Dynamics of Filaments: Modeling, Analysis and Application

这位研究人员研究了与细丝结构变化相关的动力学。弹性丝状结构理论用来描述不同类型的不稳定性、丝状结构的自组织和波的传播。研究人员考虑了Kirchhoff模型的推广，以包括生长效应(如在许多生物过程中发现的)、一般截面(应用于带的动力学)和粘性效应，并对平衡构型进行了动力学系统和分叉分析。这种分析是通过推导和分析接近不稳定性的解的行为的振幅方程来完成的。该项目依赖于不同方法的有效结合，如摄动理论、动力系统分析、偏微分方程组的振幅方程和数值分析。从分子、DNA和聚合物的微观链到太阳耀斑中宏观的编织磁通量管，自然界中都可以观察到丝状结构。细丝的核心问题之一是了解可能的构型变化以及变化所涉及的动力学。值得注意的是，尽管它们的长度尺度和微观结构不同，但不稳定的细丝似乎遵循普遍的构型变化，如扭曲、卷曲、超级卷曲和环状。这个项目的目的是研究与细丝构型变化相关的动力学。这将提供对普遍变化和自组织纤维的更好的理解，以及在DNA构型、聚合物结构、生物纤维的进化和电缆扭结方面的应用。

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.