Professor Vakilian's project involves a number of problems in statistical mechanics. One set deals with the specific heat for layered aperiodic Ising models. The solution of this problem could lead to the discovery of a new phase of matter intermediate between random and quasicrystalline forms. Additional problems deal with trace maps of aperiodic dynamical systems and one-dimensional aperiodic Schrodinger operators. The general area of research of Professor Vakilian is mathematical physics. In this research project, the principal investigator will concentrate on the mathematical aspects of models of matter which are not regular but not completely random. This type of matter is typified by the quasicrystalline forms recently found in nature.
