A single mathematical equation—the Boltzmann transport equation—governs how radiation particles move through materials, but current methods for solving it rely on decades-old techniques that struggle with complex real-world scenarios. This matters because accurate radiation modelling is essential for designing new nuclear reactors (both fission and fusion), safely decommissioning old ones, delivering effective medical radiation therapy, and protecting satellites and spacesuits from high-energy radiation in space. The existing approaches, based on simulated particle counting and Monte Carlo methods, have seen limited input from the mathematical sciences community since the 1980s. Meanwhile, modern mathematical theories have emerged that could handle far more complex situations—such as time-dependent behaviour, rare-event sampling, and multi-physics modelling—but they have not yet been applied to radiation transport. If successful, this programme will combine probability theory, advanced Monte Carlo methods, and inverse problems to produce predictive models with quantifiable accuracy and software prototypes ready for real-world use. The UK could gain a disruptive advantage in the 21st-century nuclear industry, with safer reactors, more effective cancer treatments, and more resilient space technologies.
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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.
Alexander Cox (Co-Investigator)Ana Lourenco (Co-Investigator)Andreas Kyprianou (Principal Investigator)Colin Baker (Co-Investigator)Emma Horton (Co-Investigator)Eugene Shwageraus (Co-Investigator)Geoffrey Parks (Co-Investigator)Sarah O S Osman (Co-Investigator)Tristan Pryer (Co-Investigator)
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