Computational Materials Science

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Introduction
The research projects I have been working on include Computational Fluid Dynamics (Hele-Shaw problem), Crystal Growth and Nanostructure Patterning in thin films. These are typical examples of systems driven out of equilibrium. The pattern formation in such systems is very intriguing and challenging. The primary, long-term goal of my research is to develop numerical tools capable of simulating the evolution of these non-equilibrium systems and predicting the evolving morphologies. Of particular interest to me is to design a strategy to precisely control the pattern shape and evolving interfacial instabilities, such as Mullins-Sekerka type instability. I also work with experimentalist to verify my numerical findings.
Hele-Shaw flow and Crystal Growth
Isotropic surface tension: the repeated tip splitting leads the evolving shape to ramified, fractal-like structures.			Anisotropic surface tension: the repeated side branching leads the evolving shape to dendritic, tree-like structures.
Controlling the driving force (Flux Const. C) leads the evolution to a variety of universal, self-similarly evolving, limiting shapes.			The universal shapes are independent of their initial configurations, see the above 6-fold shape for instance.
Nanostructure Pattern Formation Under Construction
Example evolution movies
v A ramified shape v A 6-fold symmetric shape v A 7-fold symmetric shape v A 8-fold symmetric shape
Publications
v S. Li, J. Lowengrub, P. Leo and V. Cristini, Nonlinear Theory of Self-Similar Crystal Growth and Melting, Journal of Crystal Growth 267, p703-713, 2004. v S. Li, X. Li, J. Lowengrub, P. Leo and V. Cristini, Nonlinear Crystal Growth and Control of the Mullins-Sekerka Instability, MRS Proceedings 859E (JJ5.5), Eds. J. Evans, C. Orme, M. Asta and Z. Zhang, 2005.  v S. Li, J. Lowengrub, P. Leo, Nonlinear Morphological Control of growing Crystals, Physica D: Nonlinear Phenomena 208, p209-219, 2005. v S. Li, J. Lowengrub, P. Leo and V. Cristini, Nonlinear Stability Analysis of Self-Similar Crystal Growth:  Control of the Mullins-Sekerka Instability, Journal of Crystal Growth  277, p578-592, 2005.   v Martin E. Glicksman, J. Lowengrub,  S. Li,  Non-monotone Temperature Boundary Conditions in Dendritic Growth, Proc. Modeling of Casting, Welding and Adv. Solid Processes XI, Eds. C.A. Gandin, M. Bellet, 521-528, 2006.   v Martin E. Glicksman, J. Lowengrub, S. Li, X. Li, A deterministic mechanism for dendritic solidification kinetics, Journal of the Minerals, Metals and Materials Society (JOM), Aug., 27-34, 2007.    v S. Li, X. Li, J. Lowengrub and M. Glicksman, A deterministic mechanism for side-branching in dendritic growth, Fluid Dynamics and Materials Processing, in press. v Z. Hu, S. Li, J. Lowengrub, Morphological stability analysis of the epitaxial growth of a circular island: Application to nanoscale shape control, Physica D: Nonlinear Phenomena, 233, p151-166, 2007. v S. Li, J. Lowengrub, P. Leo, A rescaling scheme with application to the long time simulation of viscous fingering in a Hele-Shaw cell, Journal of Computational Physics 225, 554-567, 2007.

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