SAMBa builds on, and brings together, research carried out throughout the Department of Mathematical Sciences, working in collaboration with industry, policy-makers, and academics from other disciplines.
Find out about some of the different projects undertaken by our students, what attracted them to research, and how their projects have progressed.
Emma Horton - Neutron Transport
The goal of my research is to use the probabilisitic theory of branching processes to design efficient algorithms for the simulation of nuclear reactors.
I was attracted to this project as it builds on a lot of interesting mathematics I had studied as an undergraduate, bringing them together to tackle a really important real world application. We are working in collaboration with Wood PLC, a multinational energy services company, to develop fast and accurate simulations of neutron transport, scattering and absorption in a reactor. I have been using mathematical ideas and tools from probability theory, statistics and analysis, combined with advanced programming and optimisation techniques. I have produced an open-source simulation package based on my work and written three scientific papers, including one published in the Journal of Statistical Physics.
Aoibheann Brady - Statistical Trends in Peak River Flow
I work on the application of Bayesian spatial methods to statistically quantify environmental trends, particularly focusing on peak river flow.
Coming into SAMBa I was certain that I wanted to do a research project connected with statistics, and that it needed to have an important real-world application, in order to provide some practical meaning to my work and help shape my thoughts. I have had plenty of opportunities to find out about the research going on in Bath, and was attracted to work with Illaria Prosdocimi on the Bayesian analysis of trends in peak river flows. My supervisory team also includes Julian Faraway, and I feel I've been very lucky with this combination - there's always a new way to look at a problem as we all have different perspectives, and both of them have been incredibly supportive to me throughout.
Our recent paper, published in the Hydrological Sciences Journal, presents evidence for a clear upwards trend in the magnitude of peak rivers flows in Great Britain in recent decades. We apply a multilevel Bayesian framework to disentangle the effects of different climate indices, allowing for a better understanding of damaging trend.
Matt Durey - Bouncing Droplets
My research is on mathematical models of the bouncing and self-propulsion of a liquid droplet ‘walking’ on the surface of a vibrating fluid bath.
Since their discovery in 2005, the 'quantum-like' wave-particle interactions observed in the famous experiments of bouncing liquid droplets have been a source of a huge amount of excitement in the mathematics and physics communities. When Paul Milewski (SAMBa co-director) first showed me a movie of the walking droplets I was instantly hooked, and I knew it had to be the topic of my PhD. The problem interests me for several reasons: the system is incredibly rich and a real challenge to model due to vastly different length and time scales. The accompanying Faraday wave field guides the droplet, providing an example of a macroscopic pilot-wave system that exhibits several features previously thought to be exclusive to the quantum realm.
During my PhD I published papers on the modelling and analysis of this system in Chaos, and the Journal of Fluid Mechanics. Recently, I have been exploring the effect of different submerged geometries to guide the droplets' motion. Together with colleagues at Bath and MIT (where I now work), we have recently submitted a paper on the dynamics of a single droplet trapped in a circular well, and we are now working on studying more complex geometries.
Kate Powers - Flow Instability in Turbochargers
Many modern cars rely on a turbocharger to deliver more power from a smaller engine, but these can be susceptible to damage caused by instability in gas flow. I build and analyse mathematical models with the aim of predicting a particular phenomenon called "surge".
This project came out of a collaboration between mechanical engineering and mathematics in Bath. Turbochargers use exhaust gasses from a car engine to drive a compressor, which raises the pressure of the air entering the engine. They mean more power can be generated from a smaller, greener, engine. Surge is a flow instability that occurs at low flow rates: if there isn’t enough air going through the compressor, the flow will want to actually reverse, causing pressure oscillations, and a large temperature increase, all of which are damaging to the compressor and its installation.
I have always had an interest in engineering and I enjoy the mathematics of modelling and dynamical systems so this project was the best of both worlds for me. I visited the Mech Eng lab to find out more about the project, and was instantly taken by it. We have one paper about to be published in Journal of Turbomachinery, which I presented at the ASME Turbo Expo in Phoenix, AZ this June.
Owen Pembery - Uncertainty Quantification for Wave Propagation
I work on uncertainty quantification for waves in random media; I study waves moving through materials that are random. I spend some of my time proving things about the PDEs modelling these waves and some of my time designing and analysing algorithms that compute properties of these waves.
Uncertainty quantification lies at the intersection of analysis, numerical analysis, and probability. It's so varied, which means I need to get my head around a lot of things! The broad grounding I got in my first year of SAMBa has been really helpful. I took courses across the full SAMBa spectrum and I can now understand and work with a wide range of topics across a lot of areas of mathematics. I've also written a lot of code as part of my PhD, and the computing skills I've learned during my time in SAMBa have been vital for that - I've been able to use version control to track changes to my code (and undo when I've made a mistake!), and I've made my work reproducible, so other researchers can easily take what I've done, check it, and build on it.
The outputs from my project so far include two papers, with more to come when I finish my thesis! I've also really enjoyed being able to travel quite a bit to present my work at lots of different academics events, from Oxford and London to Minnesota, Rhode Island, Chile, and Vienna.