Applications of Filament Dynamics to Physics, Biology, and Engineering

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Klapper 9704486 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 Michael Tabor at the University of Arizona 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.