Free Access
Issue |
Math. Model. Nat. Phenom.
Volume 15, 2020
Growth phenomena
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Article Number | 8 | |
Number of page(s) | 21 | |
DOI | https://doi.org/10.1051/mmnp/2019034 | |
Published online | 17 February 2020 |
- G. Babakhanova, Z. Parsouzi, S. Paladugu, H. Wang, Y.A. Nastishin, S.V. Shiyanovskii, S. Sprunt and O.D. Lavrentovich, Elastic and viscous properties of the nematic dimer CB7CB. Phys. Rev. E 96 (2017) 062704. [PubMed] [Google Scholar]
- J.M. Ball and A. Majumdar, Nematic liquid crystals: from Maier-Saupe to a continuum theory. Mol. Cryst. Liquid Cryst. 525 (2010) 1–11. [CrossRef] [Google Scholar]
- J.M. Ball and A. Zarnescu, Orientability and energy minimization in liquid crystal models. Arch. Ration. Mech. Anal. 202 (2011) 493–535. [Google Scholar]
- P. Bauman, J. Park and D. Phillips, Analysis of nematic liquid crystals with disclination lines. Arch. Ration. Mech. Anal. 205 (2012) 795–826. [Google Scholar]
- F. Bethuel, H. Brezis and F. Hélein, Ginzburg-Landau vortices, Progress in Nonlinear Differential Equations and their Applications, in Vol. 13. Birkhäuser Boston, Inc., Boston, MA (1994). [Google Scholar]
- L. Bronsard and R.V. Kohn, Motion by mean curvature as the singular limit of Ginzburg-Landau dynamics. J. Differ. Equ. 90 (1991) 211–237. [Google Scholar]
- X. Chen, Generation and propagation of interfaces for reaction-diffusion equations. J. Differ. Equ. 96 (1992) 116–141. [Google Scholar]
- P. de Mottoni and M. Schatzman, Geometrical evolution of developed interfaces. Trans. Am. Math. Soc. 347 (1995) 1533–1589. [Google Scholar]
- L.C. Evans, H.M. Soner and P.E. Souganidis, Phase transitions and generalized motion by mean curvature. Commun. Pure Appl. Math. 45 (1992) 1097–1123. [Google Scholar]
- D. Golovaty, J.A. Montero and P. Sternberg, Dimension reduction for the Landau-de Gennes model in planar nematic thin films. J. Nonlinear Sci. 25 (2015) 1431–1451. [Google Scholar]
- D. Golovaty, M. Novack, P. Sternberg and R. Venkatraman, A model problem for nematic-isotropic transitions with highly disparate elastic constants. Preprint arXiv:1811.12586 (2018). [Google Scholar]
- D. Golovaty, M. Novack and P. Sternberg, A novel Landau-de Gennes model with quartic elastic terms. Preprint arXiv:1906.09232 (2019). [Google Scholar]
- R. Hardt and F.-H. Lin, Harmonic maps into round cones and singularities of nematic liquid crystals. Math. Z. 213 (1993) 575–593. [CrossRef] [Google Scholar]
- T. Ilmanen, Convergence of the Allen-Cahn equation to Brakke’s motion by mean curvature. J. Differ. Geom. 38 (1993) 417–461. [Google Scholar]
- A. Kaznacheev, M. Bogdanov and S. Taraskin, The nature of prolate shape of tactoids in lyotropic inorganic liquid crystals. J. Exp. Theor. Phys. 95 (2002) 57–63. [CrossRef] [Google Scholar]
- A. Kaznacheev, M. Bogdanov and A. Sonin, The influence of anchoring energy on the prolate shape of tactoids in lyotropic inorganicliquid crystals. J. Exp. Theor. Phys. 97 (2003) 1159–1167. [CrossRef] [Google Scholar]
- T.W. Kibble, Topology of cosmic domains and strings. J. Phys. A: Math. General 9 (1976) 1387. [NASA ADS] [CrossRef] [Google Scholar]
- Y.-K. Kim, S.V. Shiyanovskii and O.D. Lavrentovich, Morphogenesis of defects and tactoids during isotropic–nematic phase transition in self-assembled lyotropic chromonic liquid crystals. J. Phys.: Condens. Matter 25 (2013) 404202. [CrossRef] [Google Scholar]
- G. Kitavtsev, J.M. Robbins, V. Slastikov and A. Zarnescu, Liquid crystal defects in the Landau–de Gennes theory in two dimensions—beyond the one-constant approximation. Math. Models Methods Appl. Sci. 26 (2016) 2769–2808. [Google Scholar]
- M. Kleman and O.D. Laverntovich, Soft matter physics: an introduction. Springer Science & Business Media (2007). [Google Scholar]
- L. Longa, D. Monselesan and H.-R. Trebin, An extension of the Landau-Ginzburg-de Gennes theory for liquid crystals. Liquid Cryst. 2 (1987) 769–796. [CrossRef] [Google Scholar]
- L. Longa, D. Monselesan and H.-R. Trebin, An extension of the Landau-Ginzburg-de Gennes theory for liquid crystals. Liquid Cryst. 2 (1987) 769–796. [CrossRef] [Google Scholar]
- A. Majumdar and A. Zarnescu, Landau-de Gennes theory of nematic liquid crystals: the Oseen-Frank limit and beyond. Arch. Ration. Mech. Anal. 196 (2010) 227–280. [Google Scholar]
- N.J. Mottram and C. Newton, Introduction to Q-tensor theory. Technical Report 10, Department of Mathematics, University of Strathclyde (2004). [Google Scholar]
- Y.A. Nastishin, H. Liu, T. Schneider, V. Nazarenko, R. Vasyuta, S.V. Shiyanovskii and O.D. Lavrentovich, Optical characterization of the nematic lyotropic chromonic liquid crystals: Light absorption, birefringence, and scalar order parameter. Phys. Rev. E 72 (2005) 041711. [Google Scholar]
- P. Prinsen and P. van der Schoot, Shape and director-field transformation of tactoids. Phys. Rev. E 68 (2003) 021701. [Google Scholar]
- P. Prinsen and P. van der Schoot, Continuous director-field transformation of nematic tactoids. Eur. Phys. J. E 13 (2004) 35–41. [CrossRef] [EDP Sciences] [Google Scholar]
- P. Prinsen and P. van der Schoot, Parity breaking in nematic tactoids. J. Phys.: Condens. Matter 16 (2004) 8835. [CrossRef] [Google Scholar]
- J. Rubinstein, P. Sternberg and J.B. Keller, Fast reaction, slow diffusion, and curve shortening. SIAM J. Appl. Math. 49 (1987) 116–133. [Google Scholar]
- J. Rubinstein, P. Sternberg and J.B. Keller, Reaction-diffusion processes and evolution to harmonic maps. SIAM J. Appl. Math. 49 (1989) 1722–1733. [Google Scholar]
- A. Sonnet and E. Virga, Dissipative Ordered Fluids: Theories for Liquid Crystals. Springer, Bücher, New York (2012). [CrossRef] [Google Scholar]
- C. Zhang, A. Acharya, N.J. Walkington and O.D. Lavrentovich, Computational modelling of tactoid dynamics in chromonic liquid crystals. Liquid Cryst. 45 (2018) 1084–1100. [CrossRef] [Google Scholar]
- S. Zhou, A.J. Cervenka and O.D. Lavrentovich, Ionic-content dependence of viscoelasticity of the lyotropic chromonic liquid crystal sunset yellow. Phys. Rev. E 90 (2014) 042505. [Google Scholar]
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