Magnetic vortex filament flows

2007/08/01 by Manuel Barros, José L. Cabrerizo, Manuel Fernández +1 · 10 citations
Engineering · Physics and Astronomy · #Characterization and Applications of Magnetic Nanoparticles #Magnetic properties of thin films #Model Reduction and Neural Networks

paper · doi:10.1063/1.2767535

Abstract

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 Schrödinger equation showing the solitonic nature of those.

Citations

• Periodic orbits in magnetic fields and Ricci curvature of Lagrangian systems
• General helices and a theorem of Lancret

Cited by

• Magnetic curves corresponding to Killing magnetic fields in \mathbb E³E3
• A new approach for magnetic curves in 3D Riemannian manifolds
• A non-Newtonian magnetic curves in multiplicative Riemann manifolds
• Dual magnetic curves and flux ruled surfaces
• Magnetic flux surfaces and magnetic curves with Bishop frame in Euclidean 3-space
• Singularity properties of null killing magnetic curves in Minkowski 3-space
• Flux ruled surfaces and the magnetic curves obtained from the curvature theory
• Magnetic spherical indicatrix of a ruled surface
• Geometric properties of lightlike magnetic curves and magnetic flux surfaces in Minkowski 3-space
• Optical hausdorff quantum energy of spherical magnetic particles. [europepmc]

Related

• MHD dynamo generation via Riemannian soliton theory
• Riemannian geometrical constraints on magnetic vortex filaments in plasmas
• Particles trajectories in magnetic filaments
• Hasimoto Transformation and Vortex Soliton Motion Driven by Fluid Helicity
• Kirchhoff's analogy for a planar ferromagnetic rod