Michael Lindstrom

Research Experience and Interests

1. Homelessness (current): Los Angeles, along with many major cities, has a huge homeless problem. Right now there are over 50,000 homeless people in Los Angeles, and the problem is very complicated. There is little understanding as to the mechanisms that yield such high rates of homelessness and how individual characteristic traits influence the outcome of homeless individuals. For over a year now, I've been studying this problem from a number of different angles, which is leading to three rather different research problems: firstly, by collaborating with the Los Angeles Police Department and analyzing arrest records, we are discovering hidden demographics within the homeless population. Secondly, by combining data such as median household income and various proxies for commerce that can be obtained for distinct geographic regions, along with annual homeless counts imputed by the Los Angeles Homeless Services Authority, it seems possible to predict, at least approximately, how the homeless population will evolve on small spatial scales known as census tracts. The main techniques used have included: topic modelling, mixture of Gaussians for clustering, and artificial neural networks. Lastly, from a more theoretical perspective, I have been working to develop a partial differential equation that models the evolution of the homeless population density. The equation is a nonlocal, nonlinear reaction-advection-diffusion equation. I have been working to prove the well-posedness of the model, ensuring that as a mathematical model it yields physically sensible results (finite total populations, non-negativity of the population -- all the stuff that really should be true if the model equation can approximate reality in a meaningful way).
2. 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. I'm wrapping up some work on time scale analysis of thin-film viscous suspensions, but the field is full of open, unanswered problems. With colleagues, we have begun to study suspensions with multiple components.
3. Gang Reduction and Youth Development (GRYD) (current): The GRYD program schedules after-school programs and other supportive interventions for youths who are deemed at risk for joining gangs. We are provided with surveys the participants take, roughly every 6 months, with the surveys asking questions that attempt to measure the participant's attitudes and inclinations towards risky behaviours such as violence or lack of family contact. By modelling the responses as a dynamical system and using Dynamic Mode Decomposition (DMD), we have been able to analyze modes of growth and periodicity within the responses. DMD has also given us a means of predicting future risk-levels with comparable performance to a shallow neural network.
4. Twitter Data (current): Twitter is a popular social network where users "tweet" short stories, comments, or ideas. The tweets themselves have a well-defined time, but also may include geotagging information such as the location the tweet was made. The amount of things one can do with this data is almost unlimited. We have focused upon dynamically clustering the tweets into topics and using the topics and information within the text of a tweet to infer a user's location information. We also found it is possible to predict the time/location of a "current event" by studying the frequency of tweets over space and time along with their corresponding topics.
5. Osteogenesis Imperfecta VI: 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 threshold of calcification-inhibiting enzymes necessary for bone development. Here are slides from our oral report.
6. Nutrient Absorption: 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 systems, only few quantitative relationships are known.
7. 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 here.
8. 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.
9. 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.
10. 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.
11. 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.
12. 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

• Conversion of Saline Water and Carbon Dioxide into Value-Added Chemicals by Electrodialysis (2017, published in Journal of CO2 Utilization), in collaboration with Saad Dara, Joseph English, Arman Bonakdarpour, Brian Wetton, and David Wilkinson.
• Assessment of the Effects of Azimuthal Mode Number Perturbations upon the Implosion Processes of Fluids in Cylinders (2017, published in Physica D).
• Effect of Surface Roughness on the Magnetic Field Profile in the Meissner State of a Superconductor (2016, published in 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, published in 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, published in 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, published in 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.

Papers in Progress

• Fast time dynamics of particle diffusion for viscous suspension flow in an inclined channel
• Arrest records reveal hidden demography of homelessness
• Using local geograhic features and fluctuations to predict changes in the visible homeless population of Los Angeles
• A Partial Differential Equation Model for the Homeless Population

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