Mathematical modelling of multiscale multiphysics structured interfaces

This PhD project is funded by the Leverhulme Trust as part of the Research Project Grant "Multiscale multiphysics structured interfaces", led by Dr Daniel Colquitt.

Whilst research in metamaterials (structured materials that can control waves and energy) has undergone a renaissance, the majority of work has focused on controlling a single physical domain - usually light. In contrast, this project seeks to develop a mathematical framework to study, design, and create multiphysical metasurfaces [1] (structured interfaces where two or more physical systems interact, such as solids and fluids) capable of manipulating waves across many physical phenomena. Structured interfaces arise in many real-world applications - anywhere two media meet, from antenna designs, to the interface between the ocean and sea-bed, the foundations of modern buildings, medical implants, and safety-critical power generation components.

Some preliminary work has been undertaken in this area [2] for fluid-loaded plates, developing the earlier work on the seismic metawedge [3]. In particular, it was demonstrated that a structured interface could be designed to mode-convert a localised subsonic interfacial wave into a bulk acoustic wave which propagates away from the interface and radiates energy at infinity.

The project will be undertaken in collaboration with an industrial partner and there will be ample opportunities to interact with industrial stakeholders and explore potential applications of the work.

The successful candidate will have a strong background in applied mathematics, as evidenced by a first-class (or strong upper second-class) MMATH/BSc in Mathematics or Theoretical Physics with a substantial applied mathematics focus (or equivalent). Applicants with a relevant MSc incorporating a substantial element of applied mathematics are also welcomed.

The successful applicant will receive formal training in the analysis of partial differential equations, including functional analysis, generalised derivatives, fundamental solutions, Green's functions, integral transforms, characteristics, multipole expansions and dipole fields, and variational approaches and weak solutions. However, prior experience in any of these areas would be advantageous.

The project will commence on 1^st July 2023. https://www.liverpool.ac.uk/study/postgraduate-research/how-to-apply/.

Please ensure you include the project title in your online application and quote reference MPPR002.

The School of Physical Sciences is an Athena SWAN Silver Award holder and is committed to encouraging, developing and supporting women in their research and academic careers. We are committed to providing an inclusive environment in which diverse students can thrive. Applications from women, disabled and Black, Asian and Minority Ethnic candidates, who are currently under-represented in the sector, are particularly encouraged