A model for the evolution of vector fields on flexible curves is investigated. Explicit solutions with radial symmetry demonstrate global existence. Numerical simulations show that configurations with constant tilt angle emerge as stationary states.
Funding informationPRIN 2017 "Variational methods for stationary and evolution problems with singularities and interfaces"; DFG GRK 1692 Existence and regularity of minimizers for a geometric variational problem is shown. The variational integral models an energy contribution of the interface between two immiscible fluids in the presence of surfactants and includes a Helfrich type contribution, a Frank type contribution and a coupling term between the orientation of the surfactants and the curvature of the interface. Analytical results are proven in a one-dimensional situation for curves.
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