Self-Contact Preventing Energy for Tubular Rods

We introduce a generalization of Möbius energy for knots to an energy functional for tubular neighbourhoods of closed inextensible curves. We prove the continuity of the energy and its boundedness for physically admissible tubes without self-contact and in particular for the torus. The functional allows to distinguish isotopy classes of the centreline through its physical resemblance to a self-repulsive electrostatic energy. If the tube has zero thickness, O’Hara’s functional is recovered. Finally, a discussion on the possible exponents in the functional is carried out and numerical examples are studied to highlight some advantages of our new definition.