Stochastic Transport in Heterogenous Flows and Media

为了更好地了解和掌握这些知识，将进行理论研究 理解支配随机性的基本物理定律 宏观非均匀介质中的输运过程 相关疾病。 对于具有“嵌段”无序的复合材料， 传统的宏观输运方程通常不 适用，并将尝试制定适当的 允许宏观描述运输的合成定律 在这样的系统中。 布朗粒子的超扩散运动 在随机分层流场中的流动将被研究。 该系统的稳态和首次通过特性 似乎受到异常波动的控制，导致 系统中基本时间尺度的多样性。 理论和 数值研究将确定适当的宏观 说明. 布朗运动不寻常的输运性质 由原型随机流场驱动的颗粒将 也可以探索。 最后，研究了 源汇流将被研究，其中相互作用之间 空间变化对流和分子扩散， 预计会产生不寻常的首次通过特性。 研究 将扩展到裂缝介质，其中快速运输 断裂以一种微妙的方式与缓慢的传输模式竞争。 该项目与该部的一个相同项目相协调 能源，基础能源科学，支持教授乔尔 纽约城市大学的科普利克正在与 雷德纳教授 %%% 分析和数值研究将进行随机 在异质介质和流中的传输。 特别是 本文将研究被动颗粒在多孔介质中的运动 在各种随机无序的影响下。 示例 包括分层地质介质中的流体流动， 岩石和其他非均质材料中断裂的扩展。 这项研究涉及统计物理学的基本问题 并且同时具有许多真实的应用。 这项研究是 与能源部的一笔相同的赠款相协调 它支持纽约城市大学的科普利克教授。

Theoretical research will be conducted in order to gain a better understanding of fundamental physical laws that govern stochastic transport processes in heterogeneous media with macroscopically correlated disorder. For composites with "block" disorder, conventional macroscopic transport equations generally do not apply, and an attempt will be made to formulate the appropriate composition laws that permit a macroscopic description of transport in such systems. The superdiffusive motion of Brownian particles in a randomly stratified flow field will then be investigated. Steady-state and first-passage characteristics of this system appear to be controlled by exceptional fluctuations, leading to a multiplicity of basic time scales in the system. Theoretical and numerical studies will determine the appropriate macroscopic description. The unusual transport properties of Brownian particles which are driven by prototypical random flow fields will also be explored. Finally, the first-passage characteristics in source-sink flow will be studied, where the interplay between spatially varying convection and molecular diffusion are anticipated to yield unusual first-passage properties. The studies will be extended to fractured media, where fast transport in fracture competes in a subtle way with slow transport modes. This project is coordinated with an identical one at the Department of Energy, Basic Energy Sciences, which supports Professor Joel Koplik of the City University of New York who is collaborating with Professor Redner. %%% Analytical and numerical research will be conducted on random transport in heterogeneous media and flows. In particular, the movement of a passive particle in porous media will be studied under the influence of various types of random disorder. Examples include fluid flow in stratified geological media and the propagation of fracture in rocks and other heterogeneous materials. The research addresses fundamental issues in statistical physics and, at the same time, has many real applications. The research is coordinated with an identical grant at the Department of Energy which supports Professor Koplik at the City University of New York.