Supervisor: Prof Tristan Pryer
Partners: MaThRad
Radiation transport plays a crucial role in numerous scientific and industrial domains, including nuclear engineering, medical physics and space technologies. These fields often require the simulation of complex systems where accurate and efficient numerical methods are essential. While both deterministic and stochastic methods have been developed for this purpose, each comes with its own advantages and limitations.
Deterministic methods, such as finite element discrete ordinates methods, are often preferred for their efficiency and accuracy in structured geometries but can struggle with handling uncertainties and highly heterogeneous environments. On the other hand, stochastic methods, Monte Carlo techniques, are the gold standard in representing random phenomena and complex geometries but can be computationally expensive and very slow to converge in certain cases. Hybrid algorithms seek to combine the strengths of both approaches, leveraging the deterministic framework where appropriate while incorporating stochastic components to handle the complexities of real-world applications.
The aim of this project is to develop, analyse and implement these hybrid numerical algorithms, assessing their performance in important applications. We will explore how to optimise these methods, focusing on error analysis, computational efficiency and adaptability to different physical settings. This work will contribute to improved simulation accuracy and reliability in critical areas of technology and science.
As well as joining the SAMBa CDT, the successful candidate will also join an active research community of mathematicians, medical physicists, engineers and industrial collaborators as part of the MaThRad programme grant. This provides many opportunities to collaborate with and visit international interdisciplinary teams.
Keywords: Numerical methods, Radiation transport, Nuclear engineering, Medical physics, Space technologies
Enquiries and Applications
Informal enquiries are encouraged and should be directed to supervisor Prof Tristan Pryer, tmp38@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.
"We are working with SAMBa to develop new tools for managing risk by combining deterministic and probabilistic methods."
"The students at SAMBa were engaging and motivated, above all interested in solving real world problems with their skills. As a result of SAMBa we have taken huge strides forward in a new technique in the assessment of arthritis related to psoriasis and the effect of treatment.
There were a couple of ongoing personal research collaborations with Novartis in the Department of Mathematical Sciences that were brought together to develop a set of challenges for Novartis’s participation in ITT12. These consisted of questions exploring modelling and data integration in pharmacokinetics models, and finding effective routes to drug development for liver disease.
“Alongside the specific potential benefits to applied flood and coastal risk management, I have seen first-hand that the SAMBa CDT produces high calibre doctoral graduates with excellent skills in problem formulation and collaborative problem solving...”
"The collaboration between SAMBa, UNAM and CIMAT has strengthened us in tools and techniques to visualize new perspectives of development and collaboration with a focus on generating value for other institutions."
“We have a great track record of successful collaboration with SAMBa, as we share a common aim – applying the latest thinking in mathematics and statistics to solve real-world problems."
"We found participating in the ITT to be an unique and engaging environment for exchanging ideas and it was also good fun. Above all it produced some truly innovative thinking."
"For a small company like ours, this research is vital in delivering our vision to create digital technologies that change what’s possible for clinicians and patients."
"Working with SAMBa students to relay how our industry understands the daily challenges in aerospace design and manufacture and for them to translate them into statistical/mathematical models and methods was a refreshing and rewarding concept."