CAREER: Anomalous Diffusion, Homogenization and Averaging

职业：异常扩散、均匀化和平均

• 批准号: 1252912
• 负责人: Gautam Iyer
• 金额: $ 48万
• 依托单位: Carnegie-Mellon University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2013
• 资助国家: 美国
• 起止时间: 2013-09-01 至 2018-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1252912&HistoricalAwards=false
• 关键词: CAREER; Anomalous; Diffusion; Homogenization; Averaging

This project studies various phenomena related to diffusive tracer particles in a strong array of opposing vorticies. One particularly interesting aspect is a seemingly anomalous diffusive behaviour exhibited on "intermediate" time scales. On long time scales this anomalous diffusive behaviour should "average" to an effectively Brownian behaviour, recovering classical homogenization results. The project crucially uses tools from both Probability and PDE. The educational component of this project aims to further interaction between these two areas from the undergraduate to the post-graduate level.Observing the movement of gravel particles shows intermittent periods of rest and travel. One aspect of this project studies an idealised system modelling this behaviour with the eventual aim of rigorously quantifying the "rest and travel". This is closely related to questions about homogenization -- the approximation of inhomogeneous media with microscopic inhomogeneities by a homogeneous one. This project crucially uses tools from two connected but different areas in Mathematics: Probability and PDE. The educational component of this project aims to further interaction between these two areas from the undergraduate level all the way to the post-graduate level.

该项目研究了各种相对涡流中与扩散示踪剂颗粒有关的各种现象。一个特别有趣的方面是在“中间”时间尺度上表现出的看似异常的扩散行为。长期以来，这种异常的扩散行为应“平均”与有效的布朗行为“平均”，从而恢复经典的均质化结果。该项目至关重要地使用概率和PDE的工具。该项目的教育组成部分旨在在这两个领域之间进一步相互作用，从本科到研究生级别。观察砾石颗粒的运动表现出间歇性的休息和旅行期。该项目的一个方面研究了一个理想化的系统，以严格量化“休息和旅行”的最终目的对这种行为进行建模。这与有关均质化的问题密切相关 - 均质不均匀性的不均匀培养基的近似。该项目至关重要地使用来自数学的两个连接但不同领域的工具：概率和PDE。该项目的教育组成部分旨在从本科水平到研究生水平的这两个领域之间进行进一步互动。