Minimizing the elastic energy of knots

@inproceedings{Mosel1998MinimizingTE,
  title={Minimizing the elastic energy of knots},
  author={Heiko von der Mosel},
  year={1998}
}
We consider the problem of minimizing the bending energy Eb = ∫ κ ds on isotopy classes of closed curves in R to model the elastic behaviour of knotted loops of springy wire. A potential of Coulomb type with a small factor θ 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 we show existence of minimizers x under a given topological knot type for each θ > 0. Moreover, allowing smaller and smaller thickness… CONTINUE READING

References

Publications referenced by this paper.
SHOWING 1-10 OF 15 REFERENCES

DERMOSEL, Geometrische Variationsprobleme h oherer Ordnung

H VON
  • Bonner Math. Schriften
  • 1996
VIEW 1 EXCERPT

KUSNER, Torus Knots Extremizing the Mobius Energy

D KIMR.
  • Experimental Math
  • 1993
VIEW 1 EXCERPT

Energy of a knot

Jun O'Hara
  • 1991
VIEW 1 EXCERPT

SINGER, Curve Straightening and a Minimax Argument for Closed Elastic Curves

D.A.J. LANGER
  • Topology 24,
  • 1985
VIEW 3 EXCERPTS