Singularities in thin magnetic films
Understanding ferromagnetic materials is not only interesting from an application point of view, but also from a mathematical point of view, as their highly complex behaviour can be captured by a fairly simple variational principle based on the micromagnetic energy. Scaling limits of the micromagnetic energy then allow for a rigorous understanding of pattern formation in ferromagnetism, and sometimes achieve a substantial reduction in complexity. A particularly striking example is the formation of point vortices, which can happen in the bulk or at the boundary of a magnetic element. Sometimes the infinite-dimensional magnetic system can be reduced to a finite dimensional one involving only the singularities.
There are several interesting directions to pursue here, especially for boundary vortices. On the static level, it would be interesting to analyse the relevant discrete to continuum limits or to classify all possible stationary points. For dynamics, there are many problems where results for interior singularities are known, but boundary counterparts are lacking. Applications could include understanding the effect of corners on pinning of magnetic boundary vortices and their influence on switching and data storage properties of thin magnetic elements.
The PhD student will work on a problem that has connections to the calculus of variations and partial differential equations, and should have some experience in this area.
Apply: This studentship is open now and will be available until it is filled. To apply please visit the University Of Nottingham application page: http://www.nottingham.ac.uk/pgstudy/apply/apply-online.aspx
For any enquiries please email: Dr Matthias Kurzke email@example.com
Summary: UK/EU students - Tuition Fees paid, and full Stipend of £13,863 (2014/15 rate). There will also be some support available for you to claim for limited conference attendance.
Eligibility/Entry Requirements: We require an enthusiastic graduate with a 1st class degree in Mathematics (or another highly mathematical field), preferably of the MMath/MSc level, or an equivalent overseas degree (in exceptional circumstances a 2:1 class degree, or equivalent, can be considered).