papers here: R. Langevin and J. O’Hara: Conformally invariant energies of knots, http://arxiv.org/abs/math/0409396 John M Sullivan: Approximating Ropelength by Energy Functions http://arxiv.org/abs/math.GT/0203205 R Kusner & JM Sullivan: Mobius invariant knot enerrgies http://torus.math.uiuc.edu/jms/Papers/knot/knot.pdf It is also pointed out that the 1/r^2 potential, viewed as a member of 1/r^p potentials class, has an infinite barrier to rope-self-crossing ("passing thru itself") for two segments of rope at right angles, if and only if p>=2. -- Warren D. Smith http://RangeVoting.org <-- add your endorsement (by clicking "endorse" as 1st step)