PhD Projects
Contact: info@mathrad.ac.ukMaThRad will offer PhD studentships at either the University of Warwick, University of Bath or the University of Cambridge. The PhD projects will be supported by our academic and industrial partners.
Opportunities will be posted here when they are available.
Interacting particle methods for improved simulation algorithms in the nuclear energy industry
Funded Studentship at the University of Bath
This project is offered by the EPSRC Centre for Doctoral Training in Statistical Applied Mathematics (SAMBa), for entry in September 2025.
Nuclear energy is and will be an important part of the future energy mix. Whilst the physical laws which underpin different stages of the nuclear energy cycle are generally well understood, solving the systems accurately and quickly remains challenging, and is an important challenge in the design, operation and safety of modern generation processes.
The ”gold standard” of numerical methods in the nuclear industry is Monte Carlo, since Monte Carlo methods are able to handle sophisticated designs and accurately incorporate complex nuclear data. Methods used in different applications include power iteration (for eigenvalue problems) and adaptive multi-level splitting for rare event problems. Both of these algorithms rely on the simulation of many particles which are simulated largely independently, but with times at which actions are performed which depend on the whole population. Such systems of particles are an example of interacting particle systems.
The aim of this project is to understand probabilistic properties of these algorithms, and how they feed into error analysis and other properties of the system, such as analysis of sensitivities of the answers to small changes in properties of the underlying system, such as fuel concentration, or rod positions.
Hybrid numerical algorithms for radiation transport
Funded Studentship at the University of Bath
This project is offered by the EPSRC Centre for Doctoral Training in Statistical Applied Mathematics (SAMBa), for entry in September 2025.
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.
