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

受一系列问题的启发，特别是观察到某些细菌细丝的迭代，拉伸和扭曲运动，研究者和他在蒙大拿州立大学的合作者Isaac Klapper开发了新的技术来研究控制弹性细丝动力学的时间相关方程（Kirchhoff方程）的线性和非线性稳定性，同时，计算方法提供了有效的数值模拟。总的来说，研究人员开发了(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）机械细丝的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，脂质双层卷起和DNA动力学的各个方面，（iv）有效和灵活的算法来模拟所描述的物理和生物过程，并测试（连续）模型的有效性，(v)模拟DNA构象的离散弹性模型，（vi）具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都涉及从微观到宏观尺度上的纤维结构。这些包括，按比例排列：分子结构，包括DNA和脂质小管和螺旋，细菌纤维，涡旋细丝，绳索和电缆，编织磁通管，如在太阳耀斑中看到的，等等。这些结构的运动对它们的结构和功能有着至关重要的影响。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。

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.