Publications

  • (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

  • (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

  • (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). abstract

  • (with Sergio A. Alvarez) Motion of a Closed Curve by Minus the Surface Laplacian of Curvature, Differential and Integral Equations, Vol 13, No. 10-12, 1583-1594 (1997). abstract

  • (with David Kinderlehrer, Florin Manolache and Shlomo Ta'asan) Remarks about Analysis and Simulation of Grain Boundary Systems, Proceeding of Third International Conference of Grain Growth, 437 - 443 (1998).

  • (with M. Carme Calderer and Karl Voss) Radial Configurations of Smectic A materials and Focal Conics, Physica D, 124, 11--22 (1998). abstract

  • (with Noel J. Walkington) Approximation of Liquid Crystal Flows, Siam Journal of Numerical Analysis, Vol 37, 725-741 (2000). abstract

  • (with Fang-Hua Lin) Existence of Solutions for Ericksen-Leslie System, Archive for Rational Mechanics and Analysis, 154, no. 2, 135-156 (2000). abstract

  • (with M. Carme Calderer) Liquid Crystal Flow: Dynamic and Static Configurations, Siam Journal of Applied Mathematics 60 (6), 1925 - 1949 (2000). abstract

  • Dynamic Theory for Incompressible Smectic-A Liquid Crystals: Existence and Regularity, Discrete and Continuous Dynamic Systems, Vol 6, Num. 3, 591-608 (2000). abstract

  • (with M. Carme Calderer) Poiseuille Flow of Nematic Liquid Crystals, International Journal of Engineering Science, 38, 1007-1022 (2000). abstract

  • (with M. Carme Calderer) Mathematical Developments in the Study of Smectic A Liquid Crystals, International Journal of Engineering Science, 38, 1113-1128 (2000). abstract

  • (with David Kinderlehrer) Evolution of Grain Boundaries, Mathematical Models and Methods in Applied Sciences (M3AS), 11 (4) , 713-729 (2001). abstract

  • (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

  • (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

  • (with Noel J. Walkington) An Eulerian Description of Fluids Containing Visco-Elastic Particles, Archive for Rational Mechanics and Analysis, 159, 229-252 (2001). abstract

  • (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

  • (with Raimund Burger and Wolfgang Wendland) Existence and Stability for Mathematical Models of Sedimentation-Consolidation Processes in Several Space Dimensions, Journal of Mathematical Analysis and Applications, 264, 288-310 (2001). abstract

  • (with Fanghua Lin) Static and Dynamic Theories of Liquid Crystals, Journal of Partial Differential Equations, Vol 14, No. 4, 289-330 (2001). article

  • (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

  • (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

  • (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

  • (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

  • (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

  • (with Jie Shen) A Phase Field Model for the Mixture of Two Incompressible Fluids and its Approximation by a Fourier-Spectral Method, Physica D, 179, 4, 211-228 (2003). abstract

  • (with Mingjun Lai and Paul Wenston) Bivariate Spline Method for Numerical Solution of Time Evolution Navier-Stokes Equations Over Polygons in Stream Function Formulation, Numerical Methods for Partial Differential Equations, Vol. 19, No. 6, 776-827 (2003). abstract

  • (with Mingjun Lai and Paul Wenston) Numerical Simulations on Two Nonlinear Biharmonic Evolution Equations, Applicable Analysis 83, no. 6, 563-577 (2004). abstract

  • (with Qiang Du and Xiaoqiang Wang) A Phase Field Approach in the Numerical Study of the Elastic Bending Energy for Vesicle Membranes, Journal of Computational Physics 198, no. 2, 450-468 (2004). abstract

  • (with Pengtao Yue, Jimmy Feng and Jie Shen) A Diffuse-Interface Method for Simulating Two-Phase Flows of Complex Fluids, Journal of Fluid Mechanics, Vol 515, 293-317 (2004). abstract

  • (with Fanghua Lin and Ping Zhang) On Hydrodynamics of Viscoelastic Fluids, Communication of Pure and Applied Mathematics, Vol 58, Issue 11, 1437 -- 1471 (2005). abstract

  • (with Qiang Du, Rolf Ryham and Xiaoqiang Wang) A Phase Field Formulation of the Willmore Problem, Nonlinearity, 18, 1249 -- 1267 (2005). abstract

  • (with Peng Yu and Qiang Du) From Micro to Macro Dynamics Via a New Closure Approximation to the FENE Model of Polymeric Fluids, SIAM Journal on Multiscale Modelling and Simulation, Vol 3, No 4, 895 -- 917 (2005). abstract

  • (with Qiang Du, Rolf Ryham and Xiaoqiang Wang) Modeling the spontaneous curvature effects in static cell membrane deformation by a phase field formulation, Communications in Pure and Applied Analysis, Vol 4, No 3, 537 -- 548 (2005). abstract

  • (with Qiang Du and Xiaoqiang Wang) Retrieving Topological Information For Phase Field Models, SIAM Journal on Applied Mathematics, Vol 65, No 6, 1913 -- 1932 (2005). abstract

  • (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

  • (with Qiang Du and Peng Yu) FENE dumbbell model and its several linear and nonlinear closure approximations, SIAM Journal on Multiscale Modeling and Simulation, Vol 4, No 3, 709 -- 731 (2005). abstract

  • (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

  • (with Pengtao Yue, Jimmy Feng and Jie Shen) Viscoelastic Effects on Drop Deformation in Steady Shear, Journal of Fluid Mechanics, 540, 427 -- 437(2005). abstract

  • (with Qiang Du and Xiaoqiang Wang) Simulating the Deformation of Vesicle Membranes under Elastic Bending Energy in Three Dimensions, Journal of Computational Physics, 212, 2, 757 -- 777 (2006). abstract

  • (with Pengtao Yue, Jimmy Feng and Jie Shen) Transient drop deformation upon startup of shear in viscoelastic fluids, Physics of Fluids, 17, 123101 (2005). abstract

  • (with Rolf Ryham and Zhiqiang Wang) On Electro-Kinetic Fluids: One Dimensional Configurations, Discrete and Continuous Dynamical Systems B, Volume 6, Number 2, 357 -- 371 (2006). abstract

  • (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)

  • (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)

  • (with Fanghua Lin and Ping Zhang) On a Micro-Macro Model for Polymeric Fluids near Equilibrium, Communications on Pure and Applied Mathematics, Vol 60. Issue 6, 838--866 (2007). abstract

  • (with Ping Lin) Simulations of singularity dynamics in liquid crystal flows: a fast C^0 Finite element approach, Journal of Computational Physics, 215 (1), 348-362 (2006). abstract

  • (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).

  • (with Xiaofeng Yang, Jimmy Feng and Jie Shen) Numerical Simulations of Jet Pinching-off and Drop Formation using an Energetic Variational Phase-Field Method, Journal of Computational Physics 218:417-428 (2006). abstract

  • (with C. Zhou, P. Yue, J Feng and Jie Shen) Heart-shaped bubbles rising in anisotropic liquids, Physics of Fluids, 19, 041703 (2007). abstract

  • (with Qiang Du, Rolf Ryham and Xiaoqiang Wang) Diffusive Interface Energies Capturing the Euler Number: Relaxation and Renormalization, Communications of Mathematical Sciences 5, pp.233-242 (2007). article

  • (with Xiaobing Feng and Yinnian He) Analysis of finite element approximations of a phase field model for two phase fluids, Mathematics of Computation 76, no. 258, 539-571 (2007). abstract

  • (with Noel J. Walkington) Convergence of Numerical Approximations of the Incompressible Navier Stokes Equations with Variable Density and Viscosity, SIAM Journal of Numerical Analysis 45, no. 3, 1287-1304 (2007). abstract

  • (with Qiang Du and Manlin Li) Analysis of a Phase Field Navier-Stokes Vesicle-Fluid Interaction Model, Discrete and Continuous Dynamical Systems B, 8, No 3, pp.539-556, (2007). abstract

  • (with Zhen Lei and Yi Zhou) Global Existence for Small Strain Viscoelasticity, Communication in Mathematical Sciences 5, No 3, 595 -- 616 (2007). article

  • (with Rolf Ryham and Ludmil Zikatanov) Mathematical Models for the Deformation of Electrolyte Droplets, Discrete and Continuous Dynamical Systems B, Volume 8, Number 3, 649 -- 661 (2007). abstract

  • (with Ping Lin and Hui Zhang) An energy law preserving C^0 finite element scheme for simulating the kinematic effects in liquid crystal dynamics, Journal of Computational Physics, Volume 227, Issue 2, 1411 --1427 (2007). abstract

  • (with Zhen Lei and Yi Zhou) Global Solutions for Incompressible Viscoelastic Fluids, Archive for Rational Mechanics and Analysis 188, 371 - 398 (2008). abstract

  • (with Hailiang Liu) Boundary Conditions for the Microscopic FENE Models, SIAM Journal of Applied Mathematics Volume 68, Issue 5, 1304--1315 (2008). abstract

  • (with Yunkyong Hyon, Jose A. Carrillo and Qiang Du) A Macroscopic Closure Approximation to the Micro-Macro FENE Models with Maximum Entropy Principle for Polymeric Materials, Kinetic and Related Models, Volume 1, Number 2, 171 -- 184 (2008). abstract

  • (with Ping Sheng and Jianwei Zhang) Onsager Principle and Electrorheological Fluid Dynamics, Progress of Theoretical Physics Supplement 175, 131 - 143 (2008). abstract

  • (with Aaron Naber, Jimmy Feng and Christopher A. Bertelo) The Nucleation and Growth of Gas Bubbles in a Newtonian Fluid: An Energetic Variational Phase Field Approach, in Moving Interface Problems and Applications in Fluid Dynamics (AMS Contemporary Mathematics Series, Vol. 466, eds. K. B. Cheong, Z. Li and P. Lin). pp. 95-120. American Mathematics Society (2008).

  • (with Yunkyong Hyon and Qiang Du) An Enhanced Macroscopic Closure Approximation to the Micro-macro FENE Models for Polymeric Materials, SIAM Journal of Multiscale Modeling and Simulation, Volume 7, Number 2, 978 -- 1002 (2008). abstract

  • (with Jianwei Zhang, Xiuqing Gong, Weijia Wen and Ping Sheng) Electrorheological Fluid Dynamics, Physical Review Letters 101, 194503 (2008). abstract

  • (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

  • (with Qiang Du, Rolf Ryham and Xiaoqiang Wang) Energetic Variational Approaches to Modeling Vesicle and Fluid Interactions, Physica D, 238, 923--930 (2009). abstract

  • (with Pengtao Sun and Jinchao Xu) Phase Field Model of Thermo-Induced Marangoni Effects in the Mixtures and its Numerical Simulations with Mixed Finite Element Methods, Communications in Computational Physics, 6, 1095 -- 1117(2009). abstract

  • (with Yunkyong Hyon and Do Young Kwak) Energetic Variational Approach in Complex Fluids : Maximum Dissipation Principle, Discrete and Continuous Dynamical Systems, Volume 26, Number 4, 1291 -- 1304 (2010). abstract

  • (with Xiang Xu and Liyun Zhao) Axisymmetric Solutions to a coupled Navier-Stokes/Allen-Cahn Equations, SIAM Journal of Mathematical Analysis, Volume 41, Issue 6, 2246-2282 (2010). abstract

  • (with Qiang Du and Yunkyong Hyon) On some PDF based moment closure approximations of micro-macro models for viscoelastic polymeric fluids, Journal of Computational and Theoretical Nanoscience, 7, 738 -- 755 (2010). abstract

  • (with Norifumi Sato and Yoshihiro Tonegawa) On the Existence of Mean Curvature Flow with Transport Term, Interfaces and Free Boundaries 12, No 2, 251-277 (2010). abstract

  • (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

  • (with Yunkyong Hyon and Robert Eisenberg) Energy Variational Analysis EnVarA of Ions in Water and Channels: Field Theory for Primitive Models of Complex Ionic Fluids, Journal of Chemical Physics 133, 104104 (2010) . abstract

  • (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

  • (with Yunkyong Hyon and Robert Eisenberg) A Mathematical Model for the Hard Sphere Repulsion in Ionic Solutions, Communications in Mathematical Sciences 9(2), pp.459-475, 2011. article

  • (with Chiun-Chang Lee, Hijin Lee, Yunkyong Hyon and Taichia Lin) New Poisson-Boltzmann Type Equations: One-Dimensional Solutions, Nonlinearity 24, pp.431-458, 2011. abstract

  • (with Jinsong Hua, Ping Lin and Qi Wang) Energy Law Preserving C^0 Finite Element Schemes for Phase Field Models in Two-Phase Flow Computations, Journal of Computational Physics 230, 7115 - 7131 (2011). abstract

  • (with James H. Adler, James Brannick, Thomas Manteuffel and Ludmil Zikatanov) First-order system least squares and the energetic variational approach for two-phase flow, Journal of Computational Physics 230(17):6647-6663 (2011). abstract

  • (with Xiaofeng Yang, M. Gregory Forest and Jie Shen) Shear Cell Rupture of Nematic Droplets in Viscous Fluids, Journal of Non-Newtonian Fluid Mechanics 166:487Ð499 (2011). abstract

  • (with Yoichiro Mori and Robert S. Eisenberg) A Model of Electrodiffusion and Osmotic Water Flow and its Energetic Structure, Physica D: Nonlinear Phenomena, 240(22), 1835-1852 (2011). abstract

  • (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, Volume 45, Issue 3-4, 319-345 (2012). abstract

  • (with Yunkyong Hyon, James E. Fonseca and Robert Eisenberg) Energy Variational Approach To Study Charge Inversion (Layering) Near Charged Wall, Discrete and Continuous Dynamical Systems - Series B, Volume 17, Issue 8, 2725-2743 (2012). abstract

  • (with Xinpeng Xu and Tiezheng Qian) Hydrodynamic Boundary Conditions for One-Component Liquid-Gas Flows on Non-isothermal Solid Substrates, Communications for Mathematical Sciences, Volume 10, Issue 4, 1027-1053 (2012). abstract

  • (with Norifumi Sato and Yoshihiro Tonegawa) Two-Phase Flow Problem Coupled with Mean Curvature Flow, Interfaces and Free Boundaries, Volume 14, Issue 2, 185Ð203 (2012). abstract

  • (with Tzyy-Leng Hrong, Tai-Chia Lin and Robert Eisenberg) PNP equations with Steric Effects: a Model of Ion Flow through Channels, Journal of Physical Chemistry, 116 (37), 11422Ð11441 (2012). abstract

  • (with Xiang Xu and Hao Wu) On the General Ericksen-Leslie System: ParodiÕs Relation, Well-posedness and Stability. Archive for Rational Mechanics and Analysis, Volume 208, Issue 1, 59-107, (2013). abstract

  • (with Xiaofeng Yang, M. Gregory Forest, Huiyuan Li, Jie Shen and Qi Wang) Numerical Investigation Of The Dynamics Of Drop Formation And Pitch-Off Using A Phase-Field Model For Two-Phase Complex Fluids, Journal of Computational Physics, Volume 236, 1, Pages 1-14 (2013). abstract

  • (with Pengtao Sun, Lixiang Zhang and Jinchao Xu) Full Eulerian modeling and effective numerical studies for the dynamic fluid-structure interaction problem, Contemporary Mathematics, Volume 586, 351-363, (2013). abstract

  • (with Yi Du and Qingtian Zhang) Blow-up criterion for compressible visco-elasticity equations in three dimensional space. Communication of Mathematical Sciences, Volume 12, Number 3, Pages: 473 Ð 484 (2013). abstract

  • (with Shixin Xu and Ping Sheng) An Energetic Variational Approach for Ion Transport. Communications on Mathematical Sciences, Vol. 12, No. 4, pp. 779-789 (2014). abstract

  • (with Allen Flavell, Michael Machen, Bob Eisenberg, and Xiaofan Li) A Conservative Finite Difference Scheme for Poisson-Nernst-Planck Equations. Journal of Computational Electronics, Vol. 13, 235-249 (2014). abstract

  • (with Li Wan, Shixin Xu, Maijia Liao, and Ping Sheng) Self-Consistent Approach to Global Charge Neutrality in Electrokinetics: A Surface Potential Trap Model. Physical Review X, 4, 011042 (2014). abstract

  • (with Yunkyong Hyon and Robert Eisenberg) An Energetic Varitional Approach to Ion Channel Dynamics, Mathematical Methods in the Applied Sciences, Volume 37, Issue 7, Pages 952 (2014). abstract

  • (with Shixin Xu, Minxin Chen and Sheereen Majd) Modeling and Simulating Asymmetrical Conductance Changes in Gramicidin Pores. Molecular Based Mathematical Biology (MBMB), Volume 2, Issue 1, Page 34 (2014). abstract

  • (with Minxin Chen and Xiantao Li) Computation of the Memory Functions in the Generalized Langevin Models for Collective Dynamics of Macromol ecules, Journal of Computational Physics, Volume 141, 064112 (2014). abstract

  • (with Li Wan, Shixin Xu, Maijia Liao, and Ping Sheng) Self-Consistent Approach to Global Charge Neutrality in Electrokinetics: A Surface Potential Trap Model. Physics, Vol 34, Issue 9, Page 590 - 596 (2014). abstract

  • (with Chia-Yu Hsieh, Yunkyong Hyon, Hijin Lee And Tai-Chia Lin) Transport Of Charged Particles: Entropy Production And Maximum Dissipation Principle, Nonlinear Analysis, Vol 422, Page 309 - 336 (2015). abstract

  • (with Xiaofeng Yang and Jie Shen) Decoupled Energy Stable Schemes For A Phase-Field Model Of Two-Phase Incompressible Flows With Variable De nsity. Journal of Scientific Computing, Vol 62, Page 601--622 (2015). abstract

  • (with Hao Wu, Taichia Lin) Diffusion limit of kinetic equations for multiple species charged particles. Archive for Rational Mechanics and Analysis, Vol 215, 419--441 (2015). abstract

  • (with Wenrui Hao, Zhiliang Xu and Guang Lin) A Fictitious Domain Method with a Hybrid Cell Model for Simulating Motion of Cells in Fluid Flow, Journal of Computational Physics, Volume 280, Pages 345--362 (2015). abstract

  • (with Jerry Yang, Chao Mao and Xiantao Li) On the Cauchy-Born Approximation at Finite Temperature, Computational Materials Science, Volume 99, Pages 21--28 (2015). abstract

  • (with Geng Chen and Tao Huang) Finite time singularities for hyperbolic systems, SIAM Journal of Mathematical Analysis, 47(1), 758–785 (2015). abstract

  • (with Huan Sun, James Brannick and Tiezheng Qian) Diffuse Interface Method for Multiple Phase Materials: An Energetic Variational Approach, to appear in Journal of Numerical Mathematics (2014). abstract

  • (with Chiun-Chang Lee, Hijin Lee, YunKyong Hyon and Tai-Chia Lin) Boundary layer solutions of Charge Conserving Poisson-Boltzmann equations: one-dimensional case, to appear in Communication of Mathematical Sciences (2015).