Research - Science & Engineering

Throughout my life, I have found the natural world to be a source fascination and inspiration. Thus, it is not surprising that science and engineering are strong undercurrents in my research. I am always on the look out for opportunities to use the methods and techniques of computational science & engineering and applied mathematics to further our understanding of the world around us.

My research in science and engineering have been focused in the following areas:

Within these areas, I am currently working on


Computational Material Science

Microstructure of Polycrystalline Materials

Collaborators: S.S. Jerry Quek, David T. Wu, Chin Yi Chee

Coming Soon!

Phase Field Modeling of Polycrystalline Materials

Collaborators: S.S. Jerry Quek, David T. Wu, Chin Yi Chee

Coming Soon!

Working notes

Dislocation Dynamics and Grain Boundary Evolution

Collaborators: David J. Srolovitz, Mikko Haataja, S.S. Jerry Quek, Zi Chen, Adele Lim
Six interacting dislocation lines
Six interacting dislocation lines. (Image courtesy of Zhaoxuan Wu)

Understanding the role of dislocations and grain boundary evolution in the plastic deformation of materials continues to present an important and interesting challenge for material scientists. We studied both of these microstructural entities using mesoscopic computational models based on the level set method.

In our model, dislocations are represented by the intersection of the zero level sets of two level set functions. An important consequence of this implicit representation of the dislocation line is that topological changes that occur when dislocation lines interact with obstacles and with each other take place automatically without requiring complicated ``surgical procedures.''

To address the computational complexity of modeling dislocation networks and grain boundaries using the level set method, we have implemented the Level Set Method Dislocation Dyanmics (LSMDD) library. This software library is designed to support high-performance, parallel computation and to be modular enough to allow for exploration of novel numerical models and algorithms for simulating dislocation dynamics and interactions.


References


Biophysics

Collaborators: Keng-Hwee Chiam

Coming Soon!


Electrochemical Transport

Collaborators: Martin Z. Bazant
Concentration field
Diffusion currents
Steady electrochemical transport around a polarizable sphere immersed in an electrolyte solution when a large, uniform electric field is applied: concentration profile of neutral salt (top) and diffusion currents (bottom). In these two images, the electric field is aligned with the z-axis.
Graphical representation of surface conservation laws
Graphical representation of surface conservation laws.

Novel electrochemical devices being explored for microfluidic and micro/nano-power source applications often electrochemical systems into operating regimes that test the limits of traditional macroscopic theories in electrochemistry. We study electrochemical transport in these extreme operating regimes by analyzing the classical Poisson-Nernst-Planck equations using asymptotic analysis and numerical simulations.

One of the main conclusions of our work is that for weak electrolytes, large concentration gradients develop even at relatively small applied electric fields/voltages. These concentration gradients imply that the common approach of modeling electrochemical transport using linear circuit models is questionable for systems driven by strong electric fields/voltages.

Using novel asymptotic analysis techniques, we have also formally derived effective nonlinear electrochemical transport equations in the thin double-layer limit, which generalize linear circuit models. The foundation for this work is a novel formulation of surface conservation laws which allows us to derive effective boundary conditions that capture the physics of the double layer without requiring linearization of the concentration and potential fields.


References


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