Recent Publications
Spatially locallized structures in diblock copolymer
mixtures , SIAM J. Appl. Math, Vol. 70 (2010).
Long time evolution of aeolian sand dune fields:
Influence of dune formation and collision, with S. Diniega and S. Byrne, Geomorphology (2009).
Coarsening and self-organization in dilute diblock
copolymer melts and mixtures , with R. Choksi, Physica D, Vol. 238 (2009).
Viscosity solutions for a model of contact line motion , with I. Kim,
Interfaces and Free boundaries (2009).
Ostwald Ripening in Thin Film Equations , SIAM J.
Appl. Math., Vol. 69 (2008).
Ostwald Ripening of Droplets: The Role of Migration , w/ F. Otto, T. Rump. D. Slepcev, Euro. J. Appl. Math. (2008).
The dynamics of pendant droplets on a one dimensional surface, Phys. Fluids, Vol. 19, (2007).
A Diffuse Interface Model for Electrowetting Droplets
in a Hele-Shaw Cell , w/ H.-W. Lu, A. Bertozzi, C.-J. Kim, JFM, Vol. 590, 411-435 (2007).
Homogenization of contact line dynamics, Int. Free Bound., Volume 8, (2006).
Grain boundary motion arising from the gradient flow of the Aviles-Giga functional , Physica
D,Volume 215, pp. 80-98 (2006).
A boundary integral formulation of quasi-steady fluid wetting,
J. Comp. Phys., 207, pp. 529-541 (2005).
Collision vs. collapse of droplets in coarsening of
dewetting thin films, with T. P. Witeslski, Physica D, 209, 80-104 (2005).
Variational models for moving contact lines and the quasi-static approximation
, Euro. J. Appl. Math, 16, pp. 1-28 (2005).
Spreading of droplets under the influence
of intermolecular forces, Phys. of Fluids, Vol.15, pp. 1837-1842 (2003).
Coarsening Dynamics of Dewetting Films,
with T. P. Witelski, Phys. Rev. E, Vol. 67, 016302 (2003).
A Diffuse Interface Approach to Hele-Shaw
Flow , Nonlinearity , Vol. 16, 1-18 (2003).
Solute Trapping and the Non-equilibrium Phase
Diagram for Solidification of Binary Alloys , Physica D ,
151 (1-4) (2001) pp. 253-270.
Nonlinear Preconditioning for Diffuse Interfaces ,
Journal of Computational Physics,
Vol. 174, No. 2, Dec 2001, pp. 695-711.
Rapid Growth and Critical Behavior in Phase
Field Models of Solidification, European J. Appl. Math,
Vol. 12, pp. 39-56, (2001).
Dual Fronts in a Phase Field Model,
with R. Almgren, Physica D , 146, pp. 328-340 (2000).
Traveling Waves in Rapid Solidification,
Elec. J. Diff. Eq. , 2000, #16, pp. 1-28 (2000).