Binan Gu

Applied mathematics · PDEs · stochastic dynamics · networks

Binan Gu

I develop mathematical and computational models for transport, waves, and evolving geometry on networks.

My work connects PDEs on metric graphs, stochastic processes, numerical simulation, and reduced models for complex media, with applications in water waves, heat and mass transport in porous and fractured media, membrane filtration, and biological transport.

I am an Assistant Research Professor in the Department of Mathematical Sciences at Worcester Polytechnic Institute. I am looking for academic positions for Fall 2027.

Research overview Publications Teaching Curriculum vitae

News and whereabouts

Recent talks, conferences, workshops, and professional activities.

Oct 2026
Applied Mathematics and Computation Seminar

Presenting recent work Nonlinear Transport Dynamics on Metric Graphs at UMass Amherst, Amherst, MA.

Nov 2026
APS Division of Fluid Dynamics Conference

Presenting recent work Nonlinear Transport Dynamics on Metric Graphs at APS DFD Conference in Orlando.

Research at a glance

Full research overview

I study how local dynamics on edges, coupling laws at vertices, network topology, and stochastic events combine to determine global behavior in physical and biological systems.

PDEs on graphs

Wave propagation, transport, reaction, and geometry evolution on metric networks.

Stochastic network dynamics

Random walks, blocking, fouling, topology change, and graph-based performance metrics.

Reduced physical models

Graph models derived from conservation laws, asymptotics, and continuum mechanics.

Current projects

See all projects

Water waves · metric graphs · scattering

Shallow-water waves on graphs

Vertex coupling laws determine how waves transmit and reflect through river, canal, and branched coastal networks.

Mathematical core: Saint-Venant equations, characteristic variables, quantum graphs, width-weighted scattering, source-relative balance.

Note that the left-most edge has no back propagating mode (flat red line), indicating no reflection. It is a result of a particular frequency forced at the incoming boundary that leads to destructive cancellation of all reflected waves generated by the downstream vertex where three internal paths meet. How do you select this frequency?

Key question: Does the Neumann-Kirchhoff vertex condition (conservation of flux and continuity of wave height) always hold for any river channels, independent of geometry (width and angles) and topology (connectivity)?

Read more →
Fractured Rock

Porous media · Geochemistry · spectral methods

Reactive transport and geothermal networks

Reduced pore and network models describe how thermal forcing, chemical reactions, and evolving permeability interact in aquifer thermal energy storage. Figure courtesy of Pyramid Environmental & Engineering.

Mathematical core: coupled flow, heat and mass transport, permeability evolution, spectral network solvers.

Key question: How do fluid, heat and mass transport take place in this evolving fractured system?

Read more →
Random pore-network model for membrane filtration

Filtration · Porous Media · Random Graphs · Fouling

Membrane filtration and stochastic fouling

Membrane pore networks evolve under adsorption and sieving, combining deterministic conductance loss with random particle-driven blocking.

Mathematical core: weighted graph Laplacians, flux-guided random walks, temporal graphs, persistence-based structure metrics.

Key question: How do fluid and contaminant transport take place in this evolving pore network?

Read more →
Biological transport through deformable tissue microstructures

Mathematical biology · physiological flows · growth · mechanics

Mathematical biology in deformable networks

Models of tissue growth in elastic scaffold networks and neutrophil transit through viscoelastic endothelial clefts connect biological transport to evolving geometry.

Mathematical core: low-Reynolds-number flow, advection–diffusion–reaction, elasticity and viscoelasticity, moving boundaries, and graph coupling.

Figure courtesy of Cerutti & Ridley (2017).

Key question: How do immune cells magically squeeze themselves through tight endothelial junctions to fight inflammations on the brain side?

Read more →

Teaching and mentoring

Teaching page

Teaching focus

I teach applied mathematics through computation, modeling, and structure. Students should learn not only how to execute an algorithm, but why it works, when it fails, and what it reveals about the underlying mathematical problem.

  • Numerical methods for linear and nonlinear systems
  • Calculus and multivariable calculus
  • Probability, stochastic processes, and graph-based models

Student research directions

Many of my projects naturally split into student-scale problems involving modeling, computation, asymptotics, or graph algorithms.

  • Wave propagation on networks
  • Random walks and transport in porous media
  • Numerical PDEs on metric graphs
  • Filtration, fouling, and biological transport models

Selected publications

Full publication list
  1. Stochastic Modeling of Filtration with Sieving in Graded Pore Networks. B. Gu, P. Sanaei, L. Kondic, L. J. Cummings. Journal of Fluid Mechanics, 2026.
  2. Transient Interfracture Permeability Evolution Generated by Thermal-Carbonaceous Reaction Kinetics in Aquifer Thermal Storage Applications. B. Gu, B. S. Tilley, T. Baumann. Mathematical Geosciences, 2026.
  3. Filtration in Pore Networks. L. J. Cummings, B. Gu, L. Kondic. Annual Review of Fluid Mechanics, 2026.
  4. Flow through Pore-Size Graded Membrane Pore Networks. B. Gu, L. Kondic, L. J. Cummings. Physical Review Fluids, 2023.

Contact

For research collaboration, student projects, or teaching inquiries, contact me at bgu [at] wpi [dot] edu.

Current postdoc advisor: Prof. Andre Nachbin.
Former postdoc advisor: Prof. Burt Tilley.
PhD advisors: Prof. Linda J. Cummings and Prof. Lou Kondic.