The shapes of physical trefoil knots

We perform a compare-and-contrast investigation between the equilibrium shapes of physical and ideal trefoil knots, both in closed open configurations. Ideal knots are purely geometric abstractions for tightest configuration tied perfectly flexible, self-avoiding tube with an inextensible centerline undeformable cross-sections. Here, we construct realizations tight elastomeric rod, use X-ray tomography 3D finite element simulation detailed characterization. Specifically, evaluate role elasticity dictating knot’s overall shape, self-contact regions, curvature profile, cross-section deformation. compare shape our elastic to prior computations corresponding Our results on exhibit many similarities their counterparts, but also some striking dissimilarities that examine detail. These observations raise hypothesis regions localized deformation, not captured by models, could act as precursors weak spots compromise strength knotted filaments.