Reduced Models for Transport of Particles in Heterogeneous Media

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The overall objective of this project is to study physical systems in heterogeneous environments. Heterogeneous environments are ubiquitous. Some examples are ocean flows, atmospheric turbulence, oil-bearing sands, and biological tissues. Understanding overall properties of such media is relevant to aspects of virtually every branch of science and engineering; especially materials science, chemical engineering, geophysics, medical imaging and fluid dynamics. One of the projects of this research concerns changes in salinity or chlorofluorocarbon on the surface of the ocean. Oceanic vortices may dramatically change mixing rates of various chemical compounds. The aim of this project is to estimate these rates in simpler mathematical models to illuminate the mechanisms present in the full problem. Another project of this research concerns light propagation through the atmosphere. The main source of distortion in these devices comes from atmospheric turbulence. The aim of this project is to understand the mechanism of this distortion.This work carries out mathematical studies of particle propagation in cluttered environments and of convection-diffusion processes in fluids. The first project concentrates on the effect of long-range correlations. This is a novel direction in the theory of propagation in random media, and approximate models of propagation in slowly decorrelating media are not yet developed. The goal is to explain how long-range correlations lead to time-scale separation of various phenomena. The second project concentrates on the interaction of the standard and the fractional diffusion with incompressible flows. The intellectual challenge of the proposed work is to understand this interaction for incompressible flows with large amplitude. This is particularly relevant to understanding diffusion in turbulent flows.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.