Mathematical Sciences: Studies in Heterogeneous Media and Turbulent Fluid Transport

本研究涉及三个方面：1）宏观层面 非均匀介质和复杂流体中的输运特性 模式;具体而言，在随机环境中模拟异常扩散 具有长程相关性的速度场，如达西 在大型地下水库中观察到的速度， 在湍流中产生与空间/时间相关的速度中， 扩散，ii）多孔介质的流体渗透率的测定 间接测量和互相关的媒体 多孔介质中的各种场（电、磁、声） 固体，iii）复合材料的微观建模 在物理性质之间表现出强耦合，例如 压电材料 数学分析和计算机建模/模拟将 用于研究物理或工程模型 涉及异质材料。 的重要组成部分 这项活动是培训和与研究生一起工作， 博士后研究员作为一般教育计划的一部分 在纽约的柯朗数学科学研究所 大学

This research involves three components: 1) macroscopic transport properties in heterogeneous media and in complex fluid patterns; specifically, modelling anomalous diffusion in random velocity fields with long-range correlations, such as the Darcy velocities as observed in large-scale groundwater reservoirs or in space/time- dependent velocities which arise in turbulent diffusion, ii) determination of fluid permeability of porous media from indirect measurements and the cross-correlation of various fields (electrical, magnetic, acoustic) in a porous solid, iii) microscopic modelling of composite materials exhibiting strong coupling among physical properties, such as piezoelectric materials. Mathematical analysis and computer modelling/simulation will be used to study models of physical or engineering interest involving heterogeneous materials. An important component of this activity is training and working with graduate students and post-doctoral fellows as part of the general educational program of the Courant Institute of Mathematical Sciences at New York University.