  Probably the most natural energy functional to be considered for knotted
strings is the one given by the electrostatic repulsion. In the absence of
counter-charges, a charged, knotted string evolving along the energy gradient
of electrostatic repulsion would progressively tighten its knotted domain into
a point on a perfectly circular string. However, in the presence of charge
screeningthe self-repelling knotted strings can get stabilised. It is known
that energy functionals in which repulsive forces between repelling charges
grow inversely proportional to the third or higher power of their relative
distance stabilise self-repelling knots. Especially interesting is the case of
the third power since the repulsive energy becomes scale invariant and does not
change upon Moebius transformations (reflections in spheres) of knotted
trajectories. We observe here thatknots minimising their repulsive Moebius
energy show quantization of the energy and writhe (measure of chirality) within
several tested families of knots.
