
SCIENTIFIC PROGRAMS AND ACTIVITIES 

December 2, 2016  
Fields Day on Mathematical Modeling

Schedule


9:30  9:45  Opening Remarks 
9:45  10:45 
John Ockendon, Oxford University Modelling with Free Boundaries 
10:45  11:00  Coffee Break 
11:00  12:00  Keith Promislow, Simon Frasier
University The Mathematics of Fuel Cells 
12:00  1:15  Lunch Break 
1:15  2:15  Don Schwendaman, RPI Combined Analytical and Numerical Methods in Industrial Mathematics Click here for talk slides 
2:15  2:30  Afternoon Tea 
2:303:30  Tom Hurd, McMaster Finance portfolio selection in jump diffusion markets 
Speakers:
John Ockendon, Oxford University
Modelling with Free Boundaries
This talk will discuss free boundary differential equation models in
cases where the morphology can be irregular. The models will be motivated
by problems in fluid and solid mechanics, heat and mass transfer and
superconductivity.
Keith Promislow, Simon Frasier University
The Mathematics of Fuel Cells
Working in conjunction with scientists at Ballard Power Systems, the
world leader in fuel cell technology for automotive
applications, we have developed models of the crucial process of water
management in fuel cell electrodes. This involves issues of phase change
in porous media, multiphase flow and front tracking, all coupled to
electrochemical reactions and heat and mass transport in the porous
fuel cell electrodes. This collaboration has lead us to study rich classes
of mathematical problems and afforded us the resources to do solid science.
I will discuss these efforts against
the broader backdrop of the rewards and demands of multidisciplinary
research, and the role played by the MITACS NCE and the Pacific Institute
for the Mathematical Sciences.
Don Schwendeman, RPI
Combined Analytical and Numerical Methods in Industrial Mathematics
In order to examine the solution of mathematical problems arising from
industrial applications, scientists and engineers often turn to largescale
numerical simulations to obtain results. While such simulations may
give detailed information about specific cases, it is often difficult
to sort out fundamental features of the problem and to determine how
the solution depends on the various parameters involved. On the other
side, purely analytical solutions of simplified models may
only provide a qualitative understanding of the full problem. Experience
with problems brought to industrial workshops at Rensselaer and elsewhere
has shown that a combined approach involving both analytical and numerical
methods is effective in solving mathematical problems from industry.
In this talk, the speaker will survey some problems brought to
industrial workshops and the combined analytical and numerical approaches
used to solve them.
Tom Hurd, McMaster University
Finance portfolio selection in jump diffusion markets
This talk will address Merton's portfolio optimization problem in the
setting of an exponential Levy stock
market. This stochastic control problem leads to HamiltonJacobiBellman
equations which are nonlinear partial
integrodifferential equations with interesting properties. For three
canonical examples of utility functions I will give the general solution
of both the optimal problem and the associated dual problem. These solutions
exhibit some important new features which can not arise in pure diffusion
markets.
This oneday workshop will be a good learning opportunity for graduate students, postdoctoral fellows and other researchers interested in Mathematical Modeling and Industrial Mathematics.
Limited financial support will be available for graduate students and postdocs.
Any questions or cancellations should be directed to modelling@fields.utoronto.ca