Mathematical Sciences: Mathematical Problems in Statistical Mechanics and Condensed Matter Theory

这项研究涉及到使用数学模型和分析来研究材料研究中出现的问题。有三个具体项目有待研究。第一种是一相大液滴浸入另一相中的动力学行为。第二个项目是对最近一种气凝胶模型的研究。第三个项目是首次通过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。虽然这些问题出现在材料研究中，但需要发展新的数学来研究这些问题。特别是，泛函分析和概率分析的工具将是有用的。***

Chayes 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. ***