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.

Research team

Student: Mr Jack Wildman;   Primary supervisor: Dr Daniel Colquitt;   Secondary supervisor: Dr Stewart Haslinger;   Post-doctoral Research Associate: Vacant.

Postdoctoral research associate

We are seeking to appoint a Postdoctoral Research Associated in in the Mathematical Modelling of Wave Propagation in Complex Media. You will work closely with Dr Daniel Colquitt, along with industrial partners and academic collaborators, on the Research Project Grant 'Multiscale Multiphysics structured interfaces' funded by The Leverhulme Trust and led by Dr Colquitt. You will join the Waves & Continuum Mechanics Group in the Department of Mathematical Sciences, at the University of Liverpool.

As part of the research team, you will develop novel mathematical models of Multiphysics multiscale interfaces. You should have (or be about to obtain) a PhD in applied mathematics. You should have strong numerical and analytical skills, along with experience in applying them to physical problems. Experience of tackling challenging problems related to wave propagation in structured media would be a distinct advantage. Applications from candidates familiar with asymptotic analysis and methods associated with integral equations, including the Weiner-Hopf approach, would be particularly welcomed. You will be expected to work effectively as a member of the research team. You should demonstrate excellent verbal and written communication skills and be able to write clearly and succinctly for publication.

The post is available as soon as possible but must commence no later than July 2024. It is a fixed term post for 24 months.

Applications closed

Application deadline: 30th September 2023.

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.

Research team

Student: Mr Finley Boulton;   Primary supervisor: Dr Daniel Colquitt;   Secondary supervisor: Dr Sebastian Timme;   Industrial Supervisor: Dr Duncan Williams, Chief Scientist Acoustics, Dstl.

The project, undertaken in collaboration with the Dstl, 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. The project started on October 1st 2023 and runs for four years.

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.

Research team

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

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.

Research team

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

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. The project started on October 1st 2022 and runs for four years.

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.

Research team

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.