# Kevin A. Mitchell (CV)

I am a graduate student in the Department of Mathematics at Simon Fraser University. I am pursuing my PhD in Applied Mathematics.

## Research

### Equatorial Kelvin Waves

I am investigating equatorial Kelvin waves that occur in the rotating shallow water (RSW) model for atmospheric fluid flow. I am interested in developing a method by which these Kelvin waves can be incorporated into the full-sphere, quasi-geostrophic potential vorticity (PV) model developed by my supervisor Prof. David Muraki and Andrea Blazenko as part of her M.Sc. thesis. PV isolates the slow-wave dynamics in RSW but does not currently include the climatologically important Kelvin wave, which plays a role in the propagation of atmospheric disturbances near the equator such the El Niño-Southern Oscillation.

### Fourier computing on the sphere

Together with Andrea Blazenko and under the supervision of Prof. David Muraki I have been working on a numerical scheme for spectrally computing PDEs on the sphere. This scheme uses the regular Fast Fourier Transform rather than a decomposition into spherical harmonics. Here is a link to the Matlab source code.

### Snow surface morphology

I completed my M.Sc. in the UBC dept. of Phys. and Astro. under the supervision of Prof. Tom Tiedje. The topic of my thesis was the application of a pattern forming chaotic partial differential equation to the formation of suncups in snow.

### Chaos and pattern formation

Since arriving at SFU I have also been working with Prof. Ralf Wittenberg on the mathematical side of the PDE I studied in my Masters thesis. The equation is similar to the chaotic Kuramoto-Sivashinsky equation

th = - ∇2h - ∇4h - (∇h)2

but with the additional nonlinear term ∇2(∇h)2 which interestingly causes solutions to become "less chaotic" as well as increase in time and length scale.

## Course Notes

• Spring 2009: MATH 795 - Stochastic Differential Equations

## Teaching

• Spring 2013: MACM 316 - Numerical Analysis
• Spring 2011: MACM 316 - Numerical Analysis
• Fall 2010: MACM 316 - Numerical Analysis
• Summer 2009: MACM 316 - Numerical Analysis

## Computing

I use the GNU/Linux operating system pretty much exclusively for all my computing needs. My distribution of choice is Debian for its breadth, stability and commitment to free software principles.

On this note, I have been shifting away from using non-free Matlab in my research in favour of free software alternatives based on the Python programming language. Numpy is a powerful extension to Python that allows you to perform advanced operations on arrays and vectors similar to Matlab and is essential to almost any scientific computing in Python. Scipy uses Numpy to provide higher level numerical computing tools like black box ODE integrators, optimisation, and image processing. Matplotlib and Mayavi are very powerful 2d and 3d Python plotting libraries that can be used to produce truly impressive figures. Finally Ipython provides a more versatile command line interface to Python with command history and tab completion.