Numerical Analysis Seminars: Geometry of field lines in elasticity and MHD
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).
Contact David.Bourne@durham.ac.uk for more information