PUBLICATIONS:

1. Phase field models and simulations of vesicle bio-membranes, Ph.D thesis, Pennsylvania State University, 2005.
    
2. A Phase Field Approach in the Numerical Study of the Elastic Bending Energy for Vesicle Membranes, with Qiang Du and Chun Liu, Journal of Computational Physics, 198, pp. 450-468, 2004
    
3. Tessellation and Clustering by Mixture Models and Their Parallel Implementations, with Qiang Du, Proceeding of the fourth SIAM international conference on Data Mining, (regular paper), Orlando, FL, 2004, SIAM, pp257-268.
    
4. Centroidal Voronoi tessellation based algorithms for vector fields visualization and segmentation, with Qiang Du, IEEE Proceedings of Visualization 2004 (VIS2004), (regular paper), Austin, Texas, pp43-50, 2004
    
5. A phase field formulation of the Willmore problem, with Qiang Du, Chun Liu and Rolf Ryham, Nonlinearity, 18, pp. 1249-1267, 2005
    
6. Modeling the Spontaneous Curvature Effects in Static Cell Membrane Deformations by a Phase Field Formulation, with Qiang Du, Chun Liu and Rolf Ryham, Communications in Pure and Applied Analysis, 4, pp. 537-548, 2005
    
7. Retrieving topological information for phase field models, with Qiang Du and Chun Liu, SIAM Journal on Applied Mathematics, 65, pp. 1913-1932, 2005
    
8. Ideal point distributions, best mode selections and optimal spatial partitions via centroidal Voronoi tessellations, with Qiang Du, Maria Emelianenko and Hyung-Chun Lee, Proceedings of 2nd Inter Symposium on Voronoi Diagrams in Sciences and Engineering (refereed), Seoul, Korea, Oct 2005 (VD2005), pp. 325-333, 2005
    
9. Simulating the Deformation of Vesicle Membranes under Elastic Bending Energy in Three Dimensions, with Qiang Du and Chun Liu, Journal of Computational Physics, 212, pp. 757-777, 2006
    
10. Centroidal Voronoi Tessellation Algorithms for Image Compression, Segmentation, and Multichannel Restoration, with Qiang Du, Max Gunzburger and Lili Ju,  Journal of Mathematical Imaging and Vision, 2006, Volume 24, Issue 2, pp 177-194
     
11. Convergence of numerical approximations to a phase field bending elasticity model of membrane deformations, with Qiang Du, International Journal of Numerical Analysis and Modelling, Vol. 4, Number 3-4, pp. 441-459, 2007
     
12. Diffuse Interface Energies Capturing the Euler Number: Relaxation and Renomalization, with Qiang Du, Chun Liu and Rolf Ryham, Comm. Math. Sci., 2007, Volume 5, Issue 1, pages 233-242
     
13. Modeling and Simulations of Multi-component Lipid Membranes and Open Membranes via Diffusive Interface Approaches, with Qiang Du, Journal of Mathematical Biology, 56, no3, pp.347-371, 2008
     
14. Asymptotic Analysis of Phase Field Formulations of Bending Elasticity Models, SIAM Mathematical Analysis, Vol. 39, No. 5, pp. 1367- 1401, 2008
     
15. An Edge-Weighted Centroidal Voronoi Tessellation Model For Image Segmentation, with Jie Wang and Lili Ju, IEEE Transactions on Image Processing, Vol. 18, pp. 1844 - 1858, 2009.
     
16. Diffusive Interface Model for Actomyosin Driven Cell Oscillations, submitted to Discrete and Continuous Dynamical Systems - Series B, 2009
     

17. Energetic variational approaches in modeling vesicle and fluid interactions, with Qiang Du, Chun Liu and Rolf Ryham, Physica D, 238, pp.923-930, 2009
     

18. Edge-Weighted Centroidal Voronoi Tessellations, with Jie Wang, Numerical Mathematics: Theory, Methods And Applications, Vol. 3, no. 2, pp. 223-244, 2010.
     

19. Image segmentation using local variation and edge-weighted centroidal Voronoi tessellations, with Jie Wang and Lili Ju, IEEE Transactions on Image Processing, Vol. 20, pp. 3242-3256, 2011;
     

20. VCells: Simple and Efficient Superpixels Using Edge-Weighted Centroidal Voronoi Tessellations, with Jie Wang, Pattern Analysis and Machine Intelligence, IEEE Transactions on 34.6 pp. 1241-1247. 2012.
     

21. Generalized edge-weighted centroidal Voronoi tessellations for geometry smoothing, with Yu Wang, Lili Ju and Desheng Wang, Computers & Mathematics with Applications, Vol. 64, pp. 2663-2681, 2012;
     

22. Simulating Vesicle-Substrate Adhesion Using Two Phase Field Functions, with Rui Gu and Max Gunzburger, Journal of Computational Physics, 275, pp. 626-641, 2014
     

23. New Asymptotic Analysis Method for Phase Field Models in Moving Boundary Problem with Surface Tension, with Jie Wang,  Discrete & Continuous Dynamical Systems - Series B . Vol. 204 Issue 9, p3185-3213. 2015.
     

24. A Two Phase Field Model for Tracking Vesicle-Vesicle Adhesion, with Rui Gu and Max Gunzburger, submitted to Journal of Mathematical Biology, 2015.
     

25. A fuzzy edge-weighted centroidal Voronoi tessellation model for image segmentation, with Xiaochuan Fan, Lili Ju, and Song Wang, Computers & Mathematics with Applications, to appear, 2015
     

26. Efficient and Stable Exponential Time Differencing Runge-Kutta Methods for Phase Field Elastic Bending Energy Models, with Lili Ju and Qiang Du, submitted to Journal of Computational Physics, 2015