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Department of Mathematical Sciences

Seminar Archives

On this page you can find information about seminars in this and previous academic years, where available on the database.

Numerical Analysis Seminars: Geometry of field lines in elasticity and MHD

Presented by Mitchell Berger, University of Exeter

6 May 2016 14:00 in CM105

I will explore two topics concerning the geometry of field lines. In elasticity theory, a solid in equilibrium has a divergence-free stress tensor. We can regard rows of the stress tensor as vector fields; mapping where their field lines go provides a picture of how forces flow through a solid. This leads to a method for finding average stress and strain in a volume in a way which automatically preserves the elastic energy. The linking of magnetic field lines provides a conserved quantity in MHD known as magnetic helicity. I will discuss recent proposals for defining an absolute measure of helicity when the field lines are not closed, but instead have endpoints (e.g. on the surface of the sun).

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