Waves on a vortex filament: exact solutions of dynamical equations

Brugarino, T.; Mongiovı̀, Maria Stella; Sciacca, Michele

doi:10.1007/s00033-014-0450-5

Cited by 5 publications

(3 citation statements)

References 28 publications

(34 reference statements)

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“…Note that in Fig. 4 the amount of vortex line grows, because of the appearance of Kelvin waves along the straight vortices, induced by the growth of sc (a similar phenomenon has been studied by Brugarino, Mongiovì & Sciacca 2015) for He II. At q = 1, the straight vortex regime ceases, because the topology of the vortex lines changes: the vortex tangle takes part in the superfluid, and the vortex line density undergoes a sudden increase at q = 1, as shown in Fig. 6.…”

Section: A P P L I C At I O N To T H E V E L a P U L S A Rsupporting

confidence: 59%

A mathematical description of glitches in neutron stars

Mongiovı̀

Russo

Sciacca

2017

Monthly Notices of the Royal Astronomical Society

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In a pulsar, there are gaps and difficulties in our knowledge of glitches, mainly because of the absence of information about the physics of the matter of the star. This has motivated several authors to suggest dynamical models that interpret most of the astronomical data. Many predictions are based on the assumption that the inner part is analogous to the structure of matter of superfluids. Here, we illustrate a new mathematical model, partially inspired by the dynamics of superfluid helium. We obtain two evolution equations for the angular velocities (of the crust and of superfluid), which are supported by another evolution equation for the average vortex line length per unit volume. This third equation is more delicate from an analytical perspective and is probably at the origin of glitches. We identify two stationary solutions, corresponding to the straight vortex regime and the turbulent regime.

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Section: A P P L I C At I O N To T H E V E L a P U L S A Rsupporting

confidence: 59%

A mathematical description of glitches in neutron stars

Mongiovı̀

Russo

Sciacca

2017

Monthly Notices of the Royal Astronomical Society

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“…After a reconnection, two waves run along each vortex line (in opposite direction one to each other, as in Figure 3 in [14]), but Kelvin waves can be also triggered in the waves cascade, if it starts. The propagation speed of Kelvin waves along a vortex line can be approximated by v g ∝ K (K being the wave number) quite well for K < 500 cm −1 as shown in Figure 3 of [28]. The time a Kelvin wave needs to run for a length aλ (a being a constant of the order of unity and the wavelength…”

Section: Range Of Validity Of the Modelmentioning

confidence: 99%

Fractal dimension of superfluid turbulence: a random-walk toy model

Mongiovı̀¹,

Sciacca²,

Jou³

2014

Communications in Applied and Industrial Mathematics

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This paper deals with the fractal dimension of a superfluid vortex\ud tangle. It extends a previous model [J. Phys. A: Math. Theor. {\bf\ud 43}, 205501 (2010)] (which was proposed for very low temperature),\ud and it proposes an alternative random walk toy model, which is valid\ud also for finite temperature. This random walk model combines a\ud recent Nemirovskii's proposal, and a simple modelization of a\ud self-similar structure of vortex loops (mimicking the geometry of the loops of\ud several sizes which compose the tangle). The fractal dimension of\ud the vortex tangle is then related to the exponents describing how\ud the vortex energy per unit length changes with the length scales,\ud for which we take recent proposals in the bibliography.\ud The range between 1.35 and 1.75 seems the most consistent one

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“…[7,42]. The former interpreted the steep increase of L at Re 2 as the beginning of vortex reconnection, namely, to the production of a high number of free vortex loops as a consequence of the crossing and cutting and recombining of vortex lines that in turbulence T I were most of them pinned to the walls [43]. The increase of L in turbulence T I, instead, is basically due to Kelvin wave excitations in pinned vortex lines.…”

Section: Quantum Turbulence: Explicit Evaluationmentioning

confidence: 99%

Effective thermal conductivity of helium II: from Landau to Gorter–Mellink regimes

Sciacca

Jou

Mongiovı̀

2014

Z. Angew. Math. Phys.

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The size-dependent and flux-dependent effective thermal conductivity of narrow channels filled with He II is analyzed. The classical Landau evaluation of the effective thermal conductivity of quiescent He II is extended to describe the transition to fully turbulent regime, where the heat flux is proportional to the cubic root of the temperature gradient (Gorter–Mellink regime). To do so, we use an expression for the quantum vortex line density L in terms of the heat flux considering the influence of the walls. From it, and taking into account the friction force of normal component against the vortices, we compute the effective thermal conductivity as a function of the heat flux, and we discuss in detail the corresponding size dependence

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Waves on a vortex filament: exact solutions of dynamical equations

Cited by 5 publications

References 28 publications

A mathematical description of glitches in neutron stars

A mathematical description of glitches in neutron stars

Fractal dimension of superfluid turbulence: a random-walk toy model

Effective thermal conductivity of helium II: from Landau to Gorter–Mellink regimes

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