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PhD in Mathematics: Magnetic Helicity Flow in the Sun and Heliosphere, University of Exeter, UK

The Centre for Geophysical and Astrophysical Fluid Dynamics at Exeter is one of the leading research groups of its kind in the UK. Our research encompasses the Fluid Dynamics of Weather and Climate, Theoretical Fluid Dynamics, Astrophysical Fluid Dynamics, Solar-Terrestrial Plasmas and Space Weather. We invite applications to study for a fully-funded PhD starting in Sept 2016.

This project will investigate the mathematics and physics of magnetic helicity transport. Applications will include plasma physics (helicity transport and decay in laboratory devices), space physics (the atmosphere of the sun and the heliosphere), and elasticity theory (twisting and buckling of elastic rods and molecules).

Helicity integrals measure geometric and topological properties of a magnetic field such as twisting, writhing, and linking of field lines. While they are readily calculated in volumes with planar or spherical boundaries, other volumes of interest (e.g. cubes, tori, hemispheres) present interesting complications. Using tools from differential geometry such as the Gauss Bonnet theorem, we will develop computer codes for calculating helicity in these volumes. One applications lies in finding the net helicity flow into each hemisphere of the sun and heliosphere, taking advantage of recent and upcoming observations (e.g. SoHO, SDO, STEREO and Cluster). Another application involves providing tools for analysing numerical experiments in MHD theory which employ rectangular volumes. The expressions for helicity flow through boundaries can be employed in analysing vortex motion on surfaces. The twist and writhe of polymer molecules with ends pinned on a surface can also be studied using the techniques we will develop.
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