Publications

  1. Force convergence for the de Gennes-Cahn-Hilliard energy, with Abba Ramadan and Joe Renzi, submitted. 
  2. Minimizers for the de Gennes-Cahn-Hilliard energy under strong anchoring conditions, with Abba Ramadan,  Numer. Methods Partial Differ. Eq. 40 (2024), e23127. https://doi.org/10.1002/num.23127
  3. On the Cahn-Hilliard equation with no-flux and strong anchoring conditions, with Toai Luong, Nonlinear Differential Equations and Applications, (2023) 30:49. ​
  4. Gamma convergence of the de Gennes-Cahn-Hilliard energy, with Joe Renzi and Steve Wise, Communications in Mathematical Sciences. Vol 21, No. 8 (2023), pp. 2131-2144. DOI: https://dx.doi.org/10.4310/CMS.2023.v21.n8.a3 (arXiv:2210.16492).
  5. Geometric evolution of bilayers under the degenerate functionalized Chan-Hilliard equation, with Toai Luong and Xiang Ma, Multiscale Modeling and Simulation, Vol. 20, No. 3 (2022), pp. 1127–1146.
  6. On nonnegative solutions for the Functionalized Cahn-Hilliard equation with degenerate mobility, with Qiang Liu, Toai Luong, and Keith Promislow, Results in Applied Mathematics, Volume 12, November 2021, 100195.
  7. Codimension one minimizers of highly amphiphilic mixtures, with Keith Promislow,  Journal of Computational and Applied Mathematics, 388 (2021), 113320 (arXiv:2009.02821v1).
  8. Minimizers for the Cahn-Hilliard energy under strong anchoring conditions, with Bo Li and Toai Luong, SIAM J. Appl. Math, Vol. 80, No. 5 (2020), 2299-2317. 
  9. 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.
  10. ​Weak Solutions for the Functionalized Cahn-Hilliard Equation with Degenerate Mobility, with Qiang Liu and Keith Promislow, Applicable Analysis, Vol. 100, No. 1 (2021), 1-16 (Published online 04 March 2019, DOI: 10.1080/00036811.2019.1585536).
  11. 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).
  12. 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.
  13. 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.
  14. Competitive geometric evolution of amphiphilic interfaces, with Keith Promislow, SIAM J. Math. Anal. Vol. 47, No. 1 (2015), 347–380.
  15. 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.
  16. Geometric evolution of bilayers under the functionalized Cahn-Hilliard equation, with Keith Promislow, Proc. Royal Soc. A, (2013) 469: 20120505.
  17. 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.
  18. On the Ostwald ripening of thin liquid films, Comm. Math. Sci., Vol. 9, Issue 1 (2011), 143-160. 
  19. On a mean field model for 1D thin film droplet coarsening, Nonlinearity, 23 (2010), 325-340.
  20. 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. 
  21. 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.
  22. 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.
  23. 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.
  24. 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.
  25. ​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