The design and safety studies of nuclear reactors requires the solution of many multi-physics problems. This approximation is often prohibitively expensive as it requires coupling of complex neutronics and thermal hydraulics dynamics. New techniques that are both efficient and accurate need to be developed to meet the challenge. The goal of this PhD work is to conceive and develop numerical schemes to solve the Boltzmann equation for neutron transport on polygonal and polyhedral meshes within the context of finite element methods for the spatial discretisation, and other related techniques for other variables. This will also encompass research on graph algorithms for partitioning a set of ordered mesh cells. This project is being done in collaboration with the CEA, the French Alternative Energies and Atomic Energy Commission.
Knowing the genealogical history of a given species helps us understand its evolution better. The genealogical history can be formally encoded into a graph known as the ancestral recombination graph (ARG). However, the ARG is never available in practice, and inferring the ARG from sequenced DNA data is a challenging problem since the computational time grows hyper-exponentially. The research objective is to study existing algorithms such as the ARGweaver and ARGinfer, as well as the conditional sequential Monte Carlo method, to make improvements for the Arbores algorithm.
In this research we describe population dynamics in ecosystems and evolutionary processes through the lens of stochastic mathematical biology and develop methods to analyse phenomena that emerge from fluctuations and uncertainty. In particular, we model the dynamics of large random ecosystems in terms of randomly distributed interaction parameters and derive solutions for the power spectral density of this stochastic process based on statistical properties of the underlying interaction network. Furthermore, we investigate the evolution of mating types in isogamous species, where the number of compatible mating types for sexual reproduction is not necessarily limited to two. Unlike in a model with neutral mutations, we find that fitness differences damp the growth of the average number of mating types and derive predictions independent of the underlying fitness distribution. This research opens up further questions on how fluctuations in ecosystems affect the evolutionary dynamics of embedded species.