Some Problems In Stochastic Flows And Random Media

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The research supported by this award is in the areas of stochastic flows and random media. The problems in stochastic flows arise from the subject of turbulent fluid flow. The seemingly random behavior of turbulent flows makes them natural candidates for stochastic models. The PI will study central limit theorems for a class of istropic Sobolev flows, and will consider the problem of determining the exponential rate of growth of a curve moving under an istotropic stochastic flow. This will give some insight into the growth of the boundary length for a body of pollutants being moved by a turbulent flow. The PI's research in random media concerns problems motivated by phenomena in statistical physics such as localization, intermittency and behavior of polymers. The PI will involve his two graduate students in some of the projects in this proposal. The PI will also conduct joint work with a Postdoctoral Fellow at U.C. Irvine. A portion of the results from the proposal will be incorporated into a book the PI is currently writing on the subject of non-stationary random media.