Liquid Crystals

  1. (with Fang-Hua Lin) Nonparabolic Dissipative Systems Modeling the Flow of Liquid Crystals, Communications on Pure and Applied Mathematics, Vol. 48, Issue 5, 501 – 537 (1995). abstract
  2. (with Fang-Hua Lin) Partial Regularity of the Dynamic System Modeling the Flow of Liquid Crystals, Discrete and Continuous Dynamic Systems, Vol 2, No 1, 1 – 23 (1996). abstract
  3. (with David Kinderlehrer) Revisiting the Focal Conic Structures in Smectic A, Proceeding of Symposium on Elasticity to honor Professor J.L. Ericksen. ASME Mechanics and Materials Conference, 217 – 225 (1996).
  4. (with M. Carme Calderer and Karl Voss) Radial Configurations of Smectic A materials and Focal Conics, Physica D, 124, 11—22 (1998). abstract
  5. (with Noel J. Walkington) Approximation of Liquid Crystal Flows, Siam Journal of Numerical Analysis, Vol 37, 725–741 (2000). abstract
  6. (with Fang-Hua Lin) Existence of Solutions for Ericksen-Leslie System, Archive for Rational Mechanics and Analysis, 154, no. 2, 135–156 (2000). abstract
  7. (with M. Carme Calderer) Liquid Crystal Flow: Dynamic and Static Configurations, Siam Journal of Applied Mathematics 60 (6), 1925 – 1949 (2000). abstract
  8. Dynamic Theory for Incompressible Smectic-A Liquid Crystals: Existence and Regularity, Discrete and Continuous Dynamic Systems, Vol 6, Num. 3, 591–608 (2000). abstract
  9. (with M. Carme Calderer) Poiseuille Flow of Nematic Liquid Crystals, International Journal of Engineering Science, 38, 1007-1022 (2000). abstract
  10. (with M. Carme Calderer) Mathematical Developments in the Study of Smectic A Liquid Crystals, International Journal of Engineering Science, 38, 1113-1128 (2000). abstract
  11. (with M. Carme Calderer and Karl Voss) Smectic A Liquid Crystal Configurations with Interface Defects, Mathematical Methods in the Applied Sciences, 24 (7), 473–489 (2001). abstract
  12. (with Jie Shen) On Liquid Crystal Flows with Free-Slip Boundary Conditions, Discrete and Continuous Dynamic Systems, Vol 7, No. 2, 307–318 (2001). abstract
  13. (with M. Carme Calderer, Dmitry Golovaty and Fanghua Lin) Time Evolution of Nematic Liquid Crystals with Variable Degree of Orientation, SIAM Journal on Mathematical Analysis, 33 (5), 1033–1047 (2001). abstract
  14. (with Fanghua Lin) Static and Dynamic Theories of Liquid Crystals, Journal of Partial Differential Equations, Vol 14, No. 4, 289–330 (2001). article
  15. (with Qi Wang, Weinan E and Pingwen Wang) Kinetic theory for flows of nonhomogeneous rodlike liquid crystalline polymers with a nonlocal intermolecular potential, Physical Review E, 65, 051504 (2002). abstract
  16. (with Noel J. Walkington) Mixed Method for the Approximation of Liquid Crystal Flows, Mathematical Modelling and Numerical Analysis, Vol. 36, No. 2, pp. 205-222 (2002). abstract
  17. (with M. Carme Calderer and Quan Shen) Axisymmetric Configurations of Bipolar Liquid Crystal Droplets, Continuum Mechanics and Thermodynamics, Vol 14, No. 4, 363–375 (2002). abstract
  18. (with Bagisa Mukherjee) On Stability of Two Nematic Liquid Crystal Configurations, Discrete and Continuous Dynamic Systems B, Vol 2, No. 4, 561 –574 (2002). abstract
  19. (with Patricia Bauman, M. Carme Calderer and Daniel Phillips) The Phase Transition Between Chiral Nematic and Smectic A* Liquid Crystals, Archive for Rational Mechanics and Analysis, 165, 2, 161 – 186 (2002). abstract
  20. (with Pengtao Yue, Jimmy Feng and Jie Shen) Interfacial Forces and Marangoni Flow on a Nematic Drop, Journal of Colloid and Interface Science, 290, 281 — 288 (2005). abstract
  21. (with Pengtao Yue, Jimmy Feng and Jie Shen) Diffuse-Interface Simulations of Drop-Coalescence and Retraction in Viscoelastic Fluids, Journal of Non-Newtonian Fluid Dynamics, Vol 129, 163 — 176 (2005). abstract
  22. (with Pengtao Yue, Jimmy Feng and Jie Shen) Variational Approach in Two-Phase Flows of Complex Fluids transport and induced elastic stress, in A. Miranville, editor, Mathematical Models and Methods in Phase Transitions,. Nova Publications, (2005). (21 pages)
  23. (with Pengtao Yue, Jimmy Feng and Jie Shen) An Energetic Variational Formulation with Phase Field Methods for Interfacial Dynamics of Complex Fluids: Advantages and Challenges, in M.C. Calderer, E. Terentjev editors, ”Modeling of Soft Matter”, IMA Volumes in Mathematics and its Applications, Institute for Mathematics and its Applications, University of Minnesota, Minneapolis, MN (2005). (29 pages)
  24. (with Ping Lin) Simulations of singularity dynamics in liquid crystal flows: a fast C0 Finite element approach, Journal of Computational Physics, 215 (1), 348–362 (2006). abstract
  25. (with Carme Calderer and Baisheng Yan) A model for total energy of nematic elastomers with non-uniform prolate spheroids. Advances in applied and computational mathematics, Advances in applied and computational mathematics, 245–259, Nova Sci. Publ., Hauppauge, NY, (2006).
  26. (with C. Zhou, P. Yue, J Feng and Jie Shen) Heart-shaped bubbles rising in anisotropic liquids, Physics of Fluids, 19, 041703 (2007). abstract
  27. (with Ping Lin and Hui Zhang) An energy law preserving C0 finite element scheme for simulating the kinematic effects in liquid crystal dynamics, Journal of Computational Physics, Volume 227, Issue 2, 1411 —1427 (2007). abstract
  28. (with Huan Sun) On Energetic Variational Approaches in Modeling the Nematic Liquid Crystal Flows, Discrete and Continuous Dynamical Systems, Volume 23, Number 2, 455 — 475 (2009). abstract
  29. (with Huan Sun) The Slip Boundary Condition in the Dynamics of Solid Particles Immersed in Stokesian Flows, Solid State Communications, Volume 150, Issues 22, 990-1002 (2010). abstract
  30. (with Shupeng Zhang and Hui Zhang) Numerical Simulations of Hydrodynamics of Nematic Liquid Crystals: Effects of Kinematic Transports, Communications in Computational Physics Vol. 9, No. 4, 974-993 (2010). abstract
  31. (with Xiang Xu and Hao Wu) Asymptotic Behavior for a Nematic Liquid Crystal Model with Different Kinematic Transport Properties, Calculus of Variations and PDE’s, published online (2011). abstract
  32. (with Xiang Xu and Hao Wu) On the General EricksenLeslie System: Parodis Relation, Well-posedness and Stability, submitted to Archive for Rational Mechanics and Analysis (2011). (37 pages) abstract