Evolving a Knotted Kirchhoff Elastic Rod

Evolving a Knotted Kirchhoff Elastic Rod

陳柏宇(Chen Bo-Yu)

指導教授 ： 林俊吉

國立臺灣師範大學/理學院/數學系/碩士(2019年)

https://doi.org/10.6345/NTNU201900361

摘要

無中文摘要

關鍵字

Geometric flows ； Fourth-order problem ； Kirchhoff elastic rods ； Gâteaux derivative of Möbius knot energy

並列摘要

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.

並列關鍵字

Geometric flows ； Fourth-order problem ； Kirchhoff elastic rods ； Gâteaux derivative of Möbius knot energy

參考文獻

[DKS02] Gerhard Dziuk, Ernst Kuwert, and Reiner Schatzle. Evolution of elastic curves in Rn: Existence

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2002.

[DP12] Anna Dall’Acqua and Paola Pozzi. A willmore-helfrich L2-flow of curves with natural boundary

conditions. Communications in Analysis and Geometry, 22, 11 2012.