Breaking news: PhD studentships (scholarships) available for UK and EU* students in the Department of Engineering Mathematics at the University of Bristol for immediate start.
Due to a number of students withdrawing for personal reasons, there are now several PhD studentships available that must be taken up by September 2016. I am looking for motivated and able students who are interested in doing research at the intersection of Applied Mathematics and Engineering/Science (my interests are quite broad!). In particular, I have three different topics that I’m actively pursuing at the moment all of which feature numerical computation/numerical analysis:
- Nonlinear dynamics of stochastic differential equations — I’m interested in investigating how the tools and concepts of nonlinear dynamics and bifurcation theory can be applied to stochastic differential equations arising from various application areas (e.g., neuroscience or climate science).
- Control-based continuation — numerical continuation is a very effective tool for investigating the nonlinear behaviour and bifurcations of mathematical models, and control-based continuation is a means for applying this tool to physical experiments (engineered systems or, hopefully, biological systems) without the need for a mathematical model. Research in this area requires a very interesting mix of numerical analysis, control theory, system identification and the theory of stochastic processes (I don’t expect students to have a background in all of these subjects!).
- Equation-free methods and agent-based modelling — equation-free methods are a means for obtaining a macroscopic model from microscopic simulations. They have been used for many physical processes previously and I am interested in how they can be extended to agent-based models, such as models of Zebrafish locomotion to investigate the dynamics of shoaling (Zebrafish are just one example).
I have also worked extensively with delay differential equations and, though I don’t have any active work in this area at the moment, I’m happy to solicit project suggestions in this area. All of these projects are very open ended and I’m happy to work with students to tailor the projects to their own interests.
There is no deadline for these studentships, though obviously it’s better to apply sooner rather than later. If you are interested, get in touch for more information.
* EU students are eligible provided they have been resident in the UK for at least 3 years. See the EPSRC website for more details.