Research projects

Here is a list of the funded research projects that I am involved in. Some of these projects have positions available for PhD students and Postdoctoral Research Associates. I am always interested in recruiting excellent PhD students and I am always happy to discuss the possibility of developing bespoke projects with potential students. If you are interested in reading for a PhD under my supervision please Get in touch.

Multiscale multiphysics structured interfaces

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 (Maradudin, 2011) capable of manipulating waves across many physical phenomena. Metasurfaces are structured interfaces where two or more physical systems interact, such as solids and fluids. 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.

This project provides for the following research and teaching positions:

PhD Studentship

Fully funded studentship for three years, which provides UK tuition fees and matainance at the UKRI Doctoral Stipend rate of £17,668 per annum (2022/23). Non-UK students may apply but will be required to pay additional tuition fees. 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.

More information and apply now

Application deadline: 31st March 2023.

Fixed term lecturer

There will be two six-month, or one twelve-month, fixed-term lectureship(s) to cover my teaching responsibilities during this research project. The candidate should hold a PhD in Mathematics. Experience of teaching undergraduate and postgraduate courses in the UK would be an advantage. Further details will be released in due course.

Applications opening soon

Position available from: September 2023.

Postdoctoral research associate

This project also provides for a two-year postdoctoral research associate (PDRA) position. The PDRA will work closely with the PhD student and our industrial partner. The successful candidate will have significant postgraduate experience in formal analysis, including asymptotic analysis, integral equations (including the Weiner-Hopf method), a numerical analysis (including finite element analysis). Further details will be released in due course.

Applications opening soon

Position available from: July 2024.

This work is graciously funded by The Leverhulme Trust through Research Project Grant RPG-2022-261 and is undertaken in collaboration with KANDE International Ltd

Machine Learning for Data Driven Sound Propagation Modelling

This project will develop a series of high-fidelity digital twins capable of encapsulating a number of critical dynamic phenomena, which affect the propagation of sound waves through ocean environments, including internal waves, multi-scale structural thermal and temporal variations and fluctuations, scattering by non-smooth interfaces and boundaries (e.g. semi-submerged structures, sea bed, surface), currents, eddies, and fronts. The resulting sound propagation models, and advanced understanding embodied within these models, will enable the Royal Navy and other users of the ocean, the means to improve the effectiveness of their sonar systems and achieve the best results from sonar deployments and operations.

The developed models will be capable of intelligently adapting their approach and selecting the best solution method based on the input data, computational and operational constraints, desired outputs, and physical configuration. These models will incorporate advances in Finite Element Methods, via GPU parallel computing capability that has been largely untapped for underwater acoustics, along with hybrid semi-analytic coupling methods. Stochastic analysis of physical scattering models, incorporating real-world data, will provide a major step forward in the capability available to investigate dynamic ocean mechanisms. Analysis of simulated and measured oceanographic and acoustic data, including the use of artificial intelligence and machine learning techniques, will be supported by a parallel PhD project in the Department of Mathematical Sciences on Advances in mathematical modelling to study complex sound propagation in an inhomogeneous moving ocean. This will help to identify the properties and behaviour of different mechanisms. New ways of representing the specified mechanisms will be developed, and environment-specific modelling tools and innovative mathematical representations will be implemented.

PhD Studentship

This project is a funded Studentship for 4 years in total, commencing on 1st October 2023, and will provide UK tuition fees and maintenance at the UKRI Doctoral Stipend rate £17,668 per annum, 2022/23 rate). This studentship is open to British and EU nationals who are willing and able to obtain UK gov security clearance.

More information and apply now

Application deadline: 31st January 2023.

Students will be based at the University of Liverpool and will be part of the Distributed Algorithms CDT and Signal Processing research community - a large, social and creative research group that works together solving tough research problems. The successful applicant will be co-supervised by Dr Daniel Colquitt and work alongside our external partner Dstl. The industry supervisor will be Dr Duncan Williams: Chief Scientist Acoustics, Dstl.

MUSICA: Modelling UltraSonic Inspection of Challenging defects for Automated analysis

We will develop automated ultrasonic data analysis tools to improve the reliability of detection, sizing, and characterisation of defects which occur in high safety significance industrial plant. The project will develop capability for defects of critical industrial importance, targeting two species: Thermal Fatigue (a service induced species) and Hydrogen cracking (a manufacturing/welding defect). Both species are known to occur and often materially impact plant availability/longevity. This project will also enable capability for other challenging defect species going forward, such as stress corrosion cracks.

This project is in collaboration with Dr. S.G. Haslinger (PI), Dr. W. Christian, Prof. J. Ralph, Mr. M. Wright, Prof. M.J.S. Lowe, & Dr. P. Huthwaite.

This work is funded by The Research Centre for Non-Destructive Evaluation as a vision-focused core project.

Using machine learning and artificial intelligence to improve the tracking of vessels in sonar spectrograms

This PhD project explores creating an AI model that can correctly classify quiet targets in waterfall (sonar) data. Currently, waterfall data is analysed by human operators; however, this is time-consuming and expensive; these human operators outperform traditional automated passive contact follower algorithms, such as the Kalman and Alpha-Beta filters: these filters are susceptible to the abundant underwater noise and struggle with crossing tracks and quiet contacts. In contrast, humans can use their experience to learn how to mitigate the challenging aspects of the task. An automatic detection and tracking model that is more accurate and robust than traditional methods would reduce the human operator’s workload.

The project, undertaken in collaboration with the Ultra Group, is hosted at the University of Liverpool and is part of the Distributed Algorithms CDT and Signal Processing research community - a large, social and creative research group that works together solving tough research problems.

Student: Mr William Shaw.
Primary supervisor: Dr Murat Uney.
Secondary supervisor: Dr Daniel Colquitt.
Industrial Supervisor: Dr Cerys Jones, Ultra.

Underwater acoustics: Advances in mathematical modelling to study complex sound propagation in an inhomogeneous moving ocean

The aim of this well-funded PhD project is to develop models for underwater sound propagation through a moving inhomogeneous ocean, with an emphasis on enhancing the understanding of critical dynamic aspects, including:

  • Internal waves;
  • Microstructure variability
  • Scattering by rough surfaces, both stationary (seabed) and moving (sea surface); high sea states bring additional dynamic challenges such as large waves and infusion of air bubbles;
  • Seasonal, diurnal, and inter-diurnal changes;
  • Slow-moving horizontal currents, fronts, and eddies.

There is a lack of clarity within current literature as to the optimal representation of these dynamic phenomena within models, even for simplified two-dimensional cases. This project will address that issue by providing new insights that will also facilitate the development of three-dimensional and full four-dimensional, time-dependent propagation models.

Student: Miss Yiyi Whitchelo.

Primary supervisor: Dr Stewart Haslinger.

Secondary supervisor: Dr Daniel Colquitt.

Industrial Supervisor: Dr Duncan Williams, Chief Scientist Acoustics, Dstl.

A 4-year fully-funded EPSRC i-CASE studentship with the Defence Science and Technology Laboratory (Dstl) covering UK tuition fees, maintenance above the average UKRI Doctoral Stipend rate and an allowance for training, conference and research expenses.