|
|
Modern Physics 2026
书架式排列的近晶C相液晶中特殊解的稳定性分析
|
Abstract:
本文针对书架型几何结构下近晶C相液晶的简单剪切流问题开展线性稳定性分析，并通过能量耗散特性与约束限制条件对分析结果进行验证。通过在稳态解中引入小扰动并代入动力学方程，结合特征值，得出不同Leslie系数区间内平衡态的稳定性结论。
In this paper, we perform a linear stability analysis on the simple shear flow problem of smectic C liquid crystals under a bookshelf geometry, and verify the analytical results through energy dissipation characteristics and constraint conditions. By introducing small perturbations into the steady-state solutions and substituting them into the dynamic equations, we derive the stability conclusions of the equilibrium states for different intervals of the Leslie coefficients in combination with eigenvalue analysis.
| [1] | de Gennes, P.G. and Prost, J. (1993) The Physics of Liquid Crystals. Oxford University Press. https://doi.org/10.1093/oso/9780198520245.001.0001 |
| [2] | Collings, P.J. and Goodby, J.W. (2019) Introduction to Liquid Crystals: Chemistry and Physics. 2nd Edition, CRC Press. https://doi.org/10.1201/9781315098340 |
| [3] | Goodby, J.W., Waring, J.L., Chin, D.Y., et al. (199) Smectic Liquid Crystals: An Overview of Materials, Physical Properties and Uses. Liquid Crystals, 26, 883-927. |
| [4] | Clark, N.A. and Lagerwall, S.T. (1980) Submicrosecond Bistable Electro-Optic Switching in Liquid Crystals. Applied Physics Letters, 36, 899-901. https://doi.org/10.1063/1.91359 |
| [5] | Finkelmann, H. and Rehage, G. (1975) Investigation of the Phase Transitions in Liquid Crystals by X-Ray Diffraction. Makromolekulare Chemie, 176, 2217-2227. |
| [6] | Chen, J. and Lubensky, T.C. (1976) Landau-Ginzburg Mean-Field Theory for the Nematic to Smectic-cand Nematic to Smectic-Aphase Transitions. Physical Review A, 14, 1202-1207. https://doi.org/10.1103/physreva.14.1202 |
| [7] | Limat, L. and Prost, J. (1993) A Model for the Chevron Structure Obtained by Cooling a Smectic a Liquid Crystal in a Cell of Finite Thickness. Liquid Crystals, 13, 101-113. https://doi.org/10.1080/02678299308029057 |
| [8] | Blake, G.I. and Virga, E.G. (1996) Original Article on the Equilibrium of Smectic C Liquid Crystals. Continuum Mechanics and Thermodynamics, 8, 323-339. https://doi.org/10.1007/s001610050047 |
| [9] | Leslie, F.M., Stewart, I.W. and Nakagawa, M. (1991) A Continuum Theory for Smectic C Liquid Crystals. Molecular Crystals and Liquid Crystals, 198, 443-454. https://doi.org/10.1080/00268949108033420 |
| [10] | Mukherjee, B. and Liu, C. (2002) On the Stability of Two Nematic Liquid Crystal Configurations. Discrete and Continuous Dynamical Systems—B, 2, 561-574. https://doi.org/10.3934/dcdsb.2002.2.561 |
| [11] | Stewart, I.W. (2004) The Static and Dynamic Continuum Theory of Liquid Crystals: A Mathematical Introduction. CRC Press. |
| [12] | Beresnev, L.A., Blinov, L.M., Osipov, M.A. and Pikin, S.A. (1988) Ferroelectric Liquid Crystals. Molecular Crystals and Liquid Crystals Incorporating Nonlinear Optics, 158, 1-150. https://doi.org/10.1080/00268948808075350 |
| [13] | Gill, S.P.A. and Leslie, F.M. (1993) Shear Flow and Magnetic Field Effects on Smectic C, C*, Cm and C*m Liquid Crystals. Liquid Crystals, 14, 1905-1923. https://doi.org/10.1080/02678299308027727 |
| [14] | Carlsson, T. (1984) Theoretical Investigation of the Shear Flow of Nematic Liquid Crystals with the Leslie Viscosity α3 > 0: Hydrodynamic Analogue of First Order Phase Transitions. Molecular Crystals and Liquid Crystals, 104, 307-334. https://doi.org/10.1080/00268948408070434 |
