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Journal of Materials
Volume 2014, Article ID 145375, 8 pages
http://dx.doi.org/10.1155/2014/145375
Research Article

The Construction of the Dupin Cyclides in a Smectic A Polygonal Texture

Laboratoire de Physique des Systèmes Complexes, Université de Picardie Jules Verne, 33 rue Saint-Leu, 80039 Amiens, France

Received 28 January 2014; Accepted 22 February 2014; Published 30 March 2014

Academic Editor: Rodrigo Martins

Copyright © 2014 Claire Meyer et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. G. Friedel and F. Grandjean, “Observation geometriques sur les liquidesa coniques fo-cales,” Bulletin De La Société Française De Minéralogie, vol. 33, pp. 409–465, 1910. View at Google Scholar
  2. O. D. Lavrentovich, “Designing Dupin cyclides in micro and macro worlds,” Proceedings of the National Academy of Sciences, vol. 110, no. 1, pp. 5–6, 2013. View at Google Scholar
  3. C. E. Williams, “Helical disclination lines in smectics A,” Philosophical Magazine, vol. 32, no. 2, pp. 313–321, 1975. View at Google Scholar · View at Scopus
  4. C. Meyer, Y. A. Nastyshyn, and M. Kleman, “Helical defects in smectic-A and smectic-A* phases,” Physical Review E: Statistical, Nonlinear, and Soft Matter Physics, vol. 82, Article ID 031704, 2010. View at Google Scholar
  5. S. Elston and R. Sambles, The Optics of Thermotropic Liquid Crystals, CRC press, 1998.
  6. G. Friedel, “The mesomorphic states of matter,” Annals of Physics, vol. 18, pp. 273–474, 1922. View at Google Scholar
  7. M. Kleman and O. D. Lavrentovich, “Grain boundaries and the law of corresponding cones,” European Physical Journal E, vol. 2, pp. 47–57, 2000. View at Google Scholar
  8. I. Dierking, M. Ravnik, E. Lark, J. Healey, G. P. Alexander, and J. M. Yeomans, “Anisotropy in the annihilation dynamics of umbilic defects in nematic liquid crystals,” Physical Review E: Statistical, Nonlinear, and Soft Matter Physics, vol. 85, no. 2, Article ID 021703, 2012. View at Publisher · View at Google Scholar · View at Scopus
  9. C. Meyer, L. Le Cunff, M. Belloul, and G. Foyart, “Focal conic stacking in smectic a liquid crystals: smectic flower and apollonius tiling,” Materials, vol. 2, pp. 499–513, 2009. View at Google Scholar
  10. O. D. Lavrentovich, “Hierarchy of defect structures in space filling byflexible smectic A layers,” Journal of Experimental and Theoretical Physics, vol. 64, pp. 984–990, 1986. View at Google Scholar
  11. M. Kleman and O. D. Lavrentovich, “Liquids with conics,” Liquid Crystals, vol. 36, no. 10-11, pp. 1085–1099, 2009. View at Publisher · View at Google Scholar · View at Scopus
  12. J. P. Sethna and M. Kleman, “Spheric domains in smectic liquid crystals,” Physical Review A, vol. 26, no. 5, Article ID 3037, 1982. View at Google Scholar
  13. A. Honglawan, D. A. Beller, M. Cavallaro, R. D. Kamien, K. J. Stebe, and S. Yang, “Pillar-assisted epitaxial assembly of toric focal conic domains of smectic-A liquid crystals,” Advanced Materials, vol. 23, no. 46, pp. 5519–5523, 2011. View at Publisher · View at Google Scholar · View at Scopus
  14. A. Honglawan, D. A. Beller, M. Cavallaro Jr., R. D. Kamien, and K. J. Stebe, “Topographically-induced hierarchical assembly and geometrical transformation of focal conic domain arrays in smectic liquid crystals,” Proceedings of the National Academy of Sciences of the United States of America, vol. 110, pp. 34–39, 2013. View at Google Scholar
  15. Y. H. Kim, D. K. Yoon, H. S. Jeong, O. D. Lavrentovich, and H.-T. Jung, “Smectic liquid crystal defects for self-assembling of building blocks and their lithographic applications,” Advanced Functional Materials, vol. 21, no. 4, pp. 610–627, 2011. View at Publisher · View at Google Scholar · View at Scopus
  16. J. Lelong-Ferrand and J. M. Arnaudiès, Cours de Mathématiques, Géométrie Et Cinématique, tome 3, relation 6’, Dunod, 2nd edition, 1977.