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1. R. A. Van Gorder, “General rotating quantum vortex filaments in the low-temperature Svistunov model of the local induction approximation,” Phys. Fluids 26, 065105 (2014).
2.LIA is an approximation of Biot–Savart law (Eq. (2) in Ref. 1, although the denominator should be cubed). According to Van Gorder, LIA can be obtained from Biot–Savart by introducing a cutoff. However, to be more precise, LIA is actually a leading term of an expansion around r plus the cutoff.
3. B. V. Svistunov, “Superfluid turbulence in the low-temperature limit,” Phys. Rev. B 52, 3647 (1995).
4. N. Hietala and R. Hänninen, “Comment on ‘Motion of a helical vortex filament in superfluid 4He under the extrinsic form of the local induction approximation,’ [Phys. Fluids 25, 085101 (2013)],” Phys. Fluids 26, 019101 (2014).
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5.A. W. Baggaley and C. F. Barenghi, “Quantum turbulent velocity statistics and quasiclassical limit,” Phys. Rev. E 84, 067301 (2011);
5.E. Kozik and B. Svistunov, “Kelvin-wave cascade and decay of superfluid turbulence,” Phys. Rev. Lett. 92, 035301 (2004);
5.V. S. L’vov and S. Nazarenko, “Spectrum of Kelvin-wave turbulence in superfluids,” JETP Lett. 91, 428 (2010).
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6.L. Boué, D. Khomenko, V. S. L’vov, and I. Procaccia, “Analytic solution of the approach of quantum vortices towards reconnection,” Phys. Rev. Lett. 111, 145302 (2013).

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Van Gorder considers a formulation of the local induction approximation, which allows the vortex to move in the direction of the reference axis [“General rotating quantum vortex filaments in the low-temperature Svistunov model of the local induction approximation,” Phys. Fluids26, 065105 (2014)]. However, in his analytical and numerical study he does not use it. A mistake in the torsion of a helical vortex is also corrected.


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