Free Access
Issue |
ESAIM: COCV
Volume 19, Number 4, October-December 2013
|
|
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Page(s) | 1014 - 1029 | |
DOI | https://doi.org/10.1051/cocv/2012042 | |
Published online | 26 July 2013 |
- L. Ambrosio, N. Fusco and D. Pallara, Functions of Bounded Variation and Free Discontinuity Problems. Oxford Science Publications (2000). [Google Scholar]
- L. Ambrosio, N. Gigli and G. Savaré, Gradient flows in metric spaces and in the space of probability measures. Lectures in Mathematics, ETH Zürich. Birkhäuser Verlag, Basel (2005). [Google Scholar]
- T. Baumgart, S. Das, W.W. Webb and J.T. Jenkins, Membrane elasticity in giant vesicles with fluid phase coexistence. Biophys. J. 89 (2005) 1067–1080. [CrossRef] [PubMed] [Google Scholar]
- T. Baumgart, S.T. Hess and W.W. Webb, Imaging coexisting fluid domains in biomembrane models coupling curvature and line tension. Nature 425 (2003) 821–824. [CrossRef] [PubMed] [Google Scholar]
- G. Bellettini and L. Mugnai, A varifolds representation of the relaxed elastica functional. J. Convex Anal. 14 (2007) 543–564. [Google Scholar]
- P.B. Canham, The minimum energy of bending as a possible explanation of the biconcave shape of the human red blood cell. J. Theor. Biol. 26 (1970) 61–80. [CrossRef] [PubMed] [Google Scholar]
- R. Choksi and M. Veneroni, Global minimizers for the doubly-constrained Helfrich energy: the axisymmetric case. Calc. Var. Partial Differ. Equ. (2012). DOI:10.1007/s00526-012-0553-9. [Google Scholar]
- L. Deseri, M.D. Piccioni and G. Zurlo, Derivation of a new free energy for biological membranes. Contin. Mech. Thermodyn. 20 (2008) 255–273. [CrossRef] [MathSciNet] [Google Scholar]
- M.P. do Carmo, Differential geometry of curves and surfaces. Prentice-Hall Inc., Englewood Cliffs, N.J. (1976). Translated from the Portuguese. [Google Scholar]
- C.M. Elliott and B. Stinner, Modeling and computation of two phase geometric biomembranes using surface finite elements. J. Comput. Phys. 229 (2010) 6585–6612. [CrossRef] [MathSciNet] [Google Scholar]
- C.M. Elliott and B. Stinner, A surface phase field model for two-phase biological membranes. SIAM J. Appl. Math. 70 (2010) 2904–2928. [CrossRef] [MathSciNet] [Google Scholar]
- E.L. Elson, E. Fried, J.E. Dolbow and G.M. Genin, Phase separation in biological membranes: integration of theory and experiment. Annu. Rev. Biophys. 39 (2010) 207–226. [CrossRef] [PubMed] [Google Scholar]
- E. Evans, Bending resistance and chemically induced moments in membrane bilayers. Biophys. J. 14 (1974) 923–931. [CrossRef] [PubMed] [Google Scholar]
- L.C. Evans and R.F. Gariepy, Measure Theory and Fine Properties of Functions. Studies in Advanced Mathematics. CRC Press (1992). [Google Scholar]
- W. Helfrich, Elastic properties of lipid bilayers: Theory and possible experiments. Z. Naturforsch. Teil C 28 (1973) 693–703. [Google Scholar]
- M. Helmers, Convergence of an approximation for rotationally symmetric two-phase lipid bilayer membranes. Technical report, Institute for Applied Mathematics, University of Bonn (2011). [Google Scholar]
- M. Helmers, Kinks in two-phase lipid bilayer membranes. Calc. Var. Partial Differ. Equ. (2012). DOI: 10.1007/s00526-012-0550-z. [Google Scholar]
- J.E. Hutchinson, Second fundamental form for varifolds and the existence of surfaces minimising curvature. Indiana Univ. Math. J. 35 (1986) 45–71. [CrossRef] [MathSciNet] [Google Scholar]
- F. Jülicher and R. Lipowsky, Domain-induced budding of vesicles. Phys. Rev. Lett. 70 (1993) 2964–2967. [CrossRef] [PubMed] [Google Scholar]
- F. Jülicher and R. Lipowsky, Shape transformations of vesicles with intramembrane domains. Phys. Rev. E 53 (1996) 2670–2683. [CrossRef] [Google Scholar]
- J.S. Lowengrub, A. Rätz and A. Voigt, Phase-field modeling of the dynamics of multicomponent vesicles: spinodal decomposition, coarsening, budding, and fission. Phys. Rev. E 79 (2009) 0311926. [CrossRef] [MathSciNet] [Google Scholar]
- R. Moser, A generalization of Rellich’s theorem and regularity of varifolds minimizing curvature. Technical Report 72, Max-Planck-Institut for Mathematics in the Sciences (2001). [Google Scholar]
- U. Seifert, Configurations of fluid membranes and vesicles. Adv. Phys. 46 (1997) 13–137. [CrossRef] [Google Scholar]
- J.S. Sohn, Y.-H. Tseng, S. Li, A. Voigt and J.S. Lowengrub, Dynamics of multicomponent vesicles in a viscous fluid. J. Comput. Phys. 229 (2010) 119–144. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
- R.H. Templer, B.J. Khoo and J.M. Seddon, Gaussian curvature modulus of an amphiphilic monolayer. Langmuir 14 (1998) 7427–7434. [CrossRef] [Google Scholar]
- X. Wang and Q. Du, Modelling and simulations of multi-component lipid membranes and open membranes via diffuse interface approaches. J. Math. Biol. 56 (2008) 347–371. [PubMed] [Google Scholar]
- T.J. Willmore, Riemannian geometry. Clarendon Press, Oxford (1993). [Google Scholar]
- G. Zurlo, Material and Geometric Phase Transitions in Biological Membranes. Ph.D. thesis, University of Pisa (2006). [Google Scholar]
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