Minimizing the Elastic Energy of Knots

Abstract

We consider the problem of minimizing the bending energy Eb = R 2 ds on isotopy classes of closed curves in IR3 to model the elastic behaviour of knotted loops of springy wire. A potential of Coulomb type with a small factor as a measure for the thickness of the wire is added to the elastic energy in order to preserve the isotopy class. With a direct method… (More)

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