Topological dynamics of quantum vortex knots and links
Reconnection of two vortex ring defects
Direct numerical simulation of the creation of a single loop from the interaction of two vortex ring defects governed by the Gross-Pitaevskii equation. The anti-parallel reconnection following the interaction of the two rings create a single, unknotted loop.
Work published by Simone Zuccher & Renzo L. Ricca, J. Fluid Mech. 942, A8 (2022).

Flight of a vortex loop from the reconnection of two vortex ring defects
Direct numerical simulation of the creation of a single loop from the interaction of two ring defects governed by the Gross-Pitaevskii equation. The anti-parallel reconnection of two vortex rings create a single, unknotted loop (inverse topological cascade), that flies away with periodic motion.
Work published by Simone Zuccher & Renzo L. Ricca, J. Fluid Mech. 942, A8 (2022).

Topological cascade of a Hopf link of vortex defects to unlinked loops
Direct numerical simulation of the topological cascade of a Hopf link of vortex defects governed by the Gross-Pitaevskii equation. The change of topology given by the defects interaction and reconnection generate a series of unlinked loops following a generic decay path.
Work published by Simone Zuccher & Renzo L. Ricca, J. Fluid Mech. 942, A8 (2022).

Topological cascade of the minimal surface of a link of vortex defects
Direct numerical simulation of the topological cascade of the minimal (Seifert) surface spanning a Hopf link of vortex defects governed by the Gross-Pitaevskii equation. The change of topology given by the defects interaction and reconnection generates the subsequent splitting of the initial surface into separate surface components.
Work published by Simone Zuccher & Renzo L. Ricca, J. Fluid Mech. 942, A8 (2022).

Head-on collision of two anti-parallel vortex ring defects
Direct numerical simulation of the topological collapse following the head-on collision of two anti-parallel vortex ring defects governed by the Gross-Pitaevskii equation. The abrupt change of topology is due to the instantaneous multiple reconnections of the vortex rings.
Work published by Simone Zuccher & Renzo L. Ricca, J. Fluid Mech. 942, A8 (2022).

Topological collapse of a torus knot (2,3) vortex defect
Direct numerical simulation of the topological collapse of a torus knot (2,3) vortex defect governed by the Gross-Pitaevskii equation. The abrupt change of topology is due to the instantaneous multiple reconnections of the vortex knot.
Work published by Simone Zuccher & Renzo L. Ricca, J. Fluid Mech. 942, A8 (2022).

Topological collapse of a torus knot (2,5) vortex defect
Direct numerical simulation of the topological collapse of a torus knot (2,5) vortex defect governed by the Gross-Pitaevskii equation. The abrupt change of topology is due to the instantaneous multiple reconnections of the vortex knot.
Work published by Simone Zuccher & Renzo L. Ricca, J. Fluid Mech. 942, A8 (2022).

Topological collapse of a torus knot (2,7) vortex defect
Direct numerical simulation of the topological collapse of a torus knot (2,7) vortex defect governed by the Gross-Pitaevskii equation. The abrupt change of topology is due to the instantaneous multiple reconnections of the vortex knot.
Work published by Simone Zuccher & Renzo L. Ricca, J. Fluid Mech. 942, A8 (2022).

Topological collapse of a torus knot (2,9) vortex defect
Direct numerical simulation of the topological collapse of a torus knot (2,9) vortex defect governed by the Gross-Pitaevskii equation. The abrupt change of topology is due to the instantaneous multiple reconnections of the vortex knot.
Work published by Simone Zuccher & Renzo L. Ricca, J. Fluid Mech. 942, A8 (2022).

Topological cycle of two vortex loop defects
Direct numerical simulation of the topological cycle of two vortex loop defects governed by the Gross-Pitaevskii equation. The two loops follow a structural cycle given by the creation of a Hopf link from two planar ellipses: 2 loops → Hopf link → 2 loops.
Work published by Simone Zuccher & Renzo L. Ricca, J. Fluid Mech. 942, A8 (2022).

Topological cycle of three vortex ring defects
Direct numerical simulation of the topological cycle of three vortex ring defects governed by the Gross-Pitaevskii equation. The three rings follow a structural cycle: 3 loops → 2 loops → 1 loop → 2 loops → 3 loops.
Work published by Simone Zuccher & Renzo L. Ricca, J. Fluid Mech. 942, A8 (2022).

Creation of a trefoil vortex knot from the interaction of two unlinked, vortex loop defects
Direct numerical simulation of the creation of a trefoil knot from the interaction of two unlinked, loop defects governed by the Gross-Pitaevskii equation. The two loops undergo a series of single reconnection events that create first a Hopf link and then a trefoil knot (inverse topological cascade).
Work published by Simone Zuccher & Renzo L. Ricca, J. Fluid Mech. 942, A8 (2022).

New defect creation from a twist phase superposition on a vortex ring
Direct numerical simulation of the instantaneous creation of a new central defect from the superposition of a twist phase on an initially isolated vortex ring defect.
Work published by Simone Zuccher & Renzo L. Ricca, Fluid Dyn. Res. 50, 011414 (2018).

New defects creation from a twist phase superposition on two vortex ring defects
Direct numerical simulation of the instantaneous creation of two new defects from the superposition of a twist phase on an initial pair of vortex ring defects.
Work published by Simone Zuccher & Renzo L. Ricca, Fluid Dyn. Res. 50, 011414 (2018).
