Dynamic Scaling, Coarsening and Stability in Physical Systems

物理系统中的动态缩放、粗化和稳定性

• 批准号: 0652558
• 负责人: Robert Pego
• 金额: $ 2.61万
• 依托单位: Carnegie-Mellon University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2006
• 资助国家: 美国
• 起止时间: 2006-07-01 至 2007-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0652558&HistoricalAwards=false
• 关键词: Dynamic; Scaling; Coarsening; Stability; Physical

The main theme of the proposed work is on understanding the widespreadphenomenon of dynamic scaling in extended physical systems, buildingon stability analysis of coherent structures such as self-similarsolutions, nonlinear wave pulses and vortices. The paradox of dynamicscaling laws is that typically they can be predicted by back of theenvelope calculations, yet defy rigorous analysis for years.We will study scaling and stability in a variety of problems of highcurrent interest: the trend to self-similar behavior in Smoluchowski'smean-field model of coagulation; scaling and stability of fingeringpatterns in viscous fluid flows; models of domain coarsening in phasetransitions; existence and stability of solitary waves ininfinite-dimensional Hamiltonian systems; and stability of Bose-Einstein condensates with vortices. The work will involve the development of improved methods for stability analysis in nonlinear systems, for the rigorous analysis and numerical computation of self-similar solutions and nonlinear waves, and for physical modeling of step-terrace structures on crystalline surfaces.The general aim of this work is to improve understanding of large-scaledynamic behavior in complex systems. We aim to develop new and effective mathematical methods and concepts for the modeling and analysis of dynamic behavior in a variety of problems of high scientific interest. We study fundamental mathematical models for the large-scale dynamics of: agglomeration of small particles; mixing patterns in viscous fluid flow; microscopic structure of metallic alloys and semiconductor surfaces; waves on fluid interfaces; and quantum vortices in super-cold gases. Many issues that will be investigated are of fundamental interest in condensed-matter physics, aerosol physics, chemical engineering, and materials science.

拟议工作的主要主题是了解扩展物理系统中动态缩放的广泛的苯丙年部，建立对相干结构（例如自相似），非线性波脉冲和涡流等相干结构的稳定性分析。动态标准定律的悖论是，通常可以通过计算后面的计算来预测它们，但多年来都可以违反严格的分析。我们将研究较高兴趣的各种问题的缩放和稳定性：Smoluchowski自我类似行为的趋势'' Smean-Field凝结模型；粘性流体流动中的指法型和稳定性；域模型在疗程中的变形；孤立波的存在和稳定性无限二维的哈密顿系统； Bose-Einstein与涡旋的稳定性。这项工作将涉及开发非线性系统中稳定性分析的改进方法，用于自相似溶液和非线性波的严格分析和数值计算，以及用于结晶表面上的踏板结构的物理建模。工作是提高对复杂系统中大规模动态行为的理解。 我们旨在开发新的有效的数学方法和概念，以在各种高科学兴趣问题中对动态行为进行建模和分析。我们研究了：小颗粒聚集的大规模动力学的基本数学模型；混合粘性流体流中的图案；金属合金和半导体表面的微观结构；流体界面上的波浪；和超冷气中的量子涡旋。 许多将要研究的问题对凝结物理学，气溶胶物理，化学工程和材料科学具有根本兴趣。