On a flow to untangle elastic knots |
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Authors: | Chun-Chi Lin Hartmut R Schwetlick |
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Institution: | 1. Department of Mathematics, National Taiwan Normal University, Taipei, 116, Taiwan 2. Department of Mathematical Sciences, University of Bath, Bath, BA2 7AY, UK
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Abstract: | In this paper we present a method to untangle smooth knots by a gradient flow for a suitable energy. We show that the flow of smooth initial knots remains smooth for all time and approaches asymptotically an “optimal embedding” in its isotopy type. The method is to set up a gradient flow for the total energy of knots, which consists of bending energy and the Möbius energy of knots. |
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