Research
Fluid
dynamics, hydrodynamic
stability and partial differential equations.
| During the course of my studies in
the graduate program in Applied Mathematics, I have completed various
independent research projects and also embarked on my own PhD research.
The following is a summary of that work. |
- Current work on Detonation
Waves
We have begun work on the stability of detonation waves. These waves are a form of combustion that propagates at supersonic speeds reaching kilometers per second. This is contrasted with deflagration waves which are relatively slow or subsonic. The applications of detonation waves are myriad, from jet engines to stellar explosions. A more in depth treatment
 |
Detonation Stability -
Third Semester presentation version
|
Some
cool links
- Video of experiment in detonation waves - GE Global Research Blog
- Computer simulation of detonation initiation - U. of Colorado Multi-scale Modeling and Simulation Laboratory (scroll to Detonation Initiation).
- A ME639 - Hydrodynamic Stability - Fall 2007
As part of
this class, we were entrusted with presenting a particular aspect of hydrodynamic
stability theory. It involved a search of relevant literature. In
my case it was the application of the mathematical theory of the method
of multiple scales to the question of the stability of the boundary
layer over a flat plate. The bulk of the work presented in the
talk below is based on the work of M. Gaster (1970), M. Bouthier
(1972), and Saric and Nayfeh (1975).
|
|
Nonparallel
Theory |
- Second semester term paper -Spring 2007
In the Program in Applied Mathematics, there is a required term paper that must be completed in the second semester. My paper deals with the moving contact line problem under the supervision of Dr. Shankar Venkataramani. What is the moving contact line problem anyway? It is an example of the failure of the equations that govern fluids (Navier-Stokes), in a case where there is no high temperature nor extreme pressures.
|
|
The
Moving Contact Line Problem |
- Brown Bag Spring 2007
This was a presentation given as
part of the student graduate colloquium, i.e. the Brown
Bag, at the Program in Applied Mathematics. It was part of some
introductory research in hydrodynamic stability with Dr. Anatoli Tumin
from the Department of Aerospace
and Mechanical Engineering.
|
|
Biorthogonal eigenfunction decompositions in inviscid flow |
- MATH586 - Case studies in Applied Mathematics - Fall 2006
Data taken by Robert
Reinking at the Applied
Mathematics Laboratory at the UofA served as the basis of this
paper. The experiments involved the motion of gas bubbles in liquids.
The task was to develop a model of that motion from literature and
apply it to the particular task at hand. This was joint work with Sairam
Rayaprolu, a fellow student in the program.
|
|
An experiment with bubble rise in liquids |
