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 and segmentation, with Qiang Du, Max Gunzburger and Lili Ju,  Journal of Mathematical Imaging and Vision, DOI: 10.1007/s10851-005-3620-4, Jan. 2006
     
  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, accepted for publication, 2006
     
  12. Diffuse Interface Energies Capturing The Euler Number: Relaxation And Renomalization, with Qiang Du, Chun Liu and Rolf Ryham, Comm. Math. Sci., accepted for publication, 2007
     
  13. Modeling Vesicle Deformations in Flow Fields via Energetic Variational Approaches, with Qiang Du, Chun Liu and Rolf Ryham, submitted to Nonlinearity, 2006.
     
  14. Modelling and Simulations of Multi-component Lipid Membranes and Open Membranes via Diffusive Interface Approaches, with Qiang Du, submitted to Journal of Mathematical Biology, 2006
     
  15. Asymptotic Analysis of Phase Field Formulations of Bending Elasticity Models, submitted to SIAM Mathematical Analysis, 2006
     
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