PhDStudentship: Computational methods for evolving-domain problems with application to phase transitions in materials

This is an interdisciplinary PhD project that unites applied mathematics (continuum mechanics, stability analysis), computational mathematics (numerical methods for PDEs, numerical analysis) and engineering (mechanics of materials).

A large range of physical phenomena, taking place in materials, involves propagating interfaces between distinct material phases. A typical example is the process of formation of oxides, where the interface is a chemical reaction front between the oxidised and the pristine phases. Behaviour of such materials is described using partial differential equations (PDEs) that are defined on domains with time-dependent interfaces – the so-called free-boundary problems. Even though these problems have been studied since mid-twentieth century, their computational handling still presents a challenge, especially in a highly non-linear case.

The aim of this project is to advance further one of the methods to handle problems with propagating interfaces – the cut-finite-element method, specifically targeting PDEs describing phase transitions in materials. Within this approach, phase boundaries are handled as sharp (infinitely-thin) interfaces that move across a fixed finite-element mesh. The developments will focus on improving accuracy and efficiency of the computational approach when applied to PDEs describing a range of material systems revealing multi-physics behaviour, such as chemo-mechanical (e.g. formation of oxide layers on metals, formation of solid-electrolyte interphase on battery electrodes) or magneto-mechanical (e.g. twin-boundary kinetics in magnetic shape-memory alloys).

The successful candidate will become a member of the Computational Science and Engineering Group (CSEG) and will join a team with extensive expertise in computational materials modelling and phase transformation processes. This studentship is fully funded by the M³4Impact programme, a £9 million Expanding Excellence in England (E3) grant. The successful candidate will be a part of a dynamically-growing research group and will benefit from training and other initiatives funded by this grant. The project will be supervised by Dr Mikhail Poluektov and co-supervised by Prof Andrew Kao and Dr Ivars Krastins.

Funding:

The successful candidate will receive a contribution to tuition fees, equivalent to the University Home Rate, currently £5,006 (FT), for the duration of their scholarship. International applicants may need to pay the remainder tuition fee for the duration of their scholarship.

This fee is subject to an annual increase.

The bursary is for 3 years with a potential extension of up to a maximum of 12 months. Funding extensions may be granted if the student demonstrates, to the satisfaction of the M³4Impact Principal Investigators and PhD supervisors, that the thesis can be completed during the granted extension period.

For exceptional international applicants the tuition fees may be covered by the M³4Impact.

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