Motion of a Vortex Filament and its Relation to Elastica

Hasimoto, Hidenori

doi:10.1143/jpsj.31.293

Cited by 93 publications

(69 citation statements)

References 3 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…Regarding the classical fluid LIA, Hasimoto [12] considered a planar vortex filament in the curvature-torsion frame of reference. This influential and often cited paper demonstrates the relation between the curvature of a vortex filament and elastica.…”

Section: Introductionmentioning

confidence: 99%

Dynamics of a planar vortex filament under the quantum local induction approximation

Gorder

2014

Proc. R. Soc. A.

View full text Add to dashboard Cite

The Hasimoto planar vortex filament is one of the rare exact solutions to the classical local induction approximation (LIA). This solution persists in the absence of friction or other disturbances, and it maintains its form over time. As such, the dynamics of such a filament have not been extended to more complicated physical situations. We consider the planar vortex filament under the quantum LIA, which accounts for mutual friction and the velocity of a normal fluid impinging on the filament. We show that, for most interesting situations, a filament which is planar in the absence of mutual friction at zero temperature will gradually deform owing to friction effects and the normal fluid flow corresponding to warmer temperatures. The influence of friction is to induce torsion, so the filaments bend as they rotate. Furthermore, the flow of a normal fluid along the vortex filament length will result in a growth in space of the initial planar perturbations of a line filament. For warmer temperatures, these effects increase in magnitude, since the growth in space scales with the mutual friction coefficient. A number of nice qualitative results are analytical in nature, and these results are verified numerically for physically interesting cases.

show abstract

Section: Introductionmentioning

confidence: 99%

Dynamics of a planar vortex filament under the quantum local induction approximation

Gorder

2014

Proc. R. Soc. A.

View full text Add to dashboard Cite

show abstract

“…Our approach is based on the observation, first made by Hasimoto [30], [31], [8], [9] in the context of fluid dynamics, that the one dimensional nonlinear Schrödinger equation (NLSE) describes string-like objects such as vortex filaments. For this he introduced a change of variables that relates the wave function of the NLSE to the Frenet frame representation of a space curve.…”

Section: Introductionmentioning

confidence: 99%

Energy functions for stringlike continuous curves, discrete chains, and space-filling one dimensional structures

Jiang

Niemi

2013

Phys. Rev. D

View full text Add to dashboard Cite

The theory of string-like continuous curves and discrete chains have numerous important physical applications. Here we develop a general geometrical approach, to systematically derive Hamiltonian energy functions for these objects. In the case of continuous curves, we demand that the energy function must be invariant under local frame rotations, and it should also transform covariantly under reparametrizations of the curve. This leads us to consider energy functions that are constructed from the conserved quantities in the hierarchy of the integrable nonlinear Schrödinger equation (NLSE). We point out the existence of a Weyl transformation that we utilize to introduce a dual hierarchy to the standard NLSE hierarchy. We propose that the dual hierarchy is also integrable, and we confirm this to the first non-trivial order. In the discrete case the requirement of reparametrization invariance is void. But the demand of invariance under local frame rotations prevails, and we utilize it to introduce a discrete variant of the Zakharov-Shabat recursion relation. We use this relation to derive frame independent quantities that we propose are the essentially unique and as such natural candidates for constructing energy functions for piecewise linear polygonal chains. We also investigate the discrete version of the Weyl duality transformation. We confirm that in the continuum limit the discrete energy functions go over to their continuum counterparts, including the perfect derivative contributions. * Electronic address: hushuangwei@gmail.com † Electronic address: yjiang@shu.edu.cn ‡ Electronic address: Antti.Niemi@physics.uu.se 1 arXiv:1210.7371v1 [hep-th]

show abstract

“…If the charged particle moves parallel to magnetic field, the Lorentzian force acting on the particle is zero. When the two vectors (velocity and the magnetic field) are perpendicular to each other, the Lorentz force is maximum (for details, see [4,2,3,6,7,9,8]). …”

Section: Introductionmentioning

confidence: 99%

Notes on magnetic curves in 3D semi-Riemannian manifolds

Özdemi̇r¹,

Gök²,

Yaylı³

et al. 2015

Turk J Math

View full text Add to dashboard Cite

A magnetic field is defined by the property that its divergence is zero in three-dimensional semi-Riemannian manifolds. Each magnetic field generates a magnetic flow whose trajectories are curves γ , called magnetic curves. In this paper, we investigate the effect of magnetic fields on the moving particle trajectories by variational approach to the magnetic flow associated with the Killing magnetic field on three-dimensional semi-Riemannian manifolds. We then investigate the trajectories of these magnetic fields and give some characterizations and examples of these curves.

show abstract

Motion of a Vortex Filament and its Relation to Elastica

Cited by 93 publications

References 3 publications

Dynamics of a planar vortex filament under the quantum local induction approximation

Dynamics of a planar vortex filament under the quantum local induction approximation

Energy functions for stringlike continuous curves, discrete chains, and space-filling one dimensional structures

Notes on magnetic curves in 3D semi-Riemannian manifolds

Contact Info

Product

Resources

About