- Mathematical and Stochastic Modelling
- Fluid Dynamics
- Partial Differential Equations
- Stochastic Processes and Applications

- Membrane Filtration via Spectral Graph Theory This work considers a membrane network as a weighted random graph. Fouling mechanisms, such as adsorption and sieving, evolve graph operators (e.g. the graph Laplacian) in continuous and discrete, deterministic and random fashion. Various performance metrics can be represented by this theoretical setup and thus analyzed using theory.
- Tortuosity and Connectivity of Random Media Tortuosity is (in one way) defined by the average distance traversed by a particle in a porous media, relative to porous media thickness. Simulating the paths of a large of number of particles is one way to estimate this quantity. However, if a network is used to represent the media, then this quantity can be explicitly computed using an asymmetric random walk on the network, obviating the simulations and thus reducing computation load.

Fall 2020: Calculus II

- On the Influence of Pore Connectivity on Performance of Membrane Filters.
B. Gu, D.R. Renaud, P. Sanaei, L. Kondic, L.J.Cummings

Journal of Fluid Mechanics,

**902**, A5 (2020) - A Graphical Representation of Membrane Filtration with Adsorption.
B. Gu, L. Kondic, L.J. Cummings (final stage of manuscript prepration).

- Stochastic Modelling of Sieving.
B. Gu, P. Sanaei, L. Kondic, L.J. Cummings (In progress).

- Modelling and Simulating Shear-Thinning Viscous Flow in a Hele-Shaw Cell.
B. Gu, J. Adriazola, L. Kondic, L.J. Cummings (final stage of manuscript prepration).

- On Temperature Effects in Reacting Porous Media Applications.
R.H. Allaire, A.G. Odu, B. Gu, W. Lu, A. Newell, P.J. Paranamana, T. Phan, H. Ruzayqat, June, 2017.