NSSEFF- Mathematical Modeling in Random Media: From Homogenization to Stochasticity

The overarching goal of the grant was to understand the propagation of uncertainty from the a prior unknown coefficients in partial differential equations to the solutions of such equations. The underlying equations model phenomena as varied as the propagation of waves in heterogeneous media, to the heat distribution or the electric current in a non-uniform medium. The unifying aspect of these problems is that the physical parameters in the system cannot be perfectly known because of the fluctuations and small-scale heterogeneities. Such phenomena are ubiquitous in nature and the basic theoretical and practical problem is quantifying the effect of uncertainty at the microscopic scales on the macroscopic phenomena.