Thin Layer Flow: Experiments, Modeling, and Analysis

剪板机DMS-0604047 最近的研究结果表明，薄液膜的科学和数学与颗粒状物质薄层的流动之间有着密切的联系。 这些研究者通过建模、分析、数值模拟和实验来探索这些联系。 他们研究avalanchemodels的偏微分方程的多维非线性系统，以及与实验的联系，以获得对颗粒和雪崩力学基本方面的新见解。 在相关的研究中，研究人员制定和分析系统的偏微分方程薄液膜驱动表面活性剂或温度控制。 这些方程给出了数学理论，解决了在实验和模拟中观察到的新的波浪结构。 研究人员探索了薄液膜的科学和数学与颗粒物质薄层流动之间的密切联系。 薄膜在表面活性剂替代疗法等医学应用中以及在工业和制造业中出现的微观涂层流动中非常重要。 颗粒物质的长度范围很大，从药品和农业谷物到滑坡中的岩石和砾石。 该项目的结果进一步加深了对具有专业科学兴趣和广泛社会意义的问题的理解，例如识别人类肺部表面活性剂运输中的波传播和模式的机制，以及雪崩中岩石和其他颗粒的大小分离。 该项目在一个多学科研究计划中，将数学和物理研究生和本科生在数学、模拟和实验物理方面的培训结合起来。代表性不足群体的参与是在最近成功的基础上进行的。 该项目的成果通过期刊出版物、国际会议特别会议和讲座、大众科学出版物上的文章以及项目网页传播。

ShearerDMS-0604047 Recent results suggest that there are strong connectionsbetween the science and mathematics of thin liquid films and theflow of thin layers of granular materials. The investigatorsexplores these connections through modeling, analysis, numericalsimulation and experiments. They study multidimensionalnonlinear systems of partial differential equations of avalanchemodels, and the connection to experiments, to gain new insightsinto fundamental aspects of granular and avalanche mechanics. Inrelated studies, the investigators formulate and analyze systemsof partial differential equations for thin liquid films driven bysurfactants or controlled by temperature. These equations giverise to mathematical theory addressing new wave structuresobserved in experiments and simulations. The investigators explore strong connections between thescience and mathematics of thin liquid films and the flow of thinlayers of granular materials. Thin films are important inmedical applications such as surfactant replacement therapy, andin microscopic coating flows that arise in industry andmanufacturing. Granular materials occur over a large range oflength scales, from pharmaceuticals and agricultural grains torocks and gravel in landslides. The results of this projectfurther the understanding of issues of both specializedscientific interest and of broad significance to society, such asthe identification of mechanisms of wave propagation and patternsin surfactant transport in human lungs, and the separation bysize of rocks and other particles in avalanches. This projectincorporates training of mathematics and physics graduate andundergraduate students in mathematics, simulation, andexperimental physics in a multidisciplinary research program. The participation of under-represented groups builds on recentsuccesses. Results from this project are disseminated throughjournal publications, special sessions and lectures atinternational conferences, articles in popular sciencepublications, and through a project web page.