CRM: Centro De Giorgi
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Entanglement and Linking

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.

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