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.
