- 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.
- A Flow-guided Weighted Random Walk on a Connected Graph with Blocking This problem arises from the modelling of the sieving fouling mechanism in membrane filtration. Particles of size similar to filter pore size arrive at the membrane surface and traverse the membrane network via fluid flow (that can be modelled by particle-laden flow). We model these particles as consecutive continuous-time random walkers that follow transition matrices induced by relative fluid flux through each pore junction (vertice). In addition to travelling, the random walkers carry size information that may or may not pass through pore throats (edges) and inevitably modify the graph topology. The weight of the graph also evolves due to a slower fouling mechanism -- adsorption. This entire dynamic process on the graph can be modelled by a stochastic temporal graph.
- 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.

Spring 2020: Calculus II

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.
B. Gu, L. Kondic, L.J. Cummings (under review at SIAM Journal of Applied Mathematics).

- On Pore Size Variations in Membrane Networks.
B. Gu, L. Kondic, L.J. Cummings (submitted to Journal of Membrane Science).

- 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).

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

- 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.