Stochastic Transport in Heterogenous Flows and Media

为了更好地理解宏观相关无序的非均匀介质中随机输运过程的基本物理规律，将进行理论研究。对于具有“嵌段”无序的复合材料，传统的宏观输运方程一般不适用，人们将尝试制定适当的组成定律，以允许宏观描述此类体系中的输运。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异常波动的控制，导致系统具有多种基本时间尺度。理论和数值研究将确定适当的宏观描述。我们还将探讨布朗粒子在典型随机流场驱动下的异常输运特性。最后，我们将研究源汇流动中的首次通过特性，其中空间变化对流和分子扩散之间的相互作用有望产生不寻常的首次通过特性。这些研究将扩展到裂隙介质，在裂隙介质中，快速输送与缓慢输送模式以一种微妙的方式竞争。这个项目与基础能源科学系的一个相同的项目协调，后者支持纽约城市大学的乔尔·科普利克教授，他正在与雷德纳教授合作。将对非均匀介质和流动中的随机输运进行解析和数值研究。特别是，在各种随机无序的影响下，被动粒子在多孔介质中的运动将被研究。例如，层状地质介质中的流体流动以及岩石和其他非均质材料中裂缝的扩展。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。这项研究是由能源部的一笔相同的拨款协调进行的，该基金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.