|Biomathematics and Fluids
|Department of Mathematics,
Who we are
Biomathematics and Fluids Seminar Series
- Computational Biology (S. Ilie)
This research is concerned with the development and analysis of
numerical methods for mathematical models in Life Sciences. A
particular focus is on developing effective and accurate algorithms
for the numerical solution of biochemical systems. Biochemical systems
may be continuous and deterministic, continuous and stochastic,
discrete and stochastic or a mixture of these (hybrid models).
Typically, these systems are nonlinear and exhibit multiple scales.
Applications to studying cellular dynamics and genetic networks are
also considered. Recent experimental techniques made it possible to
study gene regulatory networks in living cells as well as to generate
synthetic gene networks. A successful approach to studying these
networks should be based on accurate mathematical models and powerful
computational tools to simulate them.
- Mathematical Biology, Boundary
Value Problems and Boundary Layer Problems. (K. Lan)
Predator-prey systems: The dynamical
between predators and
their prey, which is one of the most important themes in ecology, can be
by establishing predator prey systems of two first-order differential
equations with suitable functional responses. The qualitative theories
of dynamical systems are used and the dynamical behaviours of such
predator-prey systems with initial states near equilibria can be
predicted for appropriate ranges of parameters involved. These dynamical
behaviours not only provide predication whether the two species will
suffer from mutual extinction but also get insight into the optimal
management of renewable resources like fishery and forestry.
Boundary value problems: Many problems
from nonlinear mechanics,
engineering, physics and biology can be changed into suitable ordinary,
fractional, and partial differential equations with various boundary
conditions. In most of these problems, the physical interest lies in the
existence and uniqueness of positive solutions of these equations. The
main interest is to establish new theories or apply the well-known
theories from nonlinear analysis to treat the existence of one or
In addition, reaction-diffusion equations arising
Falkner-Skan equations arising from boundary layer problems, and
variational inequalities and complementarity problems with applications
to partial differential inequalities are also under investigation.
- Interfacial instabilities in liquid films (J.P. Pascal) Liquid films with a free surface play an important role in many industrial and biological processes as well as phenomena encountered in the natural environment. In manufacturing, for example, liquid films are involved in coating operations. In biophysical applications examples include the tear film covering the eye and the fluid lining of mammalian lungs. Groundwater in unsaturated fractured rock is an example of a fluid film in an environmental setting.
Liquid films are subject to interfacial instability which can cause the film to rapture forming holes or a pattern resembling fingers. Flowing fluid films are also susceptible to inertial instability which leads to the formation of large amplitude wave structures propagating along the surface. Interfacial instability is often an undesired occurrence since the formation of dry patches or the development of a nonuniform thickness can adversely affect the function of the fluid layer. There are however situations where interfacial instability has a beneficial impact. In heat and mass exchangers, for example, the formation of interfacial waves improves the operation of the device since, as a result, there is an increase in the surface area of the liquid-gas interface which facilitates the heat or mass transport.
The interfacial stability of fluid films is affected by various factors such as heating and evaporation/condensation, electromagnetic fields and the presence of surfactants (contaminants in the fluid which lower the surface tension). Properties of the substrate (the solid underlying the fluid) such as having a corrugated surface or being composed of a material that is permeable to the fluid, also have an important effect on the stability of the fluid film. Mathematical models which incorporate these factors can be implemented to govern the evolution of the fluid film. They can predict the critical conditions for the onset of instability and the evolution of unstable flows.
- Blood Flow (K. Rohlf) Biological fluids such as blood exhibit complex flow behaviour that can generally be classified as non-Newtonian. Many non-Newtonian models have been used as models for blood so as to investigate the flow behaviour in physiologically meaningful geometries that arise in both healthy and diseased conditions. The majority of these models rest on the assumption that blood can be treated as a continuum, and that this assumption remains valid in all flow geometries.
The scope of this research is to use particle-based methods to incorporate complex particle interaction (such as aggregation, or the sticking together of red blood cells) in realistic flow geometries to determine the most appropriate flow model in the chosen geometry of interest.
- Mathematical Oncology and Immunology (K. Wilkie) This research develops mathematical models to help understand cancer growth and development and to predict progression and treatment outcomes. Specifically, we use mathematical techniques to test hypotheses about how various factors alter cancer progression, and about how the human body influences the disease and is in turn altered by its presence. Key factors in our work include the immune system, aging, and the microbiome. Generally systems of ordinary differential equations are used to capture essential behaviours desired from our models that are observed in biological data. Using a system's biology approach, data integration is a large focus of this work and includes model parameterization and validation, potentially across biological scales.
- Dr. Alireza Sayyidmousavi
Limited postdoctoral positions are available. Please contact the individual faculty member with whom you would like to work.
All group members have access to the
RAMLab (Ryerson Applied Mathematics Laboratory).
Past Graduate students, Undergraduates, and Postdoctoral fellows
- Click here to see Dr. Ilie's former students
- Click here to see Dr. Lan's former students
- Eglal Ellaban (currently PhD candidate at Ryerson), Flavio
Firmino-Lunda, Mahmud Hasan (currently Senior Lecturer at North
South University, Hom Kandel (currently PhD candidate at York
University, Syeda Rubaida Zafar, Neil Gonputh
- Mariya Ustymenko (MSc Candidate, Ryerson University), Tahmina Akhter (PhD, 2018, University of Waterloo),
Salil Bedkihal (Postdoctoral Fellow, Perimeter Institute, Waterloo),
Prakash Paudel, George McBirnie, Laura Liao (Postdoctoral Fellow,
Los Alamos National Lab), Laxmi Regmi, Bhai Adhikari, Pradeep Kunwar
(PhD candidate, Ryerson University), Salahaldeen
Rabba (PhD candidate, Ryerson University), Matthew DeClerico,
(This page is maintained by K. Rohlf. Last updated: February 5, 2019.)