The third order helicity of magnetic fields via link maps

Details The third order helicity of magnetic fields via link maps The third order helicity of magnetic fields via link maps

2008-08-11

arxiv.org/abs/0808.1533v3

Mathematics

Differential Geometry

30 pages, 5 figures

Scientific paper

We introduce an alternative approach to the third order helicity of a volume preserving vector field $B$, which leads us to a lower bound for the $L^2$-energy of $B$. The proposed approach exploits correspondence between the Milnor $\bar{\mu}_{123}$-invariant for 3-component links and the homotopy invariants of maps to configuration spaces, and we provide a simple geometric proof of this fact in the case of Borromean links. Based on these connections we develop a formulation for the third order helicity of $B$ on invariant \emph{unlinked} domains of $B$, and provide Arnold's style ergodic interpretation of this invariant as an average asymptotic $\bar{\mu}_{123}$-invariant of orbits of $B$.

Affiliated with

Also associated with

No associations

Rating

The third order helicity of magnetic fields via link maps does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with The third order helicity of magnetic fields via link maps, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The third order helicity of magnetic fields via link maps will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-493290