Dynamics of Filaments: Modeling, Analysis and Application

细丝动力学：建模、分析和应用

• 批准号: 9972063
• 负责人: Alain Goriely
• 金额: $ 7.66万
• 依托单位: University of Arizona
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1999
• 资助国家: 美国
• 起止时间: 1999-08-01 至 2002-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9972063&HistoricalAwards=false
• 关键词: Dynamics; Filaments; Modeling; Analysis; Application

The investigator studies the dynamics associated with changeof configurations in filaments. The theory of elastic filamentsis used as a paradigm to describe the different types ofinstabilities, the self-organization of filamentary structuresand the propagation of waves. The investigator considersgeneralization of the Kirchhoff model to include the effect ofgrowth (as found in many biological process), generalcross-sections (with application to the dynamics of ribbons) andviscous effects and perform a dynamical systems and bifurcationanalysis of the equilibrium configurations. This analysis iscompleted by the derivation and analysis of amplitude equationsfor the behavior of the solution close to the instability. Thisproject relies on the effective combination of different methodssuch as perturbation theory, dynamical system analysis, amplitudeequations for partial differential equations, and numericalanalysis. Filamentary structures can be observed in nature at allscales from the microscopic chains of molecules, DNA andpolymers, to the macroscopic braided magnetic flux tubes in solarflares. One of the central problems in filaments is tounderstand the possible changes of configurations and thedynamics involved in the changes. Remarkably, despite theirdifferent length scales and microscopic structures, unstablefilaments seem to follow universal configurational changes suchas writhing, coiling, super-coiling, and looping. The purpose ofthis project is to study the dynamics associated with the changeof configurations in filaments. This will provide a betterunderstanding of universal changes and self-organization offilaments, with applications to DNA configurations, structure ofpolymers, evolution of biological fibers, and cable kinking.

研究人员研究与细丝构型变化相关的动力学。 弹性丝理论被用作描述不同类型的不稳定性、丝结构的自组织和波传播的范例。 研究人员认为基尔霍夫模型的概括包括生长效应（在许多生物过程中发现）、一般横截面（应用于带状动力学）和粘性效应，并对平衡配置进行动态系统和分岔分析。 该分析是通过对接近不稳定的解的行为的振幅方程进行推导和分析来完成的。 该项目依赖于微扰理论、动力系统分析、偏微分方程振幅方程和数值分析等不同方法的有效结合。 从分子、DNA 和聚合物的微观链到太阳耀斑中的宏观编织磁通量管，在自然界中可以在各个尺度上观察到丝状结构。 细丝的核心问题之一是了解构型的可能变化以及变化中涉及的动力学。 值得注意的是，尽管不稳定的细丝具有不同的长度尺度和微观结构，但它们似乎遵循普遍的构型变化，例如扭动、卷曲、超级卷曲和成环。 该项目的目的是研究与细丝构型变化相关的动力学。 这将有助于更好地理解普遍变化和自组织丝，并应用于 DNA 构型、聚合物结构、生物纤维的进化和电缆扭结。