Collaborative Research: Scaling and infinite divisibility in models of coarsening and other dynamic selection problems

合作研究：粗化和其他动态选择问题模型中的缩放和无限可分性

基本信息

批准号：
0604420
负责人：
Robert Pego
金额：
$ 23.31万
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：
2006
资助国家：
美国
起止时间：
2006-07-01 至 2010-06-30
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=0604420&HistoricalAwards=false
关键词：
Collaborative Research Scaling infinite divisibility

项目摘要

Menon0605006Pego0604420 The investigators collaborate in developing mathematicalmethods that improve the understanding of dynamic behavior incomplex nonlinear systems. The focus is on the universal trendto self-similarity, or dynamic scaling, in a variety of physicalsettings, such as clustering of colloids in physical chemistry,selection of nonlinear waves in fluid mechanics and models ofpopulation biology, and coarsening of nanoscale islands inmaterials science. The goal is to devise a unified framework forthe treatment of these problems based on methods from dynamicalsystems, partial differential equations, and probability theory. The work is driven by close analogies between the mathematicalideas of infinite divisibilty and limit theorems for heavy-taileddistributions in probability theory, and apparently unrelatedproblems of dynamic scaling and selection in these diversephysical settings. Progress in this program leads to deeper understanding ofhow order emerges from complexity in a variety of problems offundamental scientific interest in the areas of aerosol physics,fluid mechanics, materials science, and physical chemistry. Thework on island coarsening promises to improve the physicalmodeling of nanoscale step-terrace structures on crystallinesurfaces. The work on coagulation aims to improve ourunderstanding of models for the formation of clouds, smoke, dustand haze, which is of potential environmental importance. Asignificant outcome is to link progress on apparently unconnectedproblems with a basic mathematical framework that ties togetherprobability and dynamical systems theory and that broadlyfacilitates the transfer of insights from one area to another.

MENON0605006PEGO0604420研究人员合作开发数学方法，以提高对动态行为无线性非线性系统的理解。重点是在各种身体集中的普遍趋势上自我相似或动态缩放，例如物理化学中胶体的聚类，流体力学中的非线性波和人群生物学模型的选择以及对纳米级岛屿的块状化。目的是设计一个统一的框架，以根据动态系统，部分微分方程和概率理论的方法来处理这些问题。这项工作是由无限分裂的数学分裂和限制概率理论中的重尾distribentions的定理和定理限制的驱动的，在这些多元化物理环境中，动态缩放和选择显然是无关的问题。该计划的进展导致对秩序的更深入了解，这是由于各种问题的复杂性而出现的，这些问题在气溶胶物理学，流体力学，材料科学和物理化学方面的领域中脱离科学兴趣。岛上的工作有望改善CrystallinesUrfaces上纳米级的置于跨层面结构的物理模型。凝血的工作旨在改善对云，烟雾，尘土和雾兹形成的模型的理解，这是潜在的环境重要性。令人振奋的结果是将明显不连续的问题的进度与一个基本的数学框架联系起来，该框架将探索性和动态系统理论联系起来，并广泛地将见解从一个领域转移到另一个领域。