Current projects

I am always open to new problems and ideas. Graduate and undergraduate
students interested in joining my group are welcome to contact me.

Projects in green are ideas for future work.
Projects in purple are currently in progress.
Projects in black are complete.

Mischellaneous problems

These projects are in collaboration with other labs.

† Decoupling motion and deformation measurements in carotid artery { Caleb }

Porous media flow modelling

A landfill is an underground cavity, where anaerobic decay processes produce usable gas.
Practices of gas collection and quantification of the amount of available gas are important
to a successful operation, both from the engineering and environmental point of view.

† The mysterious π/4 singularity: connexion to time dependent solution break-down

† Non-linear diffusion in heterogenious media: generalised curvilinear coordinates { Muriel }

† Turbulence near ingress to landfill wells: optimisation of collection efficiency

† Landfill-well flow coupling in perforated horizontal wells { Seth }

† Singularities in weakly compressible flow through a porous medium { Kate, Mahendhar }

† Modelling head losses at the ingress into a horizontal landfill well { Nikhil, Istafa }

† Controlling surface flux in landfill-well coupled flow in perforated horizontal wells { Mehrdad }

† Visualisation of ideal gas flow in a porous medium: broken axial symmetry { Michelle }

† Modelling turbulence in landfill gas flow: ingress into a horizontal well { Abhishek, Mehrdad }

† Regularity corridors in anisotropic porous medium flow: power law dependence on permeability { Nikhil }

† Exact solutions to non-linear diffusion equation with variable permeability: spherical coordinates { Mahendhar, Piyush }

† User interface for flow solution in landfill wells: broken axial symmetry { Piyush }

† Visualisation of anisotropic flow in a porous medium: spherical coordinates { Piyush }

† Exact solutions to non-linear diffusion equation with variable permeability: elliptic coordinates { Kate }

† Modelling turbulence in landfill gas flow: ingress into a vertical well { Prashanna, Abhishek }

† Unsteady landfill gas flow { Seth }

† Exact solutions to steady flow in a porous medium with variable permeability

† Simulation of planar flow for multiple perforated horizontal wells { Damian, Seth }

† Evaluation of a network flow model for weakly compressible flow at a DLC landfill { Alyssa }

† User interface for flow solution in horizontal wells { Oamar }

† Simulation of planar flow for a perforated horizontal well { Damian }

† User interface for flow solution in a network { Oamar }

† 1D and 2D flow solution for perforated horizontal wells

† Visualisation of flow solution in a network { Alexis }

† Concentric pipes wellhead to replace an orifice flowmeter

† Accurate flow rate estimation in a landfill well with an orifice plate

River life subject to dam operation

Fish living in rivers, where dams have been built, experience water recessions when the
dam discharge is limited or stopped. Better understanding of the dynamics of the river and
fish spawning grounds will help control the impact of the dam operation on this ecosystem.
These projects concern the Columbia and Kootenay Rivers in Southern British Columbia
and are in collaboration with the local industry.

† Visualisation of flow in Columbia-Kootenay Rivers confluence

† Modelling heat transfer for fish egg hatching { Mohammed GP }

† River flow solution with realistic riverbed data { Vishnu, Michelle, Grace, Krithi }

† Mesh refinement for river flow solution with realistic riverbed data { Michelle, Tess, Merieme, Grace }

Pattern formation subject to special types of diffusion

† Schrödinger equation with fractional Laplacian { Chirag }

The Gierer-Meinhardt model is a paradigmatic reaction — diffusion system
that possesses fully non-linear solutions in the form of spikes. The spikes drift,
change heights and interact with each other. These projects explore spike
pattern evolution and relate the observed phenomena to diffusion peculiarities
in cell biology, geology, chemistry and other areas of science.

† Non-local drifting eigenvalue problem

† Bifurcations in reduced Gierer-Meinhardt system with and without anomalies

† Continuously varying anomaly index with sub-diffusion

† Continuous variation of kinetic exponents { Sam }

† Numerical simulation of anomalous reaction-diffusion systems { Ying Hung, Kate }

† Anomalous diffusion on surfaces { Khazhakanush }

† Numerical soluton for Gierer-Meinhardt reaction--diffusion model with sub-diffusion { Nehemie, Juan }

† Accurate spike shape computation with Lévy flights (fractional Laplacian) { Kyle }

† Asymmetric spike constellations with time dependent diffusivity and anomaly exponent

† Spike drift with time dependent diffusivity (integer derivative)

† Spike drift with time dependent anomaly index (fractional derivative)

† Bifurcation delay with sub-diffusion