PhD, Applied Mathematics, University of British Columbia

University of California, Los Angeles

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

**Academic:**

I'm an Assistant Adjunct Professor for the Program in Computing at the University of California, Los Angeles. I completed my doctor of philosophy at the University of British Columbia in Vancouver, BC, Canada. Having reached the "other side" in that I'm no longer a grad student has its perks, but like being a grad student, this is only a temporary position and I don't know where I'll be after this.

My main responsibilities include research (see some of my topics of interest below) and teaching programming courses.

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:

- studying how the flow of viscous fluids is affected by the concentration of large particles suspended in the fluids and the inclination angle,
- exploring how nutrients are absorbed into the human body, 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 completed my university education in the beautiful city of Vancouver, BC, with tons of beautiful parks and hiking trails in close proximity. I'll miss Vancouver's excellent public transit system, delicious sushi, and amazing simultaneous views of the mountains and ocean, but I'm sure LA will be cool, too! I'm already impressed by the delicious vegetarian food and the number of juice bars. And there's actually really nice weather in the winter (I prefer it to the summer).

I really like hiking and being out in nature. 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 (reasonaby accurate depictions of what it's like to be a grad student - so many memories...).

**Teaching Positions**

I am currently teaching courses at UCLA. Prior to this, I taught for 6 years at UBC. My teaching statement is here and I will update this periodically. If you are interested in seeing my full teaching dossier, email me and I can send you a much more detailed and lengthy document.

Current and past websites for my teaching are below, including some of the exams, etc.

**Upcoming:**

- PIC 10A (intro to programming, C++), Winter Quarter 2016, UCLA

**Past:**

- PIC 10A (intro to programming, C++), Autumn Quarter 2015, UCLA
- Math 105 (integral calculus for commerce and social sciences), Term 2, Winter 2014-2015, UBC.
- Math 448 (directed studies in mathematics), Summer 2014, UBC.
- Math 215 (ordinary differential equations), Term 2, Winter 2013-2014, UBC.
- Math 104 (differential calculus for commerce and social sciences), Term 1, Winter 2012-2013, UBC.
- Math 105 (integral calculus for commerce and social sciences), Term 2, Winter 2011-2012, UBC.
- Math 103 (integral calculus for life sciences), Term 2, Winter 2010-2011, UBC.
- Math 101 (integral calculus for physical sciences), Term 2, Winter 2009-2010, UBC.

**Math Education Resources wiki**

I am contributor and administrator for the **Math Education Resources wiki**. This project began as an online database of past UBC Math Exams with hints and solutions, and has steadily expanded to a more complete online learning resource with questions by topic and interactive features. Currently we're doing an education study on the effectiveness of the wiki.

**Math Teaching Peer Review**

Within the department at UBC, we organized a teaching peer review team. Graduate and postdoctoral instructors could request a peer review of their class. The process was informal and confidential, and involved one of the members of the team meeting with an instructor to discuss any aspects of their teaching they were interested in hearing feedback about, an in-class observation, and a follow-up discussion. Perhaps I'll get around to organizing something like that here, if there's enough interest.

I have a lot of private tutoring experience - since I was in grade 7 I have been tutoring privately. Given my other work committments, it is unlikely I have time to tutor, but you can email me and check my availability. Most of my tutoring experience is in math and physics. My rate is $80/hour for individuals and $120/hour for groups of 2 or more.

I have run some large review sessions for first year math courses at UBC, some of them attended by more than 400 students at a time. Perhaps the problems will be useful for some of you out there looking for review questions. Problems are available here.

**Research Experience and Interests**

- Fluid Flows (current): There are a vast array of interesting phenomena that emerge in studying the flow of viscous fluids, based on the concentration of particles that may be in suspension and the inclination angle. Right now the field is full of open, unanswered problems such as how suspensions behave with multiple mixture components.
- Nutrient Absorption (current): Biological processes governing digestion and nutrient assimilation are complex, and mathematical modelling can yield deep, qualitative insights into how the various processes work together when, as with many biological sysems, only few quantiative relationships are known.
- 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.
- Electrodialysis: 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 was involved in simulating the system under various settings, employing a combination of asymptotics and numerics. A paper that combines the theoretical work with experiment is in progress and should be submitted soon.
- Superconductors: 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. The previous work was extended by using experimental measurements of the superconducting surfaces in the simulations, and the results can be found here.
- 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 article on the problem is 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. Another paper outlining a study of the instabilities associated with asymmetric implosions can be found here.
- 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 Heat and Mass Transfer.
- 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:

- Assessment of the Effects of Azimuthal Mode Number Perturbations upon the Implosion Processes of Fluids in Cylinders (2016, submitted to Physica D).
- Effect of Surface Roughness on the Magnetic Field Profile in the Meissner State of a Superconductor (2016, accepted to Journal of Superconductivity and Novel Magnetism), in collaboration with Ching-Yang Fang (Alex) and Rob Kiefl.
- Electric Ion Dispersion as a New Type of Mass Spectrometer (2015, accepted to Mathematics-in-Industry: Case Studies), in collaboration with Iain Moyles and Kevin Ryczko.
- Asymptotic Estimation for Minimal Plasma Radius in a Spherically Symmetric Magnetized Target Fusion Reactor Model (2015, published in SIAM Journal on Applied Mathematics)
- From Exam to Education: The Math Exam/Educational Resources wiki (2015, accepted 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, published in 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 (2015, under revision with Heat and Mass Transfer), 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:

- Doctoral Thesis (2015): Investigation into the Feasibility and Operation of a Magnetized Target Fusion Reactor : Insights from Mathematical Modelling
- 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:**

- 2015 - Slides from my PhD Defense Presentation
- 2014 - Math Department Colloquium
- 2014 - Undergraduate Math Colloquium
- 2014 - Fields-MPrime Industrial Problem Solving Workshop in Toronto. Here's our group presentation.
- 2014 - PIMS 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 (Feb 2016).