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Nematic films and radially anisotropic Delaunay surfaces

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Abstract

We develop a theory of axisymmetric surfaces minimizing a combination of surface tension and nematic elastic energies which may be suitable for describing simple film and bubble shapes. As a function of the elastic constant and the applied tension on the bubbles, we find the analogues of the unduloid, sphere, and nodoid in addition to other new surfaces.

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References

  1. J.A.F. Plateau, Statique Expérimentale et Théorique des Liquides Soumis aux Seules Forces Moléculaires (Gauthier-Villard, Paris, 1873)

  2. J.E. Taylor, Ann. Math. 103, 489 (1976).

  3. R. Lemlich, Ind. En. Chem. Fundam. 17, 89 (1978).

    Google Scholar 

  4. A.J. Markworth, J. Colloid Interface Sci. 107, 569 (1985).

  5. A. Monsalve, R.S. Schechter, J. Colloid Interface Sci. 97, 327 (1984).

    Google Scholar 

  6. M. Buchanan, arXiv:cond-mat/0206477 (2002).

  7. B.G. Chen, R.D. Kamien, in preparation (2009).

  8. J.E. Avron, J.E. Taylor, R.K.P. Zia, J. Stat. Phys. 33, 493. 421-470 (1983).

    Google Scholar 

  9. R.K.P. Zia, A. Gittis, Phys. Rev. B 35, 5907 (1987).

    Google Scholar 

  10. H. Wente, Pacific J. Math. 80, 421 (1980).

  11. M. Koiso, B. Palmer, Indiana U. Math. J. 54, 1817 (2005).

    Google Scholar 

  12. M. Koiso, B. Palmer, Pacific J. Math. 234, 345 (2008).

    Google Scholar 

  13. T.C. Lubensky, F. Mackintosh, Phys. Rev. Lett. 67, 1169 (1991).

    Google Scholar 

  14. T.C. Lubensky, J. Prost, J. Phys. II 2, 371 (1992).

    Google Scholar 

  15. O.-Y. Zhong-Can, Thin Solid Films 393, 19 (2001).

    Google Scholar 

  16. V. Vitelli, D.R. Nelson, Phys. Rev. E 74, 021711 (2006).

    Google Scholar 

  17. J.R. Frank, M. Kardar, Phys. Rev. E 77, 041705 (2008).

    Google Scholar 

  18. H. Jiang, G. Huber, R.A. Pelcovits, T.R. Powers, Phys. Rev. E 76, 021704 (2007).

    Google Scholar 

  19. V. Elser, personal communication.

  20. P.G. de Gennes, J. Prost, The Physics of Liquid Crystals, 2nd edition (Oxford University Press, Oxford, 1995) pp. 100-103.

  21. F. Morgan, Rev. Mod. Phys. 79, 821 (2007).

    Google Scholar 

  22. D.A. Dunmur, A. Fukuda, G.R. Luckhurst (Editors), Physical Properities of Liquid Crystals: Nematics (INSPEC, London, 2001) pp. 223 and 488.

  23. I. Kliakhandler, Phys. Fluids 14, 3375 (2002)

  24. N. Korevaar, R. Kusner, B. Solomon, J. Diff. Geom. 30, 465 (1989).

    Google Scholar 

  25. K. Kenmotsu, Surfaces with Constant Mean Curvature, translated by K. Moriya, Translations of Mathematical Monographs 221 (American Mathematical Society, Providence, 2003) pp. 39-52.

  26. J. Eells, Math. Intel. 9, 53 (1987).

  27. T.R. Powers, G. Huber, R.E. Goldstein, Phys. Rev. E 65, 041901 (2002).

    Google Scholar 

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Authors and Affiliations

  1. Department of Physics and Astronomy, University of Pennsylvania, 19104-6396, Philadelphia, PA, USA

    B. G. Chen & R. D. Kamien

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  1. B. G. Chen
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  2. R. D. Kamien
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Correspondence to R. D. Kamien.

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Chen, B.G., Kamien, R.D. Nematic films and radially anisotropic Delaunay surfaces. Eur. Phys. J. E 28, 315–329 (2009). https://doi.org/10.1140/epje/i2008-10441-1

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