Hangjie Ji bio photo

Hangjie Ji

I'm from Hangzhou, China. Currently in Los Angeles, USA. Passionate about mathematics and technology.

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Research


  • Thin Fluid Films


Instability and dynamics of volatile thin films

with Thomas P. Witelski

Volatile viscous fluids on partially wetting solid substrates can exhibit interesting interfacial instabilities and pattern formation. We study the dynamics of vapor condensation and fluid evaporation governed by a one-sided model in a low-Reynolds-number lubrication approximation incorporating surface tension, intermolecular effects, and evaporative fluxes.


Finite-time thin film rupture driven by generalized evaporative loss

with Thomas P. Witelski

Rupture is a nonlinear instability resulting in a finite-time singularity as a fluid layer approaches zero thickness at a point. We study the dynamics of rupture in a generalized mathematical model of thin films of viscous fluids with evaporative effects.


Global existence of solutions to a tear film model with locally elevated evaporation rates

with Yuan Gao, Jian-Guo Liu and Thomas P. Witelski

We study the dynamics of a generalized thin film model for break-up of tear films on human eyes. The governing equations form a fourth-order coupled system of nonlinear parabolic PDEs for the film thickness and salt concentration subject to non-conservative effects representing evaporation.


  • Numerical analysis


Numerical methods for thermally stressed shallow shell equations

with Longfei Li

We develop efficient and accurate numerical methods to solve a class of shallow shell problems of the von Karman type. The governing equations form a fourth-order coupled system of nonlinear biharnomic equations for the transverse deflection and Airy’s stress function. A second-order finite difference discretization with three iterative methods (Picard, Newton and Trust-Region Dogleg) are proposed for the numerical solution of the nonlinear PDE system. Three simple boundary conditions and two application-motivated mixed boundary conditions are considered.


A nodal-based finite element approximation of a phase field model for shape and topology optimization

with Xianliang Hu, Yixin Li

We propose a nodal finite element method to the problem of finding optimal structural shapes based on a phase field model motivated by the work of Takezawa et al. (2010).


  • Thin Solid Films


A vicinal surface model for epitaxial growth with logarithmic free energy

with Yuan Gao, Jian-Guo Liu and Thomas P. Witelski

We study a continuum model for solid films that arises from the modeling of one-dimensional step flows on a vicinal surface in the attachment-detachment-limited regime. The resulting nonlinear partial differential equation gives the evolution for the surface slope u as a function of the local height h in a monotone step train.