Collaborative Research: Capillary Interfaces

合作研究：毛细管接口

• 批准号: 0103937
• 负责人: Paul Concus
• 金额: $ 7.8万
• 依托单位: University of California-Berkeley
• 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=0103937&HistoricalAwards=false
• 关键词: Collaborative; Research; Capillary; Interfaces

NSF Award Abstract - DMS-0103937Mathematical Sciences: Collaborative Research: Capillary InterfacesDMS-0103937ConcusThis 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奖摘要- DMS-0103937数学科学：合作研究：毛细管界面DMS-0103937震荡本研究讨论毛细管理论数学方程的解的行为。 方程将在其充分的非线性的一般性，使用程序从物理问题的内在结构。 这些程序已被证明是互动的一个自然的方式与新开发的方法的几何测量理论，这是最初开发的特殊情况下，在其他情况下的极小曲面。 在许多有趣的案例中，溶液的惊人和不寻常的行为都是以这种方式发现的。 我们的研究将继续沿着已经发现的方向进行，这些方向已经发现了对边界数据的不连续依赖性、对称性破缺、物理条件下的不存在性、存在解的条件下的唯一性失效以及比较关系的不连续逆转。毛细管界面在许多实际情况下发挥着重要作用，特别是在重力减小的情况下或在物理长度尺度非常小的配置中。 毛细作用是描述物质在表面界面处接触而不混合的情况的基本概念。 对毛细作用方程解的数学性质的精确理解将为解决诸如如何设计轨道航天器上的燃料箱以便燃料将被容易地定位，预测石油或水在岩石的地下孔隙空间中的位置，或者确定当微电子元件浸入涂层浴中时微电子元件的表面将被部分覆盖的方式。 正在考虑的工作是特别相关的预测在这些和其他应用中的液体的意外行为。