Collaborative Research: Scaling and Infinite Divisibility in Models of Coarsening and Other Dynamic Selection Problems

Menon0605006Pego0604420 研究者们合作开发了一种改进复杂非线性系统动态行为的分析方法。 重点是在各种物理环境中的自相似性或动态标度的普遍趋势，例如物理化学中的胶体聚类，流体力学和种群生物学模型中的非线性波的选择，以及材料科学中纳米级岛屿的粗化。 我们的目标是设计一个统一的框架为基础的方法从dynamicalsystems，偏微分方程和概率论这些问题的治疗。这项工作是由无限整除性和概率论中重尾分布的极限定理之间的密切类比驱动的，显然是在这些不同的物理环境中不相关的动态缩放和选择问题。 在这个程序的进展导致更深入地了解ofhow秩序出现在气溶胶物理学，流体力学，材料科学和物理化学领域的基础科学兴趣的各种问题的复杂性。 岛状粗化的工作有望改善堆叠表面上纳米级台阶结构的物理建模。 凝结方面的工作旨在提高我们对云、烟、尘和霾的形成模式的理解，这具有潜在的环境重要性。 一个重要的成果是将显然不相关的问题的进展与一个基本的数学框架联系起来，这个框架将概率和动力系统理论联系在一起，并广泛地促进了见解从一个领域转移到另一个领域。

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.