Research output per year
Research output per year
Dr
Research activity per year
My research interests lie in applied mathematics at the intersection of asymptotic analysis of multiscale dynamical systems, nonlinear partial differential equations, and functional analysis. Currently, I am interested in mathematical climate models which involve heat convection, phase separation and solidification in sea ice. I am investigating the network formation and evolution of brine inclusions in sea ice. In this model, the salt entropy relative to the liquid water molar function provides a transparent mechanism for salt rejection under ice formation.
I also study the effective thermal conduction in sea ice in the presence of fluid flow, as an important example of an advection-diffusion process in the polar marine environment. Using new Stieltjes integral representations for the effective diffusivity in turbulent transport, we have obtained a series of rigorous bounds on the effective conductivity.
This model describes the evolution of a brine inclusion up to a ‘pinch-off point’ when a single inclusion splits into two smaller inclusions. Numerical solutions of the model equations highlight the role of thermal gradients in the pinch-off of brine channels into spherical inclusions: large gradients and warm temperatures, such as those found near the bottom of sea ice, produce a range of small and large inclusions, whereas large gradients and colder temperatures, such as those found near the top of the sea ice, will lead to equal-sized inclusions. This varying of inclusion structure and connectedness with temperature is critical to the permeability of the ice, and thus the percolation and drainage processes.
I believe anyone can love mathematics - they merely need a teacher that can light their way. Furthermore, I am firmly committed to each student as an individual and hope to give them the best possible learning experience. My main goal, as a teacher, is to provide my students with the tools and confidence to enable them to succeed.
Methods for Mathematical Computation
Mathematics & Climate
Partial Differential Equations
Ordinary Differential Equations
Linear Algebra
Calculus I
Research output: Contribution to journal › Article › peer-review
Research output: Contribution to journal › Article › peer-review
Research output: Contribution to journal › Article › peer-review
Research output: Chapter in Book/Report/Conference proceeding › Conference proceeding contribution › peer-review