SCIENTIFIC PROGRAMS AND ACTIVITIES

Fields Day on Mathematical Modeling
December 11, 2001

Organizer: H. Huang (York University)

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
2:30-3:30	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 multi-disciplinary 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 large-scale 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 Hamilton-Jacobi-Bellman equations which are nonlinear partial
integro-differential 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 one-day 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