# 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).