Analytical and numerical solutions for shapes of quiescent two-dimensional vesicles

International Journal of Non-Linear Mechanics

Volumn 44, Issue 3, 2009, Pages 257-262

  Veerapaneni, Shravan K ^a   Raj, Ritwik ^b   Biros, George ^b   Purohit, Prashant K ^b  

^a NEW YORK UNIVERSITY   (United States)

^b UNIVERSITY OF PENNSYLVANIA   (United States)

Author keywords

Helfrich energy; Vesicles

Indexed keywords

BENDING (DEFORMATION); BOUNDARY INTEGRAL EQUATIONS; DIFFERENTIAL EQUATIONS; TWO DIMENSIONAL;

ANALYTIC METHODS; ANALYTICAL AND NUMERICAL SOLUTIONS; BOUNDARY VALUES; ELASTIC ENERGIES; ELLIPTIC FUNCTIONS; ELLIPTIC INTEGRALS; EQUILIBRIUM SHAPES; HELFRICH ENERGY; NUMERICAL EXPERIMENTS; NUMERICAL SCHEMES; PRESSURE JUMPS; VESICLE MEMBRANES; VESICLES;

METHOD OF MOMENTS;

EID: 60949087263     PISSN: 00207462     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ijnonlinmec.2008.10.004     Document Type: Article

References (28)

1. Kraus M., Wintz W., Seifert U., and Lipowsky R. Fluid vesicles in shear flow. Phys. Rev. Lett. 77 (1996) 3685-3688
2. Seifert U. Configurations of fluid membranes and vesicles. Adv. Phys. 46 (1997) 13-137
3. Sackmann E. Supported membranes: scientific and practical applications. Science 271 (1996) 43-48
4. Biben T., Kassner K., and Misbah C. Phase-field approach to three-dimensional vesicle dynamics. Phys. Rev. E 72 (2005)
5. de Haas K.H., Blom C., van den Ende D., Duits M.H.G., and Mellema J. Deformation of giant lipid bilayer vesicles in shear flow. Phys. Rev. E 56 (1997) 7132-7137
6. Misbah C. Vacillating breathing and tumbling of vesicles under shear flow. Phys. Rev. Lett. 96 (2006)
7. Kantsler V., and Steinberg V. Orientation and dynamics of a vesicle in tank-treading motion in shear flow. Phys. Rev. Lett. 95 (2005)
8. V. Kantsler, V. Steinberg, Transition to tumbling and two regimes of tumbling motion of a vesicle in shear flow, Phys. Rev. Lett. 96 (2006).
9. Noguchi H., and Gompper G. Shape transitions of fluid vesicles and red blood cells in capillary flows. Proc. Natl. Acad. Sci. USA 102 (2005) 14159-14164
10. Pozrikidis C. The axisymmetric deformation of a red blood cell in uniaxial straining Stokes flow. J. Fluid Mech. 216 (1990) 231-254
11. Stevens M.J. Coarse-grained simulations of lipid bilayers. J. Chem. Phys. 121 (2004)
12. Ou-Yang Z., Liu J., and Xie Y. Geometric Methods in the Elastic Theory of Membranes in Liquid Crystal Phases (1999), World Scientific Publishing Co.
13. Arreaga G., Capovilla R., Chryssomalakos C., and Guven J. Area-constrained planar elastica. Phys. Rev. E 65 (2002)
14. Shi W., Feng X., and Gao H. Two-dimensional model of vesicle adhesion on curved substrates. Acta Mech. Sinica 22 (2006) 529-535
15. Seifert U. Adhesion of vesicles in two dimensions. Phys. Rev. A 43 12 (1991) 6803-6814
16. Fygenson D.K., Marko J.F., and Libchaber A. Mechanics of microtubule-based membrane extension. Phys. Rev. Lett. 79 (1997) 4497
17. S.K. Veerapaneni, D. Gueyffier, D. Zorin, G. Biros, A boundary integral method for simulating the dynamics of inextensible vesicles suspended in a viscous fluid in 2d, Technical Report, University of Pennsylvania, 2008, To appear in the Journal of Computational Physics.
18. Heinrich V., Bozic B., Svetina S., and Zeks B. Vesicle deformation by an axial load: from elongated shapes to tethered vesicles. Biophys. J. 76 (1999) 2056-2071
19. V.A. Toponogov, Differential Geometry of Curves and Surfaces: A Concise Guide, A Birkhauser Book, 2006.
20. Power H., and Wrobel L. Boundary Integral Methods in Fluid Mechanics (1995), Computational Mechanics Publications
21. Greenhill A.G. The Applications of Elliptic Functions (1892), Macmillan and Co.
22. DeTurck D., Gluck H., Pomerleano D., and Vick D.S. The four vertex theorem and its converse. Not. AMS 54 (2007)
23. U.M. Ascher, L.R. Petzold, Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations, Society for Industrial and Applied Mathematics, Philadelphia, PA, USA, 1998.
24. Alpert B.K. Hybrid Gauss-trapezoidal quadrature rules. SIAM J. Sci. Comput. 20 (1999) 1551-1584
25. Y. Saad, Iterative Methods for Sparse Linear Systems, second ed., SIAM, Philadelphia, PA, 2003.
26. Peterson M.A. Deformation energy of vesicles at fixed volume and surface area. Phys. Rev. A 39 (1989) 2643-2645
27. Love A.E.H. A Treatise on the Mathematical Theory of Elasticity (1944), Dover, New York
28. Fygenson D.K., Elbaum M., Shraiman B., and Libchaber A. Microtubules and vesicles under controlled tension. Phys. Rev. E 55 1 (1997) 850-859