Title: Mathematical Theory of Radiation Transport: Nuclear Technology Frontiers (MaThRad)
Funder: Engineering and Physical Sciences Research Council

Abstract: Nuclear technology is, by definition, based around the principle of subatomic physics and the interaction of radiation particles with materials. Whilst the microscopic behaviour of such systems is well understood, the degree of inhomogeneity involved means that the ability to predict the flux of particles through complex physical environments on the macroscopic (human) scale is a significant challenge. This lies at the heart of how we design, regulate and operate some of the most important technologies for the twenty-first century. This includes building new reactors (fission and fusion), decommissioning old ones, medical radiation therapy, as well as opening the way forward into space technologies through e.g. the development of space-bound mini-reactors for off-world bases and protection for high-tech equipment exposed to high-energy radiation such as satellites and spacesuits. Accurate prediction of how radiation interacts with surrounding matter is based on modelling through the so-called Boltzmann transport equation (BTE). Many of the existing methods used in this field date back decades and rely on principles of simulated (e.g. neutron) particle counting obtained by Monte Carlo and other numerical methods. Input from the mathematical sciences community since the 1980s has been limited. In the meantime, various mathematical theories have since emerged that present the opportunity for entirely new approaches. Together with powerful modern HPC and smarter algorithms, they have the capacity to handle significantly more complex scenarios e.g. time dependence, rare-event sampling and variance reduction as well as multi-physics modelling. This five-year interdisciplinary programme of research will combine modern mathematical methods from probability theory, advanced Monte Carlo methods and inverse problems to develop novel approaches to the theory and application of radiation transport. We will pursue an interactive exploration of foundational, translational and application-driven research; developing predictive models with quantifiable accuracy and software prototypes, ready for real-world implementation in the energy, healthcare and space nuclear industries. This programme grant will unite complementary research groups from mathematics, engineering and medical physics, leading to sustained critical mass in academic knowledge and expertise. Through a diverse team of researchers, we will lead advances in radiation modelling that are disruptive to the current paradigm, ensuring that the UK is at the forefront of the 21st century nuclear industry.

Lay abstract: The overarching objective of this programme grant is to integrate new mathematical perspectives into the interdisciplinary field of radiation transport modelling, through a foundational, translation and application driven approach in partnership with the energy, health service and space sectors. Foundational mathematical perspectives that have been developing in parallel to the theory of radiation transport modelling include the stochastic growth and spread of spatial branching (and indeed many other Markov) processes, the theory of Monte Carlo simulation for Feynman-Kac type functionals using a so-called interacting particle approach, uncertainty quantification, data assimilation and (Bayesian) inverse problems and optimisation. Our translational research objectives are to explore a fully integrated interdisciplinary approach with the physics and engineering of radiation transport, together with HPC considerations, weaving in new mathematical concepts into advancing Monte Carlo and numerical algorithms. Our application driven research objectives will be developed through two fundamental mechanisms: (i) A series of focused workshops three times per year will stimulate and focus research; (ii) postdocs recruited to this programme grant will each engage in a fully costed six-month internship with one or more of the many affiliated partners, ensuring impact acceleration where appropriate. These objectives are delivered through nine interrelated work packages titled as follows: - Mathematical representations of Boltzmann Transport Equation solutions - Correlation and path decomposition in spatial branching - Interacting particle systems in multiplying media - Monte Carlo for fixed source problems - Radiation transport for medical applications - Reactor modelling with higher complexity - Sensitivity and uncertainty in medical and reactor physics - Monte Carlo algorithms for future computing architectures - Case studies and industrial engagement

Research activity codes: 5.5 RADIOTHERAPY AND OTHER NON-INVASIVE THERAPIES
Health categories: GENERIC HEALTH RELEVANCE