The Nonlinear Dynamics of Filaments with Applications to Physics, Biology, and Engineering

细丝非线性动力学及其在物理、生物学和工程中的应用

• 批准号: 9704421
• 负责人: Michael Tabor
• 金额: $ 9.01万
• 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: 1997
• 资助国家: 美国
• 起止时间: 1997-09-01 至 2001-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9704421&HistoricalAwards=false
• 关键词: Nonlinear; Dynamics; Filaments; Applications; Physics

Tabor 9704421 Motivated by a range of problems and, in particular, the observed iterated, stretching and writhing motions of certain bacterial filaments, the investigator and his collaborator Isaac Klapper at Montana State University develop new techniques to study the linear and nonlinear stability of the time-dependent equations governing elastic filament dynamics (the Kirchhoff equations) and, in parallel, computational approaches to provide efficient numerical simulations. Overall, the investigators develop (i) new analytic techniques to study both the linear and nonlinear stability of elastic filaments, (ii) quantitative models of writhing instabilities and buckling phenomena in mechanical filaments, (iii) mathematical models of self-assembling bacterial fibers, lipid bi-layer roll-up and various aspects of DNA dynamics, (iv) efficient and flexible algorithms to simulate the described physical and biological processes and to test the validity of the (continuum) models, (v) discrete elastic models for simulating DNA conformations, (vi) theoretical and numerical models of solar magnetic fields with twist. A host of practical problems in the biological, physical and engineering sciences involve filamentary structures on scales varying from the microscopic to the macroscopic. These include, in progression of scales: molecular structures including DNA and lipid tubules and helices, bacterial fibers, vorticity filaments, ropes and cables, braided magnetic flux tubes as seen in solar flares, etc. The motion of these structures has a crucial impact on their structure and function. The investigators develop general computational methods to model these filaments and their uses, including the structure and function of DNA, and the self-assembly of advanced biomaterials.

Tabor 9704421受一系列问题，特别是观察到的某些细菌细丝的迭代、拉伸和扭转运动的驱使，蒙大拿州立大学的研究人员和他的合作者艾萨克·克拉珀开发了新的技术来研究控制弹性细丝动力学的依赖时间的方程(基尔霍夫方程)的线性和非线性稳定性，并并行地开发了计算方法来提供有效的数值模拟。总之，研究人员发展了(I)新的分析技术来研究弹性细丝的线性和非线性稳定性，(Ii)机械细丝中扭曲不稳定性和屈曲现象的定量模型，(Iii)自组装细菌纤维的数学模型，脂质双层卷曲和DNA动力学的各个方面，(Iv)高效和灵活的算法来模拟所描述的物理和生物过程并检验(连续)模型的有效性，(V)离散的弹性模型来模拟DNA构象，(Vi)带有扭曲的太阳磁场的理论和数值模型。生物、物理和工程科学中的许多实际问题涉及从微观到宏观的不同尺度上的丝状结构。这些结构包括：分子结构，包括DNA和脂类微管和螺旋、细菌纤维、涡度细丝、绳索和电缆、太阳耀斑中看到的编织磁通量管等。这些结构的运动对其结构和功能具有至关重要的影响。研究人员开发了通用的计算方法来模拟这些细丝及其用途，包括DNA的结构和功能，以及先进生物材料的自组装。