Research Interests
My research interests lie in nonlinear partial differential equations, applied analysis, and numerical analysis, with applications in physical, biological and materials sciences. Specific areas include:
- Network formation in amphiphilic mixtures with applications to lipid bilayer evolution and morphology in polymer electrolyte materials
- Domain coarsening and self similarity in materials science, phase transitions and thin films
- Free boundary problems
Research Projects
Molecule Solvation
This project concerns the modeling and analysis of the solvation of charged molecules.
This project concerns the modeling and analysis of the solvation of charged molecules.
Complex Amphiphilic Network Structures and Lipid Bilayers
This project studies the geometric evolution of lipid bilayers and filamentous pores in the framework of functionalized Cahn-Hilliard equation.
This project studies the geometric evolution of lipid bilayers and filamentous pores in the framework of functionalized Cahn-Hilliard equation.
Coarsening Dynamics of the Degenerate Cahn-Hilliard Equation
This project studies the coarsening dynamics of the Cahn-Hilliard equation with a diffusion mobility that is degenerate in one or both phases. We find that there is a quasi-stationary porous medium diffusion process in the degenerate phase, which provides communication between disjoint components and drives the system to coarsen. As a result, there is a delicate relation between the coarsening rate and the degenerate mobility.
This project studies the coarsening dynamics of the Cahn-Hilliard equation with a diffusion mobility that is degenerate in one or both phases. We find that there is a quasi-stationary porous medium diffusion process in the degenerate phase, which provides communication between disjoint components and drives the system to coarsen. As a result, there is a delicate relation between the coarsening rate and the degenerate mobility.
