Mathematics research

Research areas

• 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 explaining 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:

  • In his research work, Luciano Buono, PhD develops new theoretical tools in symmetric differential equations and delay-differential equations, and uses these tools for the modelling and analysis of biological phenomena such as networks of neurons in animal locomotion and other rhythmic phenomena.
  • Greg Lewis, PhD researches applied dynamical systems. His current research focuses on the bifurcation analysis of nonlinear partial differential equations using a combination of analytical and numerical methods. He is particularly interested in geophysical fluid dynamics as an area of application.
  • C. Sean Bohun, PhD, 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 involved in mathematical modelling include:

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

  *Accepting graduate students
• Computational science

  Until recent times, theoretical mathematical analysis has been the only method for reliably investigating mathematical models. In the early 1960s, the use of computer simulations began to enter the realm of scientific investigation, as exemplified by the pioneering work of Ed Lorenz in the study of meteorological phenomena, which led to the birth of what has come to be called Chaos Theory.

  The widespread access to increasingly powerful computers, and the development of new computational algorithms, has stimulated the growth of the emerging field of computational science, a new methodology for carrying out scientific investigation that is complementary to the traditional approaches of theory and experiment. Computational science combines the implementation of mathematical models, computer algorithms and knowledge in a particular area of application. It provides an additional tool for the study of phenomena, and facilitates the study of problems that are intractable or difficult to study using conventional approaches.

  • The research of Dhavide Aruliah, PhD, concerns the development, implementation and analysis of efficient algorithms for scientific computation. Dr. Aruliah's research entails both approximate numerical and exact symbolic algorithms, as appropriate, for obtaining meaningful solutions of scientific problems.

  • The computational materials science research of William R. Smith, PhD, involves the molecular-level modelling of fluids, with the aim of predicting their bulk properties. Such information is used in the design and control of many chemical processes. Ongoing projects involve the design of environmentally benign refrigerants and the development of theoretical and computational tools to accurately predict chemical speciation in aquatic systems.

  Other faculty members at our university who are involved in Computational Science include:

  • Anatoli Chkrebtii, PhD (Physics)
  • Fedor Naumkin, PhD (Chemistry)
  • Eleodor Nichita, PhD (Energy Systems and Nuclear Science)
  • Isaac Tamblyn, PhD (Physics)
  • Ed Waller, PhD (Energy Systems and Nuclear Science)