Evolving a Knotted Kirchhoff Elastic Rod
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Date
2019
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In this thesis, we study the problem on how to find an equilibrium configuration of a knotted Kirchhoff elastic rod by evolving it within the same knot class. The evolution is given by the $L^2$ gradient flow of the total energy composed of the Kirchhoff elastic energy and the Möbius knot energy. We would prove the long-time existence of smooth solutions for the gradient flow and discuss the asymptotic limit.
In this thesis, we study the problem on how to find an equilibrium configuration of a knotted Kirchhoff elastic rod by evolving it within the same knot class. The evolution is given by the $L^2$ gradient flow of the total energy composed of the Kirchhoff elastic energy and the Möbius knot energy. We would prove the long-time existence of smooth solutions for the gradient flow and discuss the asymptotic limit.
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Geometric flows, Fourth-order problem, Kirchhoff elastic rods, Gâteaux derivative of Möbius knot energy, Geometric flows, Fourth-order problem, Kirchhoff elastic rods, Gâteaux derivative of Möbius knot energy