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On the geometric flows of Kirchhoff elastic rods
Chun-Chi Lin and Hartmut Schwetlick
Rod theory has been applied to the modelling of DNA and bacterial fibers in their mechanics aspects. In this paper, we relate a geometric functional of curves to the simplest Kirchhoff elastic energy of rods so that the generalized elastic curves are the centerlines of elastic rods in equilibrium. Then, under a mild assumption, we derive the long time existence of the length preserving evolution of the elastic rods.