Preprints

  1. Geometric evolution of bilayers under the degenerate functionalized Cahn-Hilliard equation, with Toai Luong, preprint.
  2. ​Minimizers for the Cahn-Hilliard energy under strong anchoring conditions, with Bo Li and Toai Luong, submitted. 
  3. On nonnegative solutions for the Functionalized Cahn-Hilliard equation with degenerate mobility, with Qiang Liu, Toai Luong, and Keith Promislow, preprint.​
  4. ​Codimension one minimizers of highly amphiphilic mixtures, with Keith Promislow,  submitted.​​

Publications

  1. Rigorous derivation of a mean field model for the Ostwald ripening of thin films, Communications in Mathematical Sciences, Vol. 18, No. 2 (2020), 293-320.
  2. ​Weak Solutions for the Functionalized Cahn-Hilliard Equation with Degenerate Mobility, with Qiang Liu and Keith Promislow, Applicable Analysis, published online 04 March 2019, DOI: 10.1080/00036811.2019.1585536.
  3. Convergence of phase-field free energy and boundary force for molecular solvation, with Bo Li and Jianfeng Lu, Archive for Rational Mechanics and Analysis, Volume 227, Issue 1 (2018), 105-147 (arXiv:1606.04620).
  4. Computational studies of coarsening rates for the Cahn-Hilliard equation with phase-dependent diffusion mobility, with Qiang Du, Journal of Computational Physics, 310 (2016), 85—108.
  5. Weak solutions for the Cahn-Hilliard equation with degenerate mobility, with Qiang Du, Archive for Rational Mechanics and Analysis, Vol. 219, Issue 3 (2016), 1161—1184.
  6. Competitive geometric evolution of amphiphilic interfaces, with Keith Promislow, SIAM J. Math. Anal. Vol. 47, No. 1 (2015), 347–380.
  7. Coarsening mechanism for systems governed by the Cahn-Hilliard equation with degenerate diffusion mobility, with Qiang Du, Multiscale Modeling and Simulation, Vol. 12, No. 4 (2014), 1870–1889.
  8. Geometric evolution of bilayers under the functionalized Cahn-Hilliard equation, with Keith Promislow, Proc. Royal Soc. A, (2013) 469: 20120505.
  9. Motion of interfaces governed by the Cahn-Hilliard equation with highly disparate diffusion mobility, with Qiang Du, SIAM J. Appl. Math, Vol. 72, No. 6 (2012), 1818-1841.
  10. On the Ostwald ripening of thin liquid films, Comm. Math. Sci., Vol. 9, Issue 1 (2011), 143-160. 
  11. On a mean field model for 1D thin film droplet coarsening, Nonlinearity, 23 (2010), 325-340.
  12. Crossover in coarsening rates for the monopole approximation of the Mullins-Sekerka model with kinetic drag, with Barbara Niethammer and Robert L. Pego, Proc. Royal Soc. Edinburgh, Vol. 140, Issue 03 (2010), 553-571. 
  13. On the shortening rate of collections of plane convex curves by the area-preserving mean curvature flow, SIAM J. Math. Anal. Vol. 42, No. 1 (2010), 323-333.
  14. Universal bounds on coarsening rates for mean field models of phase transitions, with Robert L. Pego, SIAM J. Math. Anal. Vol. 37, No. 2 (2005), 347-371.
  15. An upper bound on the coarsening rate for mushy zones in a phase field model, with Robert L. Pego, Interfaces and Free Boundaries, 7 (2005), 187-197.
  16. On the efficiency of adaptive finite element methods for elliptic problems with discontinuous coefficients, with Zhiming Chen, SIAM J. Sci. Comput. Vol. 24, No. 2 (2002), 443-462.
  17. ​Adaptive Galerkin methods with error control for a dynamical Ginzburg-Landau model in superconductivity, with Zhiming Chen, SIAM J. Numer. Anal. Vol. 38, No. 6 (2001), 1961-1985