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Developed smectics : when exact solutions agree

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Alexander, Gareth P., Kamien, Randall and Santangelo, Christian. (2012) Developed smectics : when exact solutions agree. Physical Review Letters, Vol.108 (No.4). 047802. ISSN 0031-9007

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Official URL: http://dx.doi.org/10.1103/PhysRevLett.108.047802

Abstract

In the limit where the bending modulus vanishes, we construct layer configurations with arbitrary dislocation textures by exploiting a connection between uniformly spaced layers in two dimensions and developable surfaces in three dimensions. We then show how these focal textures can be used to construct layer configurations with finite bending modulus.

Item Type: Journal Article
Subjects: Q Science > QC Physics
Divisions: Faculty of Science > Centre for Complexity Science
Faculty of Science > Physics
Library of Congress Subject Headings (LCSH): Liquid crystals, Elasticity
Journal or Publication Title: Physical Review Letters
Publisher: American Physical Society
ISSN: 0031-9007
Date: 27 January 2012
Volume: Vol.108
Number: No.4
Page Range: 047802
Identification Number: 10.1103/PhysRevLett.108.047802
Status: Peer Reviewed
Publication Status: Published
Access rights to Published version: Restricted or Subscription Access
Funder: National Science Foundation (U.S.) (NSF)
Grant number: DMR05-47230 (NSF), DMR08-46582 (NSF)
References: [1] M. Kl�eman, Points, Lines, and Walls, (John Wiley & Sons, New York, 1983). [2] R. Schoen and K. Uhlenbeck, J. Di�erential Geom. 17, 307 (1982); 18, 329 (1983) [3] R. Hardt, D. Kinderlehrer, F. Lin, Comm. Math. Phys. 105, 547 (1986). [4] H. Pleiner, Liq. Cryst. 3, 239 (1988). [5] V.I. Marchenko, Pisma Zh. �Eksp. Teor. Fiz. 138, 754 (2010) [JETP 111, 667 (2010)]. [6] I. Bluestein and R.D. Kamien, Europhys. Lett. 59, 68 (2002). [7] G. Grinstein and R. Pelcovits, Phys. Rev. Lett. 47, 856- 859 (1981); Phys. Rev. A 26, 915-925 (1982). [8] G.F. Mazenko, S. Ramaswamy, and J. Toner, Phys. Rev. A 28 1618 (1983), but not as anomalous as one might think, see [9]. [9] S.T. Milner and P.C. Martin, Phys. Rev. Lett. 56, 77 (1986). [10] E.A. Brener and V.I. Marchenko, Phys. Rev. E 59, R4752 (1999). [11] T. Ishikawa and O.D. Lavrentovich, Phys. Rev. E 60, R5037 (1999). [12] T.C. Witten, Rev. Mod. Phys. 79, 643 (2007). [13] C.D. Santangelo, V. Vitelli, R.D. Kamien, D. R. Nelson, Phys. Rev. Lett 99, 017801 (2007). [14] G.P. Alexander, B.G. Chen, E.A. Matsumoto, and R.D. Kamien, Phys. Rev. Lett 104, 257802 (2010). [15] For identical constructions in studies of pattern forma- tion, see A.C. Newell, T. Passot, C. Bowman, N. Er- colani, and R. Indik, Physica D 97 185 (1996) and N.M. Ercolani, R. Indik, A.C. Newell, and T. Passot, J. Nolin- ear Sci. 10, 223 (2000). [16] C.D. Santangelo and R.D. Kamien, Phys. Rev. Lett. 91, 045506 (2003). [17] C.D. Santangelo and R.D. Kamien, Proc. Roy. Soc. A 461, 2911 (2005). [18] B.G. Chen, G.P. Alexander, and R.D. Kamien, Proc. Natl. Acad. Sci. 106, 15577 (2009). [19] A.-I. Nistor, arXiv:0904.1475. [20] Y. Bouligand, J. Phys. (Paris) 41, 1297 (1980). [21] R.D. Kamien, D.R. Nelson, C.D. Santangelo, and V. Vitelli, Phys. Rev. E 80, 051703 (2009). [22] L.P. Eisenhart, A Treatise on the Di�erential Geometry of Curves and Surfaces, (Ginn and Company, Boston, 1909) pp. 43{44. [23] D.R. Nelson and J. Toner, Phys. Rev. B 24, 363 (1981). [24] G.B. Whitham, Linear and Nonlinear Waves, (John Wi- ley & Sons, New York, 1978).
URI: http://wrap.warwick.ac.uk/id/eprint/42519

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