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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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WRAP_Alexander_1074054-px-130312-1110.4289.pdf - Accepted Version Download (1006Kb) |
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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