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arXiv · 2401.15454

Self-contact preventing energy for tubular rods

Chiara Lonati·Alfredo Marzocchi
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Abstract

We introduce a generalization of Mobius 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 centerline through its physical inspiration 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.

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Chiara Lonati, Alfredo Marzocchi. 2024-01-27. Self-contact preventing energy for tubular rods. https://arxiv.org/abs/2401.15454

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