A fully funded three-year PhD studentship under the supervision of Dr Michele Ruggeri, Dr Yue Wu and Prof. John Mackenzie (starting on 1 October 2023) is available in the Department of Mathematics and Statistics of the University of Strathclyde (Glasgow, United Kingdom). A recent technological innovation to increase the capacity of hard disk drives is heat-assisted magnetic recording (HAMR). Exploiting the fact that many magnetic properties of materials are temperature-dependent (for example, anisotropy, that is proportional to the strength of the magnetic field needed to write information on a disk, can be reduced by increasing the temperature), the basic idea of HAMR is to temporarily heat the disk via thermal pulses of a laser diode during writing. This reduces the anisotropy, which makes the material much more receptive to magnetic effects and allows to write to much smaller regions, increasing the overall capacity of the disk. The aim of this project is to advance the numerical analysis of the (stochastic) partial differential equations modelling HAMR. These include the (stochastic) Landau-Lifshitz-Gilbert and Landau-Lifshitz-Bloch equations, coupled with the Maxwell equations (modelling the magnetic field) and the heat equation (modelling the evolution of the temperature). We aim to develop structure-preserving finite element methods and study their rigorous convergence. This is a very exciting project which will allow the student to work at the interface between mathematical modelling, stochastic analysis and computational mathematics with applications firmly in sight.
The student will be a member of the Analysis group (Themes: Numerical Analysis and Stochastic Analysis) of the Department of Mathematics and Statistics. The project will provide training in mathematical modelling, partial differential equations, numerical analysis, scientific computing and stochastic analysis, thus equipping the student with highly desirable skills for working in either academia or industry. Further training will be provided for giving research talks, writing scientific papers and using computational software. Participation in seminars, workshops and conferences as well as research visits to the international collaborators will be strongly encouraged.
Applicants should have, or be expecting to obtain in the near future, a first class or good 2.1 honours degree (or equivalent) in mathematics or in a closely related discipline with a high mathematical content. Programming skills and some knowledge of analytical and numerical methods for the solution of (stochastic) partial differential equations are desirable.
Applications should include a motivation letter (max 1 page A4) and a curriculum vitae.
A first screening of all applications will take place on 31 May 2023.
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