This research involves three components: 1) macroscopic transport properties in heterogeneous media and in complex fluid patterns; specifically, modelling anomalous diffusion in random velocity fields with long-range correlations, such as the Darcy velocities as observed in large-scale groundwater reservoirs or in space/time- dependent velocities which arise in turbulent diffusion, ii) determination of fluid permeability of porous media from indirect measurements and the cross-correlation of various fields (electrical, magnetic, acoustic) in a porous solid, iii) microscopic modelling of composite materials exhibiting strong coupling among physical properties, such as piezoelectric materials. Mathematical analysis and computer modelling/simulation will be used to study models of physical or engineering interest involving heterogeneous materials. An important component of this activity is training and working with graduate students and post-doctoral fellows as part of the general educational program of the Courant Institute of Mathematical Sciences at New York University.
