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All issues Volume 44 / No 1 (January-February 2010) ESAIM: M2AN, 44 1 (2010) 1-31 References
Free Access
Issue
ESAIM: M2AN
Volume 44, Number 1, January-February 2010
Page(s) 1 - 31
DOI https://doi.org/10.1051/m2an/2009040
Published online 09 October 2009
  1. F. Alouges, A new algorithm for computing liquid crystal stable configurations: the harmonic mapping case. SIAM J. Numer. Anal. 34 (1997) 1708–1726. [CrossRef] [MathSciNet] [Google Scholar]
  2. F. Alouges, A new finite element scheme for Landau-Lifchitz equations. Discrete Contin. Dyn. Syst. Ser. S 1 (2008) 187–196. [CrossRef] [MathSciNet] [Google Scholar]
  3. J.W. Barrett, S. Bartels, X. Feng and A. Prohl, A convergent and constraint-preserving finite element method for the Formula -harmonic flow into spheres. SIAM J. Numer. Anal. 45 (2007) 905–927. [CrossRef] [MathSciNet] [Google Scholar]
  4. J.W. Barrett, H. Garcke and R. Nürnberg, On the parametric finite element approximation of evolving hypersurfaces in Formula . J. Comput. Phys. 227 (2008) 4281–4307. [CrossRef] [MathSciNet] [Google Scholar]
  5. S. Bartels, Stability and convergence of finite-element approximation schemes for harmonic maps. SIAM J. Numer. Anal. 43 (2005) 220–238 (electronic). [CrossRef] [MathSciNet] [Google Scholar]
  6. T. Baumgart, S.T. Hess and W.W. Webb, Imaging co-existing domains in biomembrane models coupling curvature and tension. Nature 425 (2003) 832–824. [CrossRef] [PubMed] [Google Scholar]
  7. T. Biben and C. Misbah, An advected-field model for deformable entities under flow. Eur. Phys. J. B 29 (2002) 311–316. [CrossRef] [EDP Sciences] [Google Scholar]
  8. P. Biscari and E.M. Terentjev, Nematic membranes: Shape instabilities of closed achiral vesicles. Phys. Rev. E 73 (2006) 051706. [CrossRef] [MathSciNet] [Google Scholar]
  9. F. Brezzi and M. Fortin, Mixed and hybrid finite element methods, Springer Series in Computational Mathematics 15. Springer-Verlag, New York, USA (1991). [Google Scholar]
  10. P.B. Canham, The minimum energy of bending as a possible explanation of the biconcave shape of the human red blood cell. J. Theort. Biol. 26 (1970) 61–81. [Google Scholar]
  11. Y.M. Chen, The weak solutions to the evolution problems of harmonic maps. Math. Z. 201 (1989) 69–74. [CrossRef] [MathSciNet] [Google Scholar]
  12. C.H.A. Cheng, D. Coutand and S. Shkoller, Navier-Stokes equations interacting with a nonlinear elastic biofluid shell. SIAM J. Math. Anal. 39 (2007) 742–800 (electronic). [CrossRef] [MathSciNet] [Google Scholar]
  13. P.G. Ciarlet, The finite element method for elliptic problems, Classics in Applied Mathematics 40. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, USA (2002). Reprint of the 1978 original [North-Holland, Amsterdam; MR0520174 (58 #25001)]. [Google Scholar]
  14. K. Deckelnick, G. Dziuk and C.M. Elliott, Computation of geometric partial differential equations and mean curvature flow. Acta Numer. 14 (2005) 139–232. [CrossRef] [MathSciNet] [Google Scholar]
  15. Q. Du, C. Liu and X. Wang, A phase field approach in the numerical study of the elastic bending energy for vesicle membranes. J. Comput. Phys. 198 (2004) 450–468. [CrossRef] [MathSciNet] [Google Scholar]
  16. Q. Du, C. Liu and X. Wang, Simulating the deformation of vesicle membranes under elastic bending energy in three dimensions. J. Comput. Phys. 212 (2006) 757–777. [CrossRef] [MathSciNet] [Google Scholar]
  17. G. Dziuk, Computational parametric Willmore flow. Numer. Math. 111 (2008) 55–80. [CrossRef] [MathSciNet] [Google Scholar]
  18. E. Evans, Bending resistance and chemically induced moments in membrane bilayers. Biophys. J. 14 (1974) 923–931. [CrossRef] [PubMed] [Google Scholar]
  19. J.B. Fournier and P. Galatoa, Sponges, tubules and modulated phases of para-antinematic membranes. J. Phys. II 7 (1997) 1509–1520. [CrossRef] [Google Scholar]
  20. A. Freire, S. Müller and M. Struwe, Weak compactness of wave maps and harmonic maps. Ann. Inst. H. Poincaré Anal. Non Linéaire 15 (1998) 725–754. [Google Scholar]
  21. M. Giaquinta and S. Hildebrandt, Calculus of variations I: The Lagrangian formalism, Grundlehren der Mathematischen Wissenschaften 310, [Fundamental Principles of Mathematical Sciences]. Springer-Verlag, Berlin, Germany (1996). [Google Scholar]
  22. P. Grisvard, Elliptic problems in nonsmooth domains, Monographs and Studies in Mathematics 24. Pitman (Advanced Publishing Program), Boston, USA (1985). [Google Scholar]
  23. C. Grossmann and H.-G. Roos, Numerical treatment of partial differential equations. Universitext, Springer, Berlin, Germany (2007). Translated and revised from the 3rd (2005) German edition by Martin Stynes. [Google Scholar]
  24. W. Helfrich, Elastic properties of lipid bilayers: theory and possible experiments. Z. Naturforsch. C 28 (1973) 693–703. [PubMed] [Google Scholar]
  25. W. Helfrich and J. Prost, Intrinsic bending force in anisotropic membranes made of chiral molecules. Phys. Rev. A 38 (1988) 3065–3068. [CrossRef] [PubMed] [Google Scholar]
  26. J.T. Jenkins, The equations of mechanical equilibrium of a model membrane. SIAM J. Appl. Math. 32 (1977) 755–764. [CrossRef] [MathSciNet] [Google Scholar]
  27. M.A. Johnson and R.S. Decca, Dynamics of topological defects in the Formula phase of 1,2-dipalmitoyl phosphatidylcholine bilayers. Opt. Commun. 281 (2008) 1870–1875. [CrossRef] [Google Scholar]
  28. O.A. Ladyzhenskaya and N.N. Ural'tseva, Linear and quasilinear elliptic equations. Academic Press, New York, USA (1968). Translated from the Russian by Scripta Technica, Inc. Translation editor: Leon Ehrenpreis. [Google Scholar]
  29. T. C. Lubensky and F.C. MacKintosh, Theory of “ripple” phases of bilayers. Phys. Rev. Lett. 71 (1993) 1565–1568. [CrossRef] [PubMed] [Google Scholar]
  30. F.C. MacKintosh and T.C. Lubensky, Orientational order, topology, and vesicle shapes. Phys. Rev. Lett. 67 (1991) 1169–1172. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  31. S.J. Marrink, J. Risselada and A.E. Mark, Simulation of gel phase formation and melting in lipid bilayers using a coarse grained model. Chem. Phys. Lipids 135 (2005) 223–244. [CrossRef] [PubMed] [Google Scholar]
  32. S.T.-N.J.F. Nagle, Structure of lipid bilayers. Biochim. Biophys. Acta 1469 (2000) 159–195. [CrossRef] [PubMed] [Google Scholar]
  33. P. Nelson and T. Powers, Rigid chiral membranes. Phys. Rev. Lett. 69 (1992) 3409–3412. [CrossRef] [PubMed] [Google Scholar]
  34. R. Oda, I. Huc, M. Schmutz and S.J. Candau, Tuning bilayer twist using chiral counterions. Nature 399 (1999) 566–569. [CrossRef] [PubMed] [Google Scholar]
  35. M.S. Pauletti, Parametric AFEM for geometric evolution equations coupled fluid-membrane interaction. Ph.D. Thesis, University of Maryland, USA (2008). [Google Scholar]
  36. R.E. Rusu, An algorithm for the elastic flow of surfaces. Interfaces Free Bound. 7 (2005) 229–239. [CrossRef] [MathSciNet] [Google Scholar]
  37. U. Seifert, Configurations of fluid membranes and vesicles. Adv. Phys. 46 (1997) 13–137. [CrossRef] [Google Scholar]
  38. J.V. Selinger and J.M. Schnur, Theory of chiral lipid tubules. Phys. Rev. Lett. 71 (1993) 4091–4094. [CrossRef] [PubMed] [Google Scholar]
  39. D. Steigmann, Fluid films with curvature elasticity. Arch. Ration. Mech. Anal. 150 (1999) 127–152. [CrossRef] [MathSciNet] [Google Scholar]
  40. M. Struwe, Geometric evolution problems, in Nonlinear partial differential equations in differential geometry (Park City, UT, 1992), IAS/Park City Math. Ser. 2, Amer. Math. Soc., Providence, USA (1996) 257–339. [Google Scholar]
  41. N. Uchida, Dynamics of orientational ordering in fluid membranes. Phys. Rev. E 66 (2002) 040902. [CrossRef] [Google Scholar]
  42. E.G. Virga, Variational theories for liquid crystals, Appl. Math. Math. Comput. 8. Chapman & Hall, London, UK (1994). [Google Scholar]
  43. T.J. Willmore, Riemannian geometry, Oxford Science Publications. The Clarendon Press Oxford University Press, New York, USA (1993). [Google Scholar]

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