Magnetic vortex filament flows

被引：139

作者：

Barros, Manuel ^{[1
]}

Cabrerizo, Jose L.

Fernandez, Manuel

Romero, Alfonso

机构：

[1] Univ Granada, Fac Ciencias, Dept Geometria & Topol, E-18071 Granada, Spain

[2] Univ Seville, Fac Matemat, Dept Geometria & Topol, E-41012 Seville, Spain

来源：

JOURNAL OF MATHEMATICAL PHYSICS | 2007年 / 48卷 / 08期

关键词：

D O I：

10.1063/1.2767535

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We exhibit a variational approach to study the magnetic flow associated with a Killing magnetic field in dimension 3. In this context, the solutions of the Lorentz force equation are viewed as Kirchhoff elastic rods and conversely. This provides an amazing connection between two apparently unrelated physical models and, in particular, it ties the classical elastic theory with the Hall effect. Then, these magnetic flows can be regarded as vortex filament flows within the localized induction approximation. The Hasimoto transformation can be used to see the magnetic trajectories as solutions of the cubic nonlinear Schrodinger equation showing the solitonic nature of those.

引用

页数：27

共 30 条

[1]

[Anonymous], 1962, Introduction to Nonlinear and Differential Integral Equations

[2] Models of relativistic particle with curvature and torsion revisited [J].

Arroyo, J ;

Barros, M ;

Garay, OJ .

GENERAL RELATIVITY AND GRAVITATION, 2004, 36 (06) :1441-1451

[3] Periodic orbits in magnetic fields and Ricci curvature of Lagrangian systems [J].

Bahri, A ;

Taimanov, IA .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1998, 350 (07) :2697-2717

[4] The Gauss-Landau-Hall problem on Riemannian surfaces -: art. no. 112905 [J].

Barros, M ;

Romero, A ;

Cabrerizo, JL ;

Fernández, M .

JOURNAL OF MATHEMATICAL PHYSICS, 2005, 46 (11)

[5] General helices and a theorem of Lancret [J].

Barros, M .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1997, 125 (05) :1503-1509

[6]

Besse A.L., 1987, EINSTEIN MANIFOLDS

[7] ON CURVATURE AND TORSION OF AN ISOLATED VORTEX FILAMENT [J].

BETCHOV, R .

JOURNAL OF FLUID MECHANICS, 1965, 22 :471-&

[8] Finite-gap solutions of the vortex filament equation: Genus one solutions and symmetric solutions [J].

Calini, A ;

Ivey, T .

JOURNAL OF NONLINEAR SCIENCE, 2005, 15 (05) :321-361

[9]

Da Rios L.S., 1906, CIRC MAT PALERMO, V22, P117

[10] MOTION OF A VORTEX FILAMENT AND ITS RELATION TO ELASTICS [J].

HASIMOTO, H .

JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN, 1971, 31 (01) :293-&

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