(with Fang-Hua Lin) Nonparabolic Dissipative Systems Modeling the Flow of LiquidCrystals, 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 ofLiquid 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).
(with Sergio A. Alvarez) Motion of a Closed Curve by Minus the Surface Laplacian ofCurvature, Differential and Integral Equations, Vol 13, No. 10-12, 1583–1594 (1997).
(with David Kinderlehrer, Florin Manolache and Shlomo Ta’asan) Remarks aboutAnalysis 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 materialsand 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 LiquidCrystals, 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 withInterface 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-ElasticParticles, Archive for Rational Mechanics and Analysis, 159, 229–252 (2001). abstract
(with M. Carme Calderer, Dmitry Golovaty and Fanghua Lin) Time Evolution ofNematic 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 forMathematical Models of Sedimentation-Consolidation Processes in Several SpaceDimensions, 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 ofnonhomogeneous rodlike liquid crystalline polymers with a nonlocal intermolecularpotential, 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 BipolarLiquid 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 TransitionBetween 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 itsApproximation 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 ofTime 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 NonlinearBiharmonic Evolution Equations, Applicable Analysis 83, no. 6, 563–577 (2004). abstract
(with Qiang Du and Xiaoqiang Wang) A Phase Field Approach in the Numerical Studyof 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 SimulatingTwo-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 theWillmore Problem, Nonlinearity, 18, 1249 — 1267 (2005). abstract
(with Peng Yu and Qiang Du) From Micro to Macro Dynamics Via a New ClosureApproximation 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 curvatureeffects 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 PhaseField 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 Flowon 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 nonlinearclosure 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 ofDrop-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 Deformationin Steady Shear, Journal of Fluid Mechanics, 540, 427 — 437(2005). abstract
(with Qiang Du and Xiaoqiang Wang) Simulating the Deformation of Vesicle Membranesunder 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 startupof shear in viscoelastic fluids, Physics of Fluids, 17, 123101 (2005). abstract
(with Rolf Ryham and Zhiqiang Wang) On Electro-Kinetic Fluids: One DimensionalConfigurations, 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-PhaseFlows 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 Formulationwith Phase Field Methods for Interfacial Dynamics of Complex Fluids: Advantagesand 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 Fluidsnear 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 C0Finite element approach, Journal of Computational Physics, 215 (1), 348–362 (2006).
abstract
(with Carme Calderer and Baisheng Yan) A model for total energy of nematicelastomers with non-uniform prolate spheroids. Advances in applied and computationalmathematics, 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 JetPinching-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 anisotropicliquids, Physics of Fluids, 19, 041703 (2007). abstract
(with Qiang Du, Rolf Ryham and Xiaoqiang Wang) Diffusive Interface EnergiesCapturing 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 aphase 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 theIncompressible 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-FluidInteraction 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 ofElectrolyte 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 C0finite element scheme forsimulating 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 ClosureApproximation to the Micro-Macro FENE Models with Maximum Entropy Principle forPolymeric Materials, Kinetic and Related Models, Volume 1, Number 2, 171 — 184
(2008). abstract
(with Aaron Naber, Jimmy Feng and Christopher A. Bertelo) The Nucleation and Growthof 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 Approximationto the Micro-macro FENE Models for Polymeric Materials, SIAM Journal of Multiscale
Modeling and Simulation, Volume 7, Number 2, 978 — 1002 (2008). abstract
(with Huan Sun) On Energetic Variational Approaches in Modeling the Nematic LiquidCrystal Flows, Discrete and Continuous Dynamical Systems, Volume 23, Number 2, 455
— 475 (2009). abstract
(with Qiang Du, Rolf Ryham and Xiaoqiang Wang) Energetic Variational Approachesto Modeling Vesicle and Fluid Interactions, Physica D, 238, 923—930 (2009). abstract
(with Pengtao Sun and Jinchao Xu) Phase Field Model of Thermo-Induced MarangoniEffects in the Mixtures and its Numerical Simulations with Mixed Finite ElementMethods, Communications in Computational Physics, 6, 1095 — 1117(2009). abstract
(with Yunkyong Hyon and Do Young Kwak) Energetic Variational Approach in ComplexFluids : 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 coupledNavier-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 closureapproximations 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 Flowwith 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 ParticlesImmersed in Stokesian Flows, Solid State Communications, Volume 150, Issues 22,
990-1002 (2010). abstract
(with Yunkyong Hyon and Robert Eisenberg) Energy Variational Analysis EnVarA ofIons 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 Hydrodynamicsof 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 HardSphere 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) NewPoisson-Boltzmann Type Equations: One-Dimensional Solutions, Nonlinearity 24,
pp.431–458, 2011. abstract
(with Jinsong Hua, Ping Lin and Qi Wang) Energy Law Preserving C0FiniteElement 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-phaseflow, Journal of Computational Physics 230(17):6647-6663 (2011). abstract
(with Xiaofeng Yang, M. Gregory Forest and Jie Shen) Shear Cell Rupture of NematicDroplets in Viscous Fluids, Journal of Non-Newtonian Fluid Mechanics 166:487499
(2011). abstract
To Appear:
(with Yoichiro Mori and Robert S. Eisenberg) A Model of Electrodiffusion and OsmoticWater Flow and its Energetic Structure, to appear in Physica D (2011). (49 pages)
abstract
(with Yunkyong Hyon, James E. Fonseca and Robert Eisenberg) Energy VariationalApproach To Study Charge Inversion (Layering) Near Charged Wall, to appear in
Discrete and Continuous Dynamical Systems (2010). (22 pages)
Other Publications:
Variational Approaches in Complex Fluids, Lecture Notes (2004).
Multi-scale Phenomena in Complex Fluids: Modeling, Analysis and Numerical
Simulations (Series in Contemporary Applied Mathematics) (Series in Contemporary
Applied Mathematics Cam) by Thomas Y. Hou (Author, Editor), Chun Liu (Editor),
Jian-guo Liu (Editor), World Scientific Publishing Company ( 2009). abstract and
contents
Nonlinear Conservation Laws, Fluid Systems and Related Topics (Series in Contemporary
Applied Mathematics) by Gui-Qiang Chen (Author, Editor), Ta-Tsien Li (Editor), Chun
Liu (Editor), World Scientific Publishing Company ( 2009). abstract and contents
Energetic Variational Approaches for Complex Fluids. Proceeding of the 36th Sapporo
Symposium on Partial Differential Equations, August 22 - 24, 2011, Faculty of Science,
Hokkaido University (2011).
abstract