Applied Mathematics

Listed on this page are current research projects being offered for the Vacation Scholarship Program.

For more information on this research group see: Applied Mathematics

Fluid mechanics of active granular systems

Dense arrays of microorganisms exhibit striking collective motions, jamming and turbulent-like properties, and their behaviour underpins a range of processes in biology. However, the physical principles giving rise to their collective properties are not well understood.

Co-supervised by Dr. Douglas Brumley and Professor Antoinette Tordesillas, this project will investigate the bulk properties of active suspensions, and develop simplified models to predict the flow of nearly-jammed arrays of microorganisms. Some background in fluid dynamics and computational work would be beneficial. No biological background necessary.

Contact: Douglas Brumley, Antoinette Tordesillas

What kind of random walk are these biological cells doing?

Biological cell motility is a key aspect of embryonic growth, homeostasis and disease processes. It is possible to observe isolated cells migrating, apparently in some random way, on planar substrates. How well can simple models of this random motion describe what is seen? If the model is “correct”, how accurately can the underlying parameters be deduced from limited data? Can limited data distinguish clearly between several competing plausible models?

This is an opportunity for a student with appropriate skills with Matlab or or other computational tools and an interest in probability to learn about various random walk models and run computer experiments to investigate these interesting questions.

Contact: Barry Hughes