Some Problems In Stochastic Flows And Random Media

该奖项支持的研究是在随机流动和随机介质领域。随机流动中的问题是由紊流问题引起的。湍流看似随机的行为使它们成为随机模型的自然候选者。PI将研究一类各向异性Sobolev流的中心极限定理，并将考虑确定在各向异性随机流下移动的曲线的指数增长率的问题。这将使我们对被湍流移动的污染物体的边界长度的增长有一些了解。PI对随机介质的研究涉及由统计物理现象引发的问题，如聚合物的局部化、间歇性和行为。PI将让他的两个研究生参与本提案中的一些项目。该项目还将与加州大学欧文分校的一名博士后进行联合研究。该提案的部分结果将被纳入PI目前正在撰写的关于非平稳随机介质主题的书中。

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.