念。 精确理解毛细管方程解的数学特性将为解决诸如如何设计轨道航天器上的燃料箱以便可轻松定位燃料、预测地下孔隙空间中油或水的位置等问题提供宝贵的见解。岩石，或确定微电子元件的表面在浸入涂层浴中时被部分覆盖的方式。 正在考虑的工作对于预测这些和其他应用中液体的意外行为特别相关。