Routing in wireless networks
This work is to discover efficient routing strategies for the 4g (Fourth generation) wireless networks. Mobility and power efficiency put constraints on routing decisions. We use simulation and modeling to understand and devise routing protocols.
Gaussian Cubature
Joint work with Larry Fialkow. We study cubature rules for the circle and the triangle using flat extensions of positive moment matrices. Recent results include new cubature rules for the circle and the triangle. We proved that there exists no 10-point quadrature rules for the unit disk with all points inside the disk, and found quadrature rules with 9 points inside and one outside.
Asymptotics of partial differential equations
The purpose of this research is to understand the evolution of solutions of partial differential equations (PDEs) containing small nonlinear terms. Such PDEs arise in mathematical models of water waves, acoustics, plasma physics and other applications. Analytical tools used for this research include multiple-scale expansions and perturbation methods in Laplace transform spaces. Numerical computations exploit characteristic coordinates. Our main results analytically describe the slow interaction between forward and backward going wave components in weakly nonlinear hyperbolic systems.
Non-Newtonian Fluid Mechanics
Many fluids occurring in nature exhibit complex structures, not described by the classical (Newtonian) fluid mechanics, which applies only to homogeneous fluids like water. Examples of complex fluids include blood, polymers, plastics and oil. I have studied a number of models for complex fluids using analytical and numerical techniques for partial differential equations.
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Petroleum Engineering
We study reservoir engineering models with the aim of understanding the complex fluid dynamics occurring in geological formations. Much of this activity centers around enhanced oil recovery processes to extract oil from the heavy formations in Western Canada. Research activities include
- Study of flows in elliptical reservoirs
- Understanding thermal effects in enhanced oil recovery processes
- Modeling of flow in layered reservoirs
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