Some Problems In Stochastic Flows And Random Media

该奖项支持的研究领域是随机流和随机媒体。随机流中的问题是由湍流问题引起的。湍流看似随机的行为使它们自然成为随机模型的候选对象。PI将研究一类各向同性Sobolev流的中心极限定理，并将考虑确定在各向同性随机流下移动的曲线的指数增长率的问题。这将对湍流运动的污染物的边界长度的增长有一定的洞察力。PI在随机介质中的研究涉及统计物理中的现象，如聚合物的局域性、间歇性和行为。PI将让他的两名研究生参与这项提案中的一些项目。国际和平研究所还将与加州大学欧文分校的一名博士后研究员共同开展工作。该提案的部分结果将被纳入国际和平研究所目前正在撰写的一本关于非静态随机介质的书中。

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.