Analysis on Faddeev, Skyrme and Some Complex Fluid Models

Faddeev、Skyrme及一些复杂流体模型分析

• 批准号: 0700517
• 负责人: Fang-Hua Lin
• 金额: $ 60万
• 依托单位: New York University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2007
• 资助国家: 美国
• 起止时间: 2007-06-01 至 2013-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0700517&HistoricalAwards=false
• 关键词: Analysis; Faddeev; Skyrme; Some; Complex

Analysis on Faddeev, Skyrme and some Complex Fluid ModelsAbstract of Proposed ResearchFang-Hua Lin This award will support research on two different projects that are important and interesting both mathematically and scientifically. One project is to study the particle-like solutions in both the static and evolutionary equations of Faddeev and Skyrme models. We also plan to study the discrete analogs of these problems (or lattice-models) and to explore the connections between the discrete and continuous models. The second project will be a theoretical study of the hydrodynamics of viscoelastic fluids, and micro-macro models, of polymeric fluids. These problems involve multiple scale phenomena and are modeled by nonlinear coupled systems of partial differential equations of both hyperbolic and parabolic types. Skyrme and Faddeev models use continuously extended, topologically characterized, relativistically invariant, locally concentrated, soliton-like fields to model elementary particles. These particle-like solutions display the features of some fundamental phenomena that arise in high energy physics, biological sciences and astronomy. Indeed, it was recently shown that Faddeev models can capture the knotted structures of field configurations; something that has not been yet done for any other classical field models. A primary object of the proposed research is to conduct a systematic mathematical study of both static and dynamic models. .Another objective is to investigate the analogies between these particle-like solutions in a large scale field with the analysis of other natural phenomena which may contain many scales such as complex fluids and biological fluids.

Faddeev、Skyrme及几种复杂流体模型的分析--拟研究摘要 该奖项将支持两个不同项目的研究，这两个项目在数学和科学上都很重要和有趣。一个项目是研究Faddeev和Skyrme模型的静态和演化方程中的类粒子解。 我们还计划研究这些问题（或格子模型）的离散类似物，并探索离散和连续模型之间的联系。第二个项目将是粘弹性流体的流体力学理论研究，以及聚合物流体的微观-宏观模型。这些问题涉及多尺度现象，并模拟双曲型和抛物型偏微分方程的非线性耦合系统。 Skyrme和Faddeev模型使用连续扩展的、拓扑特征的、相对论不变的、局部集中的、类似孤子的场来模拟基本粒子。这些类粒子解反映了高能物理、生物科学和天文学中一些基本现象的特征。事实上，最近的研究表明，法捷耶夫模型可以捕捉到场结构的打结结构;这是任何其他经典场模型都没有做到的。 所提出的研究的一个主要目标是进行系统的静态和动态模型的数学研究。另一个目的是研究大尺度场中这些粒子状溶液与其他可能包含许多尺度的自然现象（如复杂流体和生物流体）的分析之间的相似性。