The principal investigator is working on the derivation of a macroscopic equation for the stochastic Ising model. Studies of the problem at low temperatures where different phases coexist indicate that the droplets of different phases evolve according to some type of "motion by mean curvature" PDE. Related problems can be proposed for either this model or its appropriate variations such as simple exclusions with speed change or the Ginzburg-Landau model. Another problem of interest is the derivation of conservation laws for asymmetric simple exclusions with speed changes. Analyzing the asymptotic behavior of a tagged particle in this model is also of great interest. An important task in statistical mechanics is to derive the evolution of a fluid from its molecular structure. At the molecular level, a fluid consists of a large number of molecules moving according to physical laws. Microscopically, molecules collide incessantly and move somewhat erratically in a random like fashion. Due to conservation laws of mass, momentum and entropy, molecules manage to organize themselves in such a way as to form a flow pattern on a large scale. Various Caricature models of a fluid will be studied to derive their macroscopic evolution from their microscopic structure in a mathematically rigorous fashion.
