Energetic Variational Approaches

November 11, 2011

Reviews:

  1. (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)
  2. (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)
  3. (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
  4. (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
  5. Variational Approaches in Complex Fluids, Lecture Notes (2004).
  6. 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

Applications:

  1. (with Noel J. Walkington) An Eulerian Description of Fluids Containing Visco-Elastic Particles, Archive for Rational Mechanics and Analysis, 159, 229–252 (2001). abstract
  2. (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
  3. (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
  4. (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
  5. (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
  6. (with Qiang Du, Rolf Ryham and Xiaoqiang Wang) A Phase Field Formulation of the Willmore Problem, Nonlinearity, 18, 1249 — 1267 (2005). abstract
  7. (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
  8. (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
  9. (with Zhen Lei and Yi Zhou) Global Existence for Small Strain Viscoelasticity, Communication in Mathematical Sciences 5, No 3, 595 — 616 (2007). article
  10. (with Zhen Lei and Yi Zhou) Global Solutions for Incompressible Viscoelastic Fluids, Archive for Rational Mechanics and Analysis 188, 371 – 398 (2008). abstract
  11. (with Jianwei Zhang, Xiuqing Gong, Weijia Wen and Ping Sheng) Electrorheological Fluid Dynamics, Physical Review Letters 101, 194503 (2008). abstract
  12. (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
  13. (with Qiang Du, Rolf Ryham and Xiaoqiang Wang) Energetic Variational Approaches to Modeling Vesicle and Fluid Interactions, Physica D, 238, 923—930 (2009). abstract
  14. (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
  15. (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
  16. (with Yoichiro Mori and Robert S. Eisenberg) A Model of Electrodiffusion and Osmotic Water Flow and its Energetic Structure, to appear in Physica D (2011). (49 pages) abstract
  17. (with Xinpeng Xu and Tiezheng Qian) Hydrodynamic Boundary Conditions for One-Component Liquid-Gas Flows on Non-isothermal Solid Substrates, submitted to Communications for Mathematical Sciences (2011). (38 pages)
  18. (with Yunkyong Hyon and Robert Eisenberg) An Energetic Varitional Approach to Ion Channel Dynamics, submitted to Mathematical Methods in the Applied Sciences (2011). (13 pages)