Binan Gu

Assistant Research Professor

Department of Mathematical Sciences

Worcester Polytechnic Institute

Current Postdoc Advisor: Prof. Andre Nachbin

Former Postdoc Advisor: Prof. Burt Tilley

PhD Advisors: Prof. Linda J. Cummings   Prof. Lou Kondic

Email: bgu [at] wpi [dot] edu

Curriculum Vitae

Research Interests:

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

Current projects:

• Shallow Water Waves on Graphs in 1D and 2D (with Andre Nachbin)
Water-wave problems are of public interest (for example civil defense), with applications such as flood-waves or landslide-tsunamis in river basins, that can be modeled through networks. Graph models are an efficient one-dimensional (1D) framework for predicting hazardous situations downstream. Water waves are also a very rich mathematical topic due to the wide range of PDE models that can be studied, in particular from the quantum-graphs perspective. Wave scattering on graphs is a mathematical topic of great interest and not much explored, notably the problem of reflectionless vertices.

Our main research question is about whether the geometric factors in 1D metric graphs embedded in a 3D space, such as the angle between graph edges, could influence water wave transmission and reflection. The idea is to first consider graph edges as 2D slabs with a small but nonzero width. Using techniques of conformal mapping, we transform graphical domains, such as forked channels, into simpler domains and proceed with numerical investigations of the wave dynamics. Then, by considering small width limits, we aim to answer questions such as whether the typical Neumann-Kirchhoff vertex/boundary conditions are sufficient for capturing vertex interactions and up to what extent of the angle between edges. Understanding the geometric influence on water wave dynamics reveal the true physically compatible boundary conditions one should use when applying the reduced 1D dynamics to real world problems.


• Nonlinear Network Dynamics with Applications in Geothermal Harnessing (with Burt Tilley and Thomas Baumann)
High-temperature aquifer storage is an important approach to providing heating and cooling in residential and commercial settings with a low-carbon footprint. Predicting the fluid, thermal and solutal transport of these systems over decades of use requires an understanding of the transport processes through low-conductivity regions. While aqueous chemistry takes place on much shorter time scales, surface dissolution, whose rate depends on the pH and temperature in the fluid and the calcite matrix alters the pore geometry and ultimately affects thermal transport on the thermal storage time scale. To better understand these competing processes, we focus on the transport dynamics in a single pore and derive a model in a three-dimensional axisymmetric cylindrical system. Assuming quasi-steady aqueous reactions and a small pore radius compared to the characteristic length of the pore, we derive a system that describes the evolution of the pore shape, thermal and calcium ion transport, and fluid mass conservation. When energy is delivered to the pore, dissolution occurs at the inlet but precipitation is observed near the pore outlet, reducing the net heat flux delivered to the system. When energy is retrieved by reversing the flow direction, precipitation can be observed with a rapid nonlinear pore closure depending on species and thermal profiles, preventing energy harnessing. The results of this work will form the foundation for adaptations for dynamic pore network models (PNM) of geothermal energy harnessing applications.


• Diapedesis and cell extravasation in viscoelastic endothelial confinement in the blood-brain-barrier (with Yangjin Kim and Sean Lawler)


• Membrane Filtration via Spectral Graph Theory and Persistence Homology (with Linda J. Cummings, Lou Kondic, Pejman Sanaei, Matt Illingworth)
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 graph theory and persistence homology.


• A Flow-guided Weighted Random Walk on a Connected Graph with Blocking (with Linda J. Cummings and Lou Kondic)
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.

Optimization and Machine Learning Seminar

Teaching:

Publications:

• Transient interfracture permeability evolution generated by thermal-carbonaceous reaction kinetics in aquifer thermal storage applications.

  B. Gu, B. S. Tilley, T. Baumann.

  Accepted at Mathematical Geosciences (2026).

• Filtration in Pore Networks.

  L.J. Cummings, B. Gu, L. Kondic.

  Annual Review of Fluid Mechanics, 58 (2026).

• Influence of topology on performance of pore networks in membrane filters.

  M. Illingworth, B. Gu, L. Kondic, L.J. Cummings.

  Physical Review E, 113 (024301), (2026).

• Fractal dimension of non-Newtonian Hele-Shaw flow subject to Saffman-Taylor instability.

  J. Adriazola, B. Gu, L. Kondic, L.J. Cummings.

  Physical Review E, 110 (065107), (2024).

• Flow through Pore-Size Graded Membrane Pore Networks

  B. Gu, L. Kondic, L.J. Cummings

  Physical Review Fluids, 8, 044502 (2023).

• Network-based membrane filters: Influence of network and pore size variability on filtration performance.

  B. Gu, L. Kondic, L.J. Cummings .

  Journal of Membrane Science, 657, 120668 (2022).

• A Graphical Representation of Membrane Filtration.

  B. Gu, L. Kondic, L.J. Cummings

  SIAM Journal on Applied Mathematics, 82, 950-975 (2022).

• 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)

Work under consideration and progress:

• Stochastic Modeling of Filtration with Sieving in Graded Pore Networks.

  B. Gu, P. Sanaei, L. Kondic, L.J. Cummings (Under revision at Journal of Fluid Mechanics).

• Long-wave scattering on balanced quantum graphs.

  C. Norton, B. Gu, A. Nachbin (Submitted to SIAM Journal on Applied Mathematics).

• Cell proliferation in a network model of tissue engineering scaffolds.

  J. Sokolik, B. Gu, P. Sanaei (Submitted to SIAM Journal on Life Sciences).

• A Spectral Representation of Nonlinear Dynamics on Networks with Applications in Reactive Transport.

  B. Gu, B. S. Tilley (In progress).

Technical Reports:

• Reduced Noise and Ringing for Image Processing.

  B. Gu, B. Tilley, F. Cao, M. Chugunova, C. Coonrod, P. Dubovski, T. Fuller, A. Iatcenko, W. Thompson, T. Thakur, N. Xu and M. Zyskin, June, 2025.

• Finding the Limits of Machine Learning in Optimization.

  D. A. Edwards, B. Gu, K. Jonston, M. Wichman, M. Zyskin, November, 2022.

• 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.