
Biomathematics and Fluids
Group 
Department of Mathematics,
Ryerson University

Who we are


Biomathematics and Fluids Seminar Series

Upcoming Seminars:

Past Seminars:
November 20, 2014, 11:10amnoon, ENG 210: Dr. Robert Strehl, Department of Mathematics, Ryerson University. Numerical challenges of chemotaxisdriven PDEs
November 13, 2014, 11:10amnoon, ENG 210: Dr. Diana Knipl, AgentBased Modelling Laboratory, York University. Modelling the spread of infectious diseases on travel networks
March 27, 2014, 11:10amnoon, ENG 210: Dr. Youcef Derbal, Ted Rogers School of Information Technology Management, Ryerson University. Finite state machine modeling of MAPK signaling pathways
March 6, 2014, 11:10amnoon, ENG 210: Dr. Anna Mkrtchyan, Department of Applied Mathematics, Western University. Modelling of tissue growth
February 6, 2014, 11:10amnoon, ENG 210: Dr. Scott Tsai, Department of Mechanical and Industrial Engineering, Ryerson University. Particle coating in low Reynolds number flows
January 30, 2014, 11:10amnoon, ENG 210: Dr. Matthew Scott, Department of Applied Mathematics, University of Waterloo. Indirect regulation of bacterial gene expression imposed by growth and division
November 21, 2013: Dr. Hossein ZivariPiran, Centre for Disease Modelling, York University. Numerical study of a largescale model for measles spread
November 7, 2013: Dr. Fei Xu, Wilfrid Laurier University. Spatial spread of an epidemic through public
transportation systems with a hub
October 31, 2013: Dr. Kunquan Lan, Ryerson University. One dimensional diffusive logistic population models with harvesting rates
April 11, 2013: Dr. Lennaert van Veen, University of Ontario Institute of Technology. Transient turbulence and homoclinic tangles in channel flow
April 4, 2013: Dr. Robert Jerrard, University of Toronto. Vortex dynamics in inhomogeneous 2d quantum fluids
March 14, 2013: PietroLuciano Buono, University of Ontario Institute of Technology. Edge Effects on Caribou Populations: Modelling via Advectiondiffusion
March 7, 2013: Dr. Catherine Beauchemin, Department of Physics, Ryerson University. Virology in silico: growing infections in a computer
February 28, 2013: Dr. Gail Wolkowicz, Department of Mathematics and Statistics, McMaster University, Chaotic dynamics in predatorprey models with time delay
Feb. 7, 2013: Dr. Felicia Magpantay, Department of Mathematics and Statistics, York University, An AgeStructured Population Model with StateDependent Delay
Jan. 31, 2013: Dr. Majid Jaberi, Department of Mathematics and Statistics, York University, Optimality of a TimeDependent Treatment Profile during an Influenza Epidemic
Nov. 22, 2012: Dr. Jian Fang, Department of Mathematics and Statistics, York University , Traveling waves of the nonlocal FisherKPP equation
Nov. 15, 2012: Dr. Daniel Munther, Department of Mathematics and Statistics, York University, Dynamics of a Three Species Competition Model
Oct. 25, 2012: Dr. Gunog Seo, Department of Mathematics, Ryerson University, Effect of Temporal Variability on Persistence Conditions in Rivers

Our Research

 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)
Predatorprey systems: The dynamical
relationship
between predators and
their prey, which is one of the most important themes in ecology, can be
modeled
by establishing predator prey systems of two firstorder differential
equations with suitable functional responses. The qualitative theories
of dynamical systems are used and the dynamical behaviours of such
predatorprey 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
arising
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 wellknown
theories from nonlinear analysis to treat the existence of one or
multiple solutions.
In addition, reactiondiffusion equations arising
from biology,
FalknerSkan 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 liquidgas 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 nonNewtonian. Many nonNewtonian 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 particlebased 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.

Graduate Students

 (Dr. Ilie) Jill Padgett, Farid Gassoumov, Dr. Robert Strehl (cosupervised)
 (Dr. Lan) Click here to see Dr. Lan's students
 (Dr. Pascal) Hom Nath Kandel
 (Dr. Rohlf) Matthew DeClerico, Dr. Robert Strehl (cosupervised)
We are currently accepting graduate students. Please contact the individual faculty member with whom you would like to work.

Postdoctoral Fellows

 Dr. Xi Huo
 Dr. Robert Strehl
Limited postdoctoral positions are available. Please contact the individual faculty member with whom you would like to work.

Undergraduate Students


Computational Resources

All group members have access to the
RAMLab (Ryerson Applied Mathematics Laboratory).

Past Graduate students, Undergraduates, and Postdoctoral fellows

 Dexter Barrows (MSc candidate, McMaster University), Selina Boatemaa, Fatemeh BavagharZaeimi (cosupervised), Monjur Morshed (PhD candidate, University of Waterloo), Raju Prasai (graduate candidate, Western University), Alexandra Teslya (PhD candidate, McMaster University), Samaneh Gholami (PhD candidate, York University), Chandra Limbu (PhD candidate, York University), Milan Patel, Ekaterina Kudashkina, Ronak Savani (MEng candidate, Ryerson University), Thai Tran, Romulo Velasquez, Alex Yakobovich (MSc candidate, Ryerson University)
 Click here to see Dr. Lan's former students
 Neil Gonputh
 Tahmina Akhter (PhD candidate, University of Waterloo), Salil Bedkihal (Postdoctoral Fellow, McGill University), Prakash Paudel, George McBirnie, Laura Liao (PhD candidate, Ryerson University), Laxmi Regmi, Bhai Adhikari, Pradeep Kunwar (MSc candidate, University of Toronto), Salahaldeen Rabba (PhD candidate, Ryerson University)
(This page is maintained by K. Rohlf. Last updated: January 5, 2015.)




