For this Presidential Young Investigator Award theoretical research will be conducted on quasicrystal growth and on the evolution of foams in two and three dimensions. A quasicrystal growth model will be developed within the context of a simple tiling model based on the six-vertex (ice) model of statistical mechanics and its three dimensional generalization. The effects of dynamics on the evolution of foams will be studied by using a simple one dimensional model. These dynamical effects will then be incorporated into more realistic models for foam evolution in two and three dimensions.
