Research

I am often too busy to keep this page updated. Rather than have a long list of outdated updates, it suffices to say that there is a lot of interesting research I do, and you can drop by the department to see it! You are better off looking at my Google Scholar for papers.

A good way to learn about what I do is to examine my PhD student talks! Here are a few that have been recorded over the last little while.

• Piotr Morawiecki gives a talk on mathematical models of flooding
• Josh Shelton gives a talk on parasitic gravity-capillary waves
• Yyanis Johnson-Llambias gives a talk on water waves due to flows past smoothed bodies

For researchers who are interested in my work on better understanding differences in flood estimation models, see a dedicated section: Asymptotics for intermodel comparisons of flood-estimation models.

My research interests include:

• Classical hydrodynamics: free-surface flows; gravity-capillary waves; wave-structure interactions; ship hydrodynamics; Korteweg-de Vries-type equations and nonlinear waves
• Low Reynolds number flows: theory and modeling of viscosity and surface-tension dominated flows, including thin film or Hele-Shaw-type problems; the study of fluid instabilities (e.g. gravity-driven dripping of thin films)
• Elasticity and solid mechanics: coupling fluid mechanics with solid mechanics; understanding fluid-structure interactions between free-surfaces and elastic membranes (e.g. contact lenses), theory and modeling of tissue and tumour growth.
• Formation and dynamics of biological patterns: studying the dynamics of patterns in reaction-diffusion problems
• Singular perturbation theory: exponential asymptotics and asymptotics beyond-all-orders; singularity formation in fluid and solid phenomena (e.g. rupturing of thin films and solids, moving contact line problems, etc.)
• Numerical methods: notably boundary integral methods for free-surface flows