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Mathematical Modelling

The study of observable phenomena (physical, biological, engineering and many others) can be approached from different perspectives and studied at various levels. Experimentalists gather data to gain an understanding of the phenomena, which may lead to a theory that explains how the underlying mechanisms function and predicts the behaviour of the phenomena.

However, analysis of the observed data in and of itself is often insufficient for providing a global understanding of a phenomenon or for establishing a coherent predictive theory. The construction of a theoretical model of the observed phenomenon that can be studied mathematically has become a successful and recognized additional method of gaining insight into the way nature works. Furthermore, some natural phenomena can only be studied using this approach, because they are not amenable to experimental manipulation - for example, global warming due to an increase in the concentration of carbon dioxide in the atmosphere, and the dynamics of galaxy evolution.

Several members of the Faculty of Science develop and study mathematical models to understand physical phenomena:

  • Dr. Luciano Buono's research work consists of developing new theoretical tools in symmetric differential equations and delay-differential equations, and using these tools for the modelling and analysis of biological phenomena such as networks of neurons in animal locomotion and other rhythmic phenomena.

  • Dr. Greg Lewis' field of research is Applied Dynamical Systems. His current research focuses on the bifurcation analysis of nonlinear partial differential equations using a combination of analytical and numerical methods. An area of application of particular interest is Geophysical Fluid Dynamics.

  • Dr. C. Sean Bohun specializes in the mathematical modelling of physical phenomena primarily driven by industry defined in the broadest sense, including anything of either commercial or societal benefit. His work includes:
    • problems concerning the growth of crystals (typically III-V) and finding growth procedures that reduce the thermoelastic stress and produce very high quality crystals
    • problems from the oil and gas industry, including wellbore flow, well logging and innovative techniques used to open fissures.
    These problems combine physical chemistry, fluid flow and heating in complicated geometries. He also:
    • models electrical motors at a fundamental level to design optimal ways of controlling torque and speed of the motor with a minimal amount of additional hardware
    • works within the field of forensics to look at the diffusion of fluids through soil in the formation of a cadaver decomposition island to help determine a time of death
    • models sewage pumps and helps identify better manufacturing techniques to increase the lifetime of the pumps.

Other faculty members at UOIT involved in Mathematical Modelling include:

  • Dr. William R. Smith (Mathematics and Physics)
  • Dr. Isaac Tamblyn* (Physics)

*Accepting graduate students

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