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.
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
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.
- Spring 2009: MATH 795 - Stochastic Differential Equations
- Spring 2013: MACM 316 - Numerical Analysis
- Spring 2011: MACM 316 - Numerical Analysis
- Fall 2010: MACM 316 - Numerical Analysis
- Summer 2009: MACM 316 - Numerical Analysis
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.
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Last modified: Thu Oct 11 11:45:20 PDT 2012