Supervisor: Dr Phil Trinh
Partners: Wessex Water
We are seeking a candidate to work at the intersection of mathematics, modelling, and data analysis, with strong enthusiasm for applying their research to environmental science and seeing real-world impact.
This project will focus on the use of mathematical modelling and fluid simulation techniques to better understand how hazardous substances may be transported within rivers and water networks. The student will focus on developing new tools in mathematical analysis and computation to address real-world challenges with meaningful environmental impact. Physics-driven approaches using differential equations and networks will be considered. This project will work in collaboration with Wessex Water and the Department of Mathematical Sciences at the University of Bath. It will involve unique opportunities to work together with multidisciplinary teams.
This is more than just research—it’s a chance to make a tangible impact on environmental sustainability. It is also a chance to develop crucial research skills that will prepare you for both academic research and industrial research, both within mathematics, and also the wider physical sciences. If you’re excited by the prospect of using mathematics to solve real-world problems, and eager to help shape the future science of water resources, then this is the opportunity you’ve been waiting for!
The challenge
With new, stricter regulations and a growing public demand for cleaner, healthier rivers, the water industry is under more pressure than ever to innovate. Over the next few years, this field will see an explosion in the use of advanced water quality sensors, generating vast amounts of real-time data. However, along with this new sensing technology is the ever-pressing need for cutting-edge mathematical and statistical analysis to model and interpret the science. The next-generation tools used by the water industry must provide real-time scientifically-justified diagnostic, predictive and source apportionment capabilities. The proposed project seeks to initiate the design of such tools, allowing simulation and modelling of contaminants transported via water recycling centres and storm overflows or from diffuse sources such as land and road run-off water.
The studentship will focus on developing advanced mathematical models that will power the future of water quality monitoring. The research path will dive deep into physics-based theoretical models, tackling how contaminants move through water recycling systems and storm overflows. The challenging inverse problem of determining where contaminants may have originated from will be considered.
You will join a unique collaboration with Wessex Water, based in the southwest of England and one of ten water supply and sewage utility companies in the UK. The student will profit from a strong supervision team that combines primary expertise from the Department of Mathematical Sciences at the University of Bath, and also expertise from the Chemical Engineering department (who will inform on real data applications), and experts from Wessex Water, notably Dr John Bagnall and the Water Resources team. Wessex Water’s main headquarters are a short walk from the University of Bath campus.
This PhD will not only provide a platform for you to develop a career as an academic researcher, but also prepare you for careers in industry and environmental scientific research.
Project keywords: Mathematical modelling, mathematics of the environment, environmental engineering, river modelling, transport phenomena, pollution dynamics
References
An example of mathematical approaches for modelling environmental problems can be found in the recent 2024 thesis work of Piotr Morawiecki.
The PhD may involve the kind of environmental modelling seen in recent work by the Chemical Engineering group at Bath.
Candidate Requirements
In addition to the SAMBa entrance requirements, the ideal candidate would have undergraduate experience in some (certainly not all!) of the following specialisations: partial differential equations, continuum/fluid mechanics, numerical methods, mathematical or physical modelling, asymptotic analysis, environmental engineering, graphs and networks, machine learning.
Contact the SAMBa team at samba@bath.ac.uk if you are unsure about your eligibility and would like to discuss your potential application.
Enquiries and Applications
Informal enquiries are encouraged and should be directed to supervisor Dr Phil Trinh hppt20@bath.ac.uk.
Applications are open for entry in September 2025. Apply via the University of Bath’s online application form for an Integrated PhD in Statistical Applied Mathematics. Early applications are encouraged.
IMPORTANT:
When completing the application form:
1. In the Finance section, enter ‘SAMBa’ when asked to name the scholarship or PhD studentship you wish to be considered for.
2. In the Your research interests section, quote the project title of this project at the top of your statement or proposal and the name of the lead supervisor in the appropriate box.
