Review PaperNo Access

OVERVIEW OF THE STUDY OF COMPLEX SHAPES OF FLUID MEMBRANES, THE HELFRICH MODEL AND NEW APPLICATIONS

Z. C. OU-YANG

Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190, P. R. China

Search for more papers by this author

and

Z. C. TU

Department of Physics, Beijing Normal University, Beijing 100875, P. R. China

Search for more papers by this author

https://doi.org/10.1142/S0217979213300223Cited by:4 (Source: Crossref)

Abstract

Some progresses in shape problems following the Helfrich model are reported. Based on the Helfrich model, we have predicted not only the exact solution for discoidal shape of red blood cells but also a special kind of toroidal vesicle with the ratio of two generation radii being . The Helfrich model can also be extended to investigate the complex structures in other soft matters such as the formation of focal conic domains in smectic liquid crystal, the tube-to-sphere transition in peptide nanostructures, and icosahedral configuration of small virus capsids.

Invited talk at the Conference in Honor of 90th Birthday of Freeman Dyson, Institute of Advanced Studies. Nanyang Technological University, Singapore, 26–29 August, 2013.

Keywords:

PACS: 87.10.-e, 87.16.D-

You currently do not have access to the full text article.
Recommend the journal to your library today!

References

N. Stensen , De solido intra solidum naturaliter contento–Dissertationis Prodromus ( Ex typographia sub Signo Stellae , Florence , 1669 ) . Google Scholar
G. Wulff, Zeitschrift fur Krystallographie und Mineralogie 34, 449 (1901). Google Scholar
J. Plateau , Experimental and Theoretical Statics of Liquids Subject to Molecular Forces Only ( Gauthier-Villars , Paris , 1873 ) . Google Scholar
J. C. C. Nitsche , Lectures on Minimal Surfaces ( Cambridge University Press , Cambridge , 1989 ) . Google Scholar
T. Young, Philosophical Trans. Roy. Soc. Lond. 95, 65 (1805), DOI: 10.1098/rstl.1805.0005. ADS, Google Scholar
P. Laplace , Traité de Mécanique Céleste ( Gauthier-Villars , Paris , 1839 ) . Google Scholar
A. D. Alexandrov, Amer. Math. Soc. Transl. 21, 341 (1962). Google Scholar
S. D. Poisson , Traité de Mécanique ( Bachelier , Paris , 1833 ) . Google Scholar
T. J. Willmore , Total Curvature in Riemannian Geometry ( John Wiley , New York , 1982 ) . Google Scholar
W. Helfrich, Z. Naturforsch. C 28, 693 (1973). Web of Science, Google Scholar
Z.-C. Ou-Yang and W. Helfrich, Phys. Rev. Lett. 59, 2486 (1987). Web of Science, Google Scholar
Z.-C. Ou-Yang and W. Helfrich, Phys. Rev. A 39, 5280 (1989). Web of Science, Google Scholar
J. C. C. Nitsche, Q. Appl. Math. 51, 363 (1993). Web of Science, Google Scholar
Y. C. Fung and P. Tong, Biophys. J. 8, 175 (1968), DOI: 10.1016/S0006-3495(68)86484-7. Web of Science, Google Scholar
L. Lopez, I. M. Duck and W. A. Hunt, Biophys. J. 8, 1228 (1968), DOI: 10.1016/S0006-3495(68)86552-X. Web of Science, Google Scholar
J. R. Murphy, J. Lab. Clin. Med. 65, 756 (1965). Google Scholar
P. Canham, J. Theor. Biol. 26, 61 (1970), DOI: 10.1016/S0022-5193(70)80032-7. Web of Science, ADS, Google Scholar
J. Hu and Z. C. Ou-Yang, Phys. Rev. E 47, 461 (1993). Web of Science, Google Scholar
W. Zheng and J. Liu, Phys. Rev. E 48, 2856 (1993), DOI: 10.1103/PhysRevE.48.2856. Web of Science, Google Scholar
Z. C. Ou-Yang, Phys. Rev. A 41, 4517 (1990). Web of Science, ADS, Google Scholar
M. Mutz and D. Bensimon, Phys. Rev. A 43, 4525 (1991), DOI: 10.1103/PhysRevA.43.4525. Web of Science, ADS, Google Scholar
H. Naito, M. Okuda and Z. C. Ou-Yang, Phys. Rev. E 48, 2304 (1993), DOI: 10.1103/PhysRevE.48.2304. Web of Science, ADS, Google Scholar
H. Naito, M. Okuda and Z. C. Ou-Yang, Phys. Rev. E 54, 2816 (1996), DOI: 10.1103/PhysRevE.54.2816. Web of Science, Google Scholar
A. Saitohet al., Proc. Natl. Acad. Sci. 95, 1026 (1998), DOI: 10.1073/pnas.95.3.1026. Web of Science, Google Scholar
R. Capovilla, J. Guven and J. A. Santiago, Phys. Rev. E 66, 021607 (2002), DOI: 10.1103/PhysRevE.66.021607. Web of Science, Google Scholar
R. Capovilla and J. Guven, J. Phys. A Math. Gen. 35, 6233 (2002), DOI: 10.1088/0305-4470/35/30/302. ADS, Google Scholar
Z. C. Tu and Z. C. Ou-Yang, Phys. Rev. E 68, 061915 (2003), DOI: 10.1103/PhysRevE.68.061915. Web of Science, Google Scholar
Z. C. Tu and Z. C. Ou-Yang, J. Phys. A Math. Gen. 37, 11407 (2004), DOI: 10.1088/0305-4470/37/47/010. ADS, Google Scholar
Z. C. Tu, J. Chem. Phys. 132, 084111 (2010), DOI: 10.1063/1.3335894. Web of Science, Google Scholar
Z. C. Tu, Chin. Phys. B 22, 028701 (2013), DOI: 10.1088/1674-1056/22/2/028701. Web of Science, Google Scholar
G. Friedel, Annls. Phys. 18, 273 (1922). Google Scholar
W. Bragg, Nature 133, 445 (1934), DOI: 10.1038/133445a0. ADS, Google Scholar
H. Naito, M. Okuda and Z. C. Ou-Yang, Phys. Rev. Lett. 70, 2912 (1993), DOI: 10.1103/PhysRevLett.70.2912. Web of Science, Google Scholar
H. Naito, M. Okuda and Z. C. Ou-Yang, Phys. Rev. E 52, 2095 (1995), DOI: 10.1103/PhysRevE.52.2095. Web of Science, Google Scholar
A. Adamczyk, Mol. Cryst. Liq. Cryst. 170, 53 (1989). Web of Science, Google Scholar
S. L. Arora, P. Palffy-Muhoray and R. A. Vora, Liq. Cryst. 5, 133 (1989), DOI: 10.1080/02678298908026356. Web of Science, Google Scholar
R. Pratibha and N. V. Madhusudana, J. Phys. II 2, 383 (1992). Web of Science, Google Scholar
X. Yanet al., Chem. Eur. J. 14, 5974 (2008), DOI: 10.1002/chem.200800012. Web of Science, Google Scholar
T. Lenoskyet al., Nature 355, 333 (1992), DOI: 10.1038/355333a0. Web of Science, ADS, Google Scholar
L. Zhou and Z. C. Ou-Yang, Europhys. Lett. 92, 68004 (2010), DOI: 10.1209/0295-5075/92/68004. ADS, Google Scholar
Z.-C. Ou-Young, Z. B. Su and C. L. Wang, Phys. Rev. Lett. 78, 4055 (1997). Web of Science, Google Scholar
J. R. Castónet al., J. Cell. Biol. 138, 975 (1997). Web of Science, Google Scholar
N. Philippeet al., Science 341, 281 (2013), DOI: 10.1126/science.1239181. Web of Science, ADS, Google Scholar
R. Lipowsky, Nature 349, 475 (1991), DOI: 10.1038/349475a0. Web of Science, ADS, Google Scholar
U. Seifert, Adv. Phys. 46, 13 (1997), DOI: 10.1080/00018739700101488. Web of Science, ADS, Google Scholar
Z. C. Ou-Yang , J. X. Liu and Y. Z. Xie , Geometric Methods in the Elastic Theory of Membranes in Liquid Crystal Phases ( World Scientific , Singapore , 1999 ) . Google Scholar
Z. C. Tu and Z. C. Ou-Yang, J. Comput. Theor. Nanosci. 5, 422 (2008), DOI: 10.1166/jctn.2008.017e. Web of Science, Google Scholar
I. M. Mladenovet al., Commun. Theor. Phys. 59, 213 (2013), DOI: 10.1088/0253-6102/59/2/14. Web of Science, Google Scholar