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- Christian E. Laing, Renzo L. Ricca, De Witt L. Sumners
- Scientific reports
- 2015

Reconnection is a fundamental event in many areas of science, from the interaction of vortices in classical and quantum fluids, and magnetic flux tubes in magnetohydrodynamics and plasma physics, to the recombination in polymer physics and DNA biology. By using fundamental results in topological fluid mechanics, the helicity of a flux tube can be calculated… (More)

In this paper we provide a mathematical reconstruction of what might have been Gauss’ own derivation of the linking number of 1833, providing also an alternative, explicit proof of its modern interpretation in terms of degree, signed crossings and intersection number. The reconstruction presented here is entirely based on an accurate study of Gauss’ own… (More)

- Simone Zuccher, Renzo L. Ricca
- Physical review. E, Statistical, nonlinear, and…
- 2015

Here we show that under quantum reconnection, simulated by using the three-dimensional Gross-Pitaevskii equation, self-helicity of a system of two interacting vortex rings remains conserved. By resolving the fine structure of the vortex cores, we demonstrate that the total length of the vortex system reaches a maximum at the reconnection time, while both… (More)

- BY RENZO L. RICCA, Renzo L. Ricca
- 2008

In this paper, we determine two quantities, of geometric and topological character, that were left undetermined in two previous results obtained byArnold (Arnold 1974 InProc. Summer School inDiff.Eqs. atDilizhan, pp. 229–256.) andMoffatt (Moffatt 1990Nature347, 367–369) on lower bounds for the magnetic energy of knots and links in ideal fluids. For… (More)

- F. Maggioni, Sagr Alamri, Carlo F. Barenghi, Renzo L. Ricca
- Physical review. E, Statistical, nonlinear, and…
- 2010

In this paper we determine the velocity, the energy, and estimate writhe and twist helicity contributions of vortex filaments in the shape of torus knots and unknots (as toroidal and poloidal coils) in a perfect fluid. Calculations are performed by numerical integration of the Biot-Savart law. Vortex complexity is parametrized by the winding number w given… (More)

For the first time since Lord Kelvin’s original conjectures of 1875 we address and study the time evolution of vortex knots in the context of the Euler equations. The vortex knot is given by a thin vortex filament in the shape of a torus knot Tp,q (p > 1, q > 1; p, q co-prime integers). The time evolution is studied numerically by using the Biot–Savart (BS)… (More)

- Renzo L. Ricca, Francesca Maggioni
- Computers & Mathematics with Applications
- 2008

In this paper we introduce and analyze a set of equations to study geometric and energetic aspects associated with the kinematics of multiple folding and coiling of closed filaments for DNA modeling. By these equations we demonstrate that a high degree of coiling may be achieved at relatively low energy costs through appropriate writhe and twist… (More)

- Xin Liu, Renzo L. Ricca
- Scientific reports
- 2016

Due to reconnection or recombination of neighboring strands superfluid vortex knots and DNA plasmid torus knots and links are found to undergo an almost identical cascade process, that tend to reduce topological complexity by stepwise unlinking. Here, by using the HOMFLYPT polynomial recently introduced for fluid knots, we prove that under the assumption… (More)

- Simone Zuccher, Renzo L. Ricca
- Physical review. E
- 2017

By numerically solving the three-dimensional Gross-Pitaevskii equation we analyze the cascade process associated with the evolution and decay of a pair of linked vortex rings. The system decays through a series of reconnections to produce finally three unlinked, unfolded, almost planar vortex loops. Total helicity, initially zero, remains unchanged… (More)

Here we present for the first time a detailed study of the cascade process of two linked quantum vortex loops under the Gross-Pitaevskii equation. After a series of successive reconnections the vortex system decays to three distinct loops. Kinetic helicity as well as various geometric and topological properties associated with helicity are examined… (More)