Research Interests
- Applied aspects of partial differential equations and the calculus of variations.
- Scientific computing and numerical analysis.
- Mathematical and computational
aspects of biochemistry and biophysics: implicit solvation of biomolecules,
hydrophobic interactions, electrostatics, diffusion and transport,
ion transport, molecular recognition, molecular docking, etc.
- Mathematical and computational aspects of materials science:
- epitaxial growth of thin films;
- martensitic phase transition and microstructure;
- stress-driven interface dynamics.
- Multiscale mathematics and numerics with applications to
materials science and biochemistry.
Current and Recent Past Research
- Computational modeling and numerical analysis of solvation of molecules, PI, NSF grant DMS-0811259, 7/1/2008 - 6/30/2011.
- Collaborative research: hybrid finite-element level-set methods for
stress-driven interface dynamics, PI, NSF
grant DMS-0451466, 7/1/04 - 6/30/07, extended to 6/30/08.
Abstract.
- Multiscale design of advanced materials based on hybrid
ab initio and quasicontinuum methods, Co-PI,
DOE
grant DE-FG02-05ER25707, 8/15/2005 - 8/14/2008.
- Mathematics and biochemistry/biophysics: solvation of biomolecules with implicit sol
vent,
hydrophobic interactions, electrostatics, diffusion, proteins, memberanes,
ion channels, memberanes, molecular docking, etc.
See more at the
Research Initiative and Project Website.
- Modeling, analysis, and simulation of epitaxial growth and morphology of thin films
(growth instabilities, roughening, coarsening, dynamic scaling,
stress, electromigration, etc.).
- Book project: Weak Convergence Methods for Variational Models of Crystalline Solids,
Springer-Verlag
(Preface).