Dynamics of Filaments: Modeling, Analysis and Application

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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.