Mathematical Sciences: Mathematics and Physics of the Condensed State

这项研究涉及使用数学模型和分析来研究材料研究中出现的问题。 将研究三个具体项目。 第一个问题涉及一个相的大液滴浸入第二个相的动力学行为。 第二个项目是研究最近的气凝胶模型。 第三个项目是对首段渗流的一些问题的研究。 这项研究涉及使用数学模型和分析来研究材料研究中出现的问题。 当材料研究中出现问题时，需要开发新的数学来研究这些问题。 特别是，从功能分析和概率的工具将是有用的。

This research involves the use of mathematical models and analysis to study problems arising in materials research. Three specific projects are to be studied. The first concerns the dynamical behavior of large droplets of one phase immersed in a second. The second project is a study of a recent model of aerogels. And the third project is a study of some problems of first passage percolation. This research involves the use of mathematical models and analysis to study problems arising in materials research. While the problems arise in materials research, new mathematics will need to be developed to study these problems. In particular, tools from functional analysis and probability will be useful.