Instability of circular cylinders and polygonal solutions for cylindrical vesicles

Journal of the Physical Society of Japan

Volumn 68, Issue 11, 1999, Pages 3603-3607

  Zhang, Shao Guang ^a,b  

^a BEIJING NORMAL UNIVERSITY   (China)

^b INSTITUTE OF THEORETICAL PHYSICS   (China)

Author keywords

Cylindrical vesicle; Membrane; Polygonal shape; Spontaneous curvature model

Indexed keywords

EID: 0033271639     PISSN: 00319015     EISSN: None     Source Type: Journal    
DOI: 10.1143/JPSJ.68.3603     Document Type: Article

References (22)

1. P. B. Canham: J. Theor. Biol. 26 (1970) 61.
2. W. Helfrich: Z. Naturforsch. 28C (1973) 693.
3. There are other variants of curvature models such as the bilayer couple (BC) model, see, e.g., S. Svetina and B. Zeks: Eur. BioPhys. J. 17 (1989) 101, and the area difference elastic (ADE) model, sec, e.g., L. Miao, U. Seifert, M. Wortis and H. G. Döbereiner: Phys. Rev. E 49 (1994) 5389. The SC, BC and ADE models have the same catalog of solutions and the phase diagram of the transitions of vesicles may be different. In the following we focus on the SC model since our interest is the solutions of the shape equation, which gives the whole catalog of solutions for all the variants of the curvature models.
4. There are other variants of curvature models such as the bilayer couple (BC) model, see, e.g., S. Svetina and B. Zeks: Eur. BioPhys. J. 17 (1989) 101, and the area difference elastic (ADE) model, sec, e.g., L. Miao, U. Seifert, M. Wortis and H. G. Döbereiner: Phys. Rev. E 49 (1994) 5389. The SC, BC and ADE models have the same catalog of solutions and the phase diagram of the transitions of vesicles may be different. In the following we focus on the SC model since our interest is the solutions of the shape equation, which gives the whole catalog of solutions for all the variants of the curvature models.
5. Ou-Yang Zhong-can and W. Helfrich: Phys. Rev. Lett. 59 (1987) 2486; Phys. Rev. A 39 (1989) 5280.
6. Ou-Yang Zhong-can and W. Helfrich: Phys. Rev. Lett. 59 (1987) 2486; Phys. Rev. A 39 (1989) 5280.
7. Ou-Yang Zhong-can: Phys. Rev. A 41 (1990) 4517.
8. H. Naito, M. Okuda and Ou-Yang Zhong-can: Phys. Rev. E 48 (1993) 2304.
9. H. Naito, M. Okuda and Ou-Yang Zhong-can: Phys. Rev. Lett. 74 (1995) 4345.
10. Hu Jian-Guo and Ou-Yang Zhong-can: Phys. Rev. E 47 (1993) 461.
11. D. W. Fawcett: The Cell (W. B. Saunders Cop., Philadelphia, 1981).
12. K. Blinzinger: J. cell Biol. 25 (1965) 293.
13. N. Ostrowsky and J. Peyraud: J. Chem. Phys. 77 (1982) 2081.
14. Zhang Shao-guang and Ou-Yang Zhong-can: Phys. Rev. E 53 (1996) 4206.
15. M. M. Kozlov and W. Helfrich: Langmuir 10 (1994) 4219.
16. T, Kawakatsu, D. Andelman, K. Kawasaki and T. Taniguchi: Phys. (Paris) II 3 (1993) 971.
17. G. C. Barker and M. J. Grimson: J. Phys. (Paris) 48 (1987) 465.
18. M. E. Fisher: Physica D 38 (1989) 112.
19. Paul F. Byrd and Morris D. Friedman: Handbook of Elliptic Integrals for Engineers and Scientists (Springer-Verlag, Berlin, Heidelberg, New York, 1971).
20. S. Leibler, R. R. Singh and M. E. Fisher: Phys. Rev. Lett. 59 (1987) 1989.
21. U. Seifert: Phys. Rev. A 43 (1991) 6803.
22. 0 are equal to 1 thus the values of Δp and λ are in dimensionless form.