Stochastic Transport in Heterogenous Flows and Media

将进行理论研究，以便更好地理解在具有宏观相关无序的异质介质中控制随机输运过程的基本物理定律。对于具有“块”无序的复合材料，传统的宏观输运方程通常不适用，并且将尝试制定适当的组成定律，允许在此类系统中对输运进行宏观描述。然后将研究布朗粒子在随机分层流场中的超扩散运动。该系统的稳态和首次通过特性似乎受到异常波动的控制，导致系统中存在多重基本时间尺度。理论和数值研究将确定适当的宏观描述。本文还将探讨布朗粒子在典型随机流场驱动下的异常输运性质。最后，将研究源-汇流的第一通道特征，其中空间变化的对流和分子扩散之间的相互作用预计会产生不寻常的第一通道特性。这些研究将扩展到压裂介质，其中裂缝中的快速输送与慢速输送模式以一种微妙的方式竞争。该项目与能源部基础能源科学部的一个相同项目协调，该部门支持纽约城市大学的Joel Koplik教授，他正在与Redner教授合作。将对非均匀介质和流动中的随机输运进行分析和数值研究。特别是，在各种类型的随机无序影响下，将研究被动粒子在多孔介质中的运动。例子包括层状地质介质中的流体流动以及岩石和其他非均质物质中的裂缝扩展。这项研究解决了统计物理学中的基本问题，同时也有许多实际应用。这项研究得到了能源部同样的资助，能源部支持纽约城市大学的Koplik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.