Energy and self-linking of magnetic torus knots

Magnetic fields confined into thin tubes in the shape of torus knots and unknots are considered and the relationships between their length, bending and torsional energy and their geometrical and topological complexity are analyzed. The winding number is taken as natural index of knot complexity. Numerical information on self-linking are compared with theoretical results by E. Fuller (2003) and the invariance of the self-linking number under dilatation is discussed.

This research is part of a PhD Project carried out under the guidance of R.L. Ricca.