I work in the area of interdisciplinary applied mathematics, also often referred to as physical applied mathematics and modeling. More specifically, my area of work is the partial differential equations (PDE)-based modeling in materials science, crystal growth, and fluid dynamics. This work requires insights into the real-world physical phenomena. Correspondingly, research is disseminated through the materials science, physics and engineering journals. Applied mathematics is used (i) to formulate sets of governing PDEs and boundary conditions, and (ii) in the analytical solutions of simplified models.
For the problems that do not allow analytical treatment, I had developed sophisticated marker-particle methods for tracking surfaces in 2D and 3D.
I often collaborate with physicists, materials scientists and engineers on projects related to nanoscience and nanotechnology. If you have an interesting project for which you need a collaborator or simply would like to discuss it, please drop me an email ! Or if you are a student looking for an engaging, multi-disciplinary project for your undergraduate or graduate Thesis, please drop me an email !
The samples below are from the completed and partially completed
projects.
Most often, the surface or bulk diffusion is the major mechanism behind physical phenomena;
mathematically, such model is formulated as IBVP for either a single parabolic
PDE,
or a system of parabolic PDEs.
These PDEs are heavily nonlinear and typically high order (fourth or sixth).