University of British Columbia

Hi! My name is Mike. Thanks for visiting my UBC Math page. Here's what you can find on this page:

**Academic:**

I'm a grad student in the Institute for Applied Mathematics, currently toiling away at a PhD :-)

My academic time is divided between research meetings (which often degenerate into amusing conversations), courses (usually math, physics, or computer science), napping on the couch (an essential element to any office), and of course actually doing research! My supervisor is Brian Wetton, who also supervises Iain Moyles.

I've always enjoyed the *applications of math* more than the theories, although theory can be both useful and beautiful. I've worked on a variety of applied projects, with a few currently underway - see the research portion of this page for details of the various projects. To be very brief, the problems I'm currently working on are:

- exploring the operation of electrodialysis machines used for water filtration
- using atomic force microscopy measurements of superconducting surfaces to better understand the likely effects of surface roughness upon the Meissner state of type 2 superconductors and
- investigating the effect of PEDF in Osteogenesis Imperfecta VI (Brittle Bone Disease).

**Personal:**

I grew up in Winnipeg, Manitoba—the mosquito capital of Canada... also famous for the fantastically cold winters, which I am pleasantly reminded of each year when I go back to see family and friends over the break. I came out to Vancouver for my undergraduate studies, and I have since become very fond of BC. The rain doesn't bother me so much—I guess I prefer it to having my eyelashes frozen together during a Manitoba winter...

There are so many amazing parks and hiking trails near Vancouver, and I really enjoy exploring them. Some other interests include: classical music - many pieces by Beethoven, Vivaldi, Mozart, Bach, Handel, or even traditional Sufi and Andean music; languages (French and I know a little Mandarin); cats (they are such amazing creatures); healthy eating, including organic/raw/vegan/fermented foods, green juices, local and sustainable food; baking (both raw and conventional); and meditation (I have been teaching meditation and related metaphysical practices for a number of years as a volunteer).

I'm also a fan of Piled Higher and Deeper comics (perfect depictions of grad student life!).

My teaching positions are below.

- Math 448, Summer 2014.
- Math 215, Term 2, Winter 2013-2014.
- Math 104, Term 1, Winter 2012-2013.
- Math 105, Term 2, Winter 2011-2012.
- Math 103, Term 2, Winter 2010-2011.
- Math 101, Term 2, Winter 2009-2010.

I tutored Math and Physics with the AMS for 3 years, and privately I have been tutoring Math and Physics since I was in grade 7.

My usual rate is $60/hour for individuals and $90/hour for groups of any size (2 or more). I will not privately tutor anyone in a course I'm teaching (and generally, though not always, this also applies to courses I am marking for) due to a conflict of interest. Contact me if you'd like private tutoring. Email is best. I may or may not be available depending on the time of year and my schedule.

**UBC Math Courses I Have Tutored:**

- Math 100, 101, 102, 103, 104, 105, 110, 152, 180, 184
- Math 200, 215, 220, 221
- Math 317, 400

In term 1 of the 2013-2104 academic year, I ran review sessions for Math 100/180. I also ran some review sessions for Math 105 for the term 2 of the 2012-2013 academic year. Problems are available here.

**Research Experience and Interests**

- Electrodialysis (current): Some modern plans for water filtration systems that purify salt water and those that can reduce the waste water of fracking use electrodialysis as a means to pass ions through selectively permeable membranes with the help of an electric potential gradient. I recently began work in trying to understand and interpret experimental data for these systems, with the aim of gaining insights into the effects of different design modifications.
- Osteogenesis Imperfecta VI (current): OI type 6 is a severe form of brittle bone disease where patients have bones that are both very soft (due to delayed mineralization) and very brittle (due to over mineralization). Researchers of the disease suspect an abnormally low concentration of a protein known as PEDF is responsible for the disease. Through an industrial workshop in Montreal, a group of us began to study the process of bone mineralization and the potential role of PEDF with mathematical models. Our work is very preliminary, but our current model qualitatively predicts the delayed bone development of OI type 6 patients if these patients have a decreased concentration theshhold of calcification-inhibiting enzymes necessary for bone development. Here are slides from our oral report. More work is being done.
- Superconductors (current): A superconductor, when in the Meissner state expels magnetic fields from its interior. Very near its surface, there is an exponential decay in field strength that is predicted by the London equation, a special limit of the Ginzburg-Landau equations, provided the surface is flat. In the superconductivity literature, the assumption of a flat interface was taken for granted, but due to experimental measurements of a non-exponential decay in field strength near the surface of a superconductor, experimentalists asked the question of whether small-amplitude perturbations could have an effect on the field profile. This paper presents the results of the analysis undertaken in trying to answer the question. More results are being compiled into a paper.
- Mass Spectrometry: A mass spectrometer separates atoms and molecules based on their mass. This has applications in detecting heavy metal or radioactive contaminants in air or water supplies. At a recent problem solving workshop, a group of us worked in collaboration with PerkinElmer on creating a new method of mass spectrometry that allows for continuous measurements of concentrations, without the costly use of magnetic fields. We found that it may be possible to create an electric field configuration that causes periodic oscillations dependent upon mass, which would allow for different chemical species to be separated spatially or detected with Fourier analysis. Our report can be found here.

- Nuclear Fusion: Magnetized target fusion is a relatively new idea for producing conditions for hydrogen fusion on earth. The essence of the idea is to confine a plasma in a magnetic field and compress it by an intense pressure-focused pulse so that it yields a high enough particle density and pressure for fusion to take place, releasing energy. A local Canadian research company has a design of such an apparatus that they are currently working on engineering: the plasma is found in an empty region of a vertical central cylindrical axis of a sphere of molten lead-lithium. Pistons deliver an immense pressure on the outer walls of the spherical lead-lithium region, with the pressure growing in magnitude as it reaches the plasma, causing it to compress to a very small radius. Simulating this design requires a careful interplay of plasma physics and fluid dynamics, and reasonable modelling skills. My research interest here is in developing a suitable model, performing numerical simulations for the hyperbolic conservation laws, and doing asymptotic analysis to estimate the influence of various factors on the reactor performance qualitatively and analytically. Here is a paper covering some of the numerical aspects and here is a paper covering some of the asymptotic estimates.
- Gas Diffusion in Fuel Cells: Fuel cells are costly to build, and developing accurate techniques to simulate their performance beforehand is essential in minimizing production costs. Unfortunately, there are many complex processes that take place within a fuel cell, one of the most important processes is gas diffusion. Those in industry who work with numerical simulations are often puzzled as to what formulation to adopt for gas diffusion: Fick (a simple gradient flow often formulated with a single Fick diffusion coefficient) or Maxwell-Stefan (a complex flow rate that depends upon the concentration gradients of all other species and experimentally determined binary diffusivities). The research I have been involved with on this topic was in studying the two formulations in a simple one-dimensional model of a PEMFC gas diffusion layer. Through nondimenzionalization, and a two-term formal asymptotic expansion, the two models provide nearly identical predictions. Furthermore, Fick diffusion is really a special limit of Maxwell-Stefan diffusion and in many industrial applications, the simpler Fick formulation can be used with reasonable precision. A paper explaining these results has been submitted to the Journal of Power Sources.
- Malaria Management: Recently, a fungus has been discovered that could help reduce malaria-prevalence in endemic regions. The fungus infects mosquitoes, but instead of killing them like a pesticide, it kills the malaria that they carry and could transmit to humans. One biological question that arises is, if this fungus is used, should it be engineered to also kill mosquitoes? A few colleagues and I came up with a model of how this fungus could be used in combating malaria, and through studying a model system of ODEs numerically and analytically, we demonstrated that under certain assumptions on the mosquito carrying capacity and growth rate, the fungus should be engineered to have minimal virulence to mosquitoes to have an optimal effect in reducing malaria. Under other assumptions on the carrying capacity, different behaviour can be observed. Our paper has been published by Malaria Journal.

Papers:

- A Quantitative Prediction of Dead Layers Induced by Surface Roughness for YBCO (2014, in preparation for submission), in collaboration with Ching-Yang Fang (Alex).
- Asymptotic Estimation for Minimal Plasma Radius in a Spherically Symmetric Magnetized Target Fusion Reactor Model (2014, submitted to SIAM Journal on Applied Mathematics)
- From Exam to Education: The Math Exam/Educational Resources wiki (2014, submitted to PRIMUS), in collaboration with Carmen Bruni, Christina Koch, Bernhard Konrad, Iain Moyles, and William Thompson.
- Investigation into Fusion Feasibility of a Magnetized Target Fusion Reactor (2014, accepted to Journal of Fusion Energy), in collaboration with Sandra Barsky and Brian Wetton.
- A Comparison of Fick and Maxwell-Stefan Diffusion Formulations in PEMFC Cathode Gas Diffusion Layers (2013, submitted to Journal of Power Sources), in collaboration with Brian Wetton.
- Assessing the optimal virulence of malaria-targeting mosquito pathogens: a mathematical study of engineered Metarhizium anisopliae (2013, published in Malaria Journal), in collaboration with Bernhard Konrad, Anja Gumpinger, Jielin Zhu, and Daniel Coombs.
- Mathematical modelling of the effect of surface roughness on magnetic field profiles in type II superconductors (2013, published in Journal of Engineering Mathematics), in collaboration with Brian Wetton and Rob Kiefl.

Proceedings:

- Modelling the Effects of Surface Roughness on Superconductors (2012, published in muSR 2011 proceedings), in collaboration with Brian Wetton and Rob Kiefl: a compact summary of our detailed paper studying surface roughness of superconductors.

Theses:

- Masters Thesis (2010): Asymptotic and Numerical Modeling of Magnetic Field Profiles in Superconductors with Rough Boundaries and Multi-Component Gas Transport in PEM Fuel Cells
- Honours Thesis (2008): Computation of Gluon Scattering Amplitudes in N=4 SYM Gauge Theory via AdS-CFT Duality

**Past:**

- 2014 - Fields-MPrime Industrial Problem Solving Workshop in Toronto.
- 2014 - PRIMS YRC 2014 in Vancouver: organizer.
- 2014 - IAM seminar retreat in Vancouver: oral presentation.
- 2013 - Simon Fraser University, Applied Math Colloquium in Burnaby: oral presentation on modelling nuclear fusion.
- 2013 - Centre de Recherce Mathematiques Industrial Problem Solving Workshop in Montreal.
- 2013 - IAM Seminar Retreat in Vancouver: oral presentation.
- 2012 - CAIMS 2012 Annual Meeting in Toronto, Ontario: oral presentation.
- 2012 - UBC Math Undergraduate Colloquium at UBC: oral presentation on industrial modelling for fuel cells and nuclear reactors.
- 2011 - Applied Mathematics, Modeling and Computational Science Conference in Waterloo, Ontario: oral presentation
- 2011 - ICIAM 2011 in Vancouver, BC: poster presentation
- 2011 - 12th International Conference on Muon Spin Rotation, Relaxation and Resonance in Cancun, Mexico: poster presentation
- 2011 - PIMS YRC 2011 in Vancouver, BC: oral presentation.
- 2011 - IAM Seminar Retreat 2011: oral presentation.

You can read my CV here (December 2013).