Entanglement and Linking in Divergence-free Vector Fields

speaker: Gunnar Hornig (The University of Dundee)

abstract: It is possible to extend the notion of the linking number between two closed curves in three dimensions to field lines of a divergence-free vector field by defining an averaged asymptotic linking number (V.I. Arnold 1974). This number is equal to the so-called helicity integral over the domain and constitutes a topological invariant. This invariant has been widely used, for example to understand the dynamics of magnetic fields in plasmas or the dynamics of vortices in fluids.

We give a short overview of the properties of the helicity integral, show how it is applied and discuss the possibility of finding similar integrals which measure other (higher-order) types of linking. We then present some recent results regarding the turbulent relaxation of braided magnetic fields which demonstrate the relevance of invariants that go beyond magnetic helicity.

timetable:
Wed 18 May, 16:45 - 17:30, Aula Dini
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