Research

My primary area of expertise is mathematical modeling, nonlinear partial differential equations and scientific computing. Using a mixture of analytical and numerical techniques, I study a wide range of nonlinear dynamics with applications in engineering, biological and physical systems. Focuses of my work include problems in fluid dynamics, dynamical systems, numerical analysis, and industrial applications.

Publications and Preprints

  1. H. Ji, K. Lafata, Y. Mowery, D. Brizel, A. L. Bertozzi, F.-F. Yin, C. Wang, Post-Radiotherapy PET Image Outcome Prediction by Deep Learning under Biological Model Guidance: A Feasibility Study of Oropharyngeal Cancer Application. Under review (2021)
  2. H. Ji, R. Taranets, M. Chugunova, Qualitative analysis of travelling wave solutions for a model of a liquid film flowing down a fiber, under review in European Journal of Applied Mathematics (2021) [arXiv]
  3. H. Ji, C. Falcon, E. Sedighi, A. Sadeghpour, Y. S. Ju, A. L. Bertozzi, Thermally-driven coalescence in thin liquid film flowing down a fiber, Journal of Fluid Mechanics, 916, A19 (2021). [Journal]
  4. T. A. Nguyen, L. Li, H. Ji, Stable and accurate numerical methods for generalized Kirchhoff-Love plates, under review in Journal of Engineering Mathematics (2021) [arXiv]
  5. A. Sadeghpour, F. Oroumiyeh, Y. Zhu, D. H. Ko, H. Ji, A. L. Bertozzi, Y. S. Ju, Experimental study of a string-based counterflow wet electrostatic precipitator for collection of fine and ultrafine particles (2021) [Journal].
  6. E. Sedighi, Z. Zeng, A. Sadeghpour, H. Ji, Y. S. Ju, A. L. Bertozzi, Capillary rise of well-wetting liquid on the outer surface of cylindrical nozzles. Under review (2021).
  7. H. Ji, A. Sadeghpour, A. L. Bertozzi, Y. S. Ju, Modeling film flows down a fibre influenced by nozzle geometry, Journal of Fluid Mechanics Rapids, volume 901 (2020) [Journal] [arXiv]
  8. Y. Dukler, H. Ji, C. Falcon, A. L. Bertozzi, Theory for undercompressive shocks in tears of wine. Physical Review Fluids 5, 034002 (2020). [Journal] [arXiv]
  9. H. Ji, C. Falcon, A. Sadeghpour, Z. Zeng, Y. S. Ju, A. L. Bertozzi, Dynamics of thin liquid films on vertical cylindrical fibers. Journal of Fluid Mechanics 865 (2019): 303-327. [Journal] [arXiv] [Video]
  10. H. Ji, T. P. Witelski, Steady states and dynamics of a thin film-type equation with non-conserved mass. European Journal of Applied Mathematics (2019): 1-34. [Journal] [arXiv]
  11. A. Sadeghpour, Z. Zeng, H. Ji, N. D. Ebrahimi, A. L. Bertozzi, Y. S. Ju, Water vapor capturing using an array of traveling liquid beads for desalination and water treatment. Science Advances 5, no. 4 (2019): eaav7662. [Journal]
  12. H. Ji, T. P. Witelski, Instability and dynamics of volatile thin films, Physical Review Fluids 3, no. 2 (2018): 024001. [Journal] [arXiv]
  13. H. Ji, L. Li, Numerical methods for thermally stressed shallow shell equations, Journal of Computational and Applied Mathematics (2018). [Journal] [arXiv]
  14. X. Hu, Y. Li, H. Ji, A nodal-based finite element approximation of a phase field model for shape and topology optimization, Applied Mathematics and Computation (2018). [Journal]
  15. Y. Gao, H. Ji, J. Liu, T. P. Witelski, A vicinal surface model for epitaxial growth with logarithmic free energy, Discrete & Continuous Dynamical Systems - B (2018): 1771-1784. [Journal] [arXiv]
  16. H. Ji, T. P. Witelski, Finite-time thin film rupture driven by modified evaporative loss, Physica D: Nonlinear Phenomena, vol 342 (2017), pp. 1-15. [Journal] [arXiv]
  17. Y. Gao, H. Ji, J. Liu, T. P. Witelski, Global existence of solutions to a tear film model with locally elevated evaporation rates, Physica D: Nonlinear Phenomena, vol 350 (2017), pp. 13-25. [Journal] [arXiv]
  18. H. Ji, Thin films with non-conservative effects, PhD Dissertation, Mathematics, Duke University, 2017 [Dissertation]

Papers in Preparation:

  1. With R. Chu, S. Christensen, A. L. Bertozzi, M. Roper, A theory for curvature-induced migration in inertial microfluidic devices (2020)
  2. with W. Chu, Q. Wang, A. L. Bertozzi, CJ. Kim, A microfluid-based modeling of droplet actuation by electro-(de)wetting (2020)