具有奇异势的Q-张量梯度流的尖锐界面极限
Sharp Interface Limit of Q-Tensor Gradient Flows with Singular Potential
摘要: 本文考虑具有奇异势的Q-张量梯度流，利用匹配渐近展开方法，形式推导出各向同性–向列相尖锐界面极限。该模型包括液晶的指向矢场n的热流和界面上的跳跃条件，并且跳跃条件由平均曲率流决定。
Abstract: In this paper, we consider the Q-tensor gradient flow with singular potential and use the matching asymptotic expansion method to derive the isotropy-nematic sharp interface model formally. The model includes the heat flow of the directed vector field n of the liquid crystal and the jump condition on the interface, and the jump condition is determined by the mean curvature flow.
文章引用：王晨晨. 具有奇异势的Q-张量梯度流的尖锐界面极限[J]. 运筹与模糊学, 2023, 13(2): 884-891. https://doi.org/10.12677/ORF.2023.132091

参考文献

[1] Fried, E. (2008) Sharp-Interface Nematic-Isotropic Phase Transitions with Flow. Archive for Rational Mechanics and Analysis, 190, 227-265. [Google Scholar] [CrossRef] 
[2] Cermelli, P., Fried, E. and Gurtin, M.E. (2004) Sharp-Interface Nematic-Isotropic Phase Transitions without Flow. Archive for Rational Mechanics and Analysis, 174, 151-178. [Google Scholar] [CrossRef] 
[3] Qian, T. and Sheng, P. (1998) Gen-eralized Hydrodynamic Equations for Nematic Liquid Crystals. Physical Review E, 58, 7475-7485. [Google Scholar] [CrossRef] 
[4] Berti, A., Berti, V. and Grandi, D. (2013) A Thermodynamic Approach to Isotropic-Nematic Phase Transitions in Liquid Crystals. Meccanica, 48, 983-991. [Google Scholar] [CrossRef] 
[5] De Gennes, P.G. (1971) Short Range Order Effects in the Isotropic Phase of Nematics and Cholesterics. Molecular Crystals and Liquid Crystals, 12, 193-214. [Google Scholar] [CrossRef] 
[6] Fei, M., Wang, W., Zhang, P. and Zhang, Z. (2015) Dy-namics of the Nematic-Isotropic Sharp Interface for the Liquid. SIAM Journal on Applied Mathematics, 75, 1700-1724. [Google Scholar] [CrossRef] 
[7] Fei, M., Wang, W., Zhang, P., et al. (2018) On the Iso-tropic-Nematic Phase Transition for the Liquid Crystal. Peking Mathematical Journal, 1, 141-219. [Google Scholar] [CrossRef] 
[8] Han, J., Luo, Y., Wang, W., et al. (2015) From Microscopic Theory to Macroscopic Theory: A Systematic Study on Modeling for Liquid Crystals. Archive for Rational Me-chanics and Analysis, 215, 741-809. [Google Scholar] [CrossRef] 
[9] Wang, W., Zhang, P. and Zhang, Z. (2013) Rigorous Deriva-tion from Landau-de Gennes Theory to Ericksen-Leslie Theory. SIAM Journal on Mathematical Analysis, 47, 127-158. [Google Scholar] [CrossRef] 
[10] Wang, W., Zhang, P. and Zhang, Z. (2012) The Small Deborah Number Limit of the Doi-Onsager Equation to the Ericksen-Leslie Equation. Communications on Pure and Applied Mathematics, 68, 1326-1398. [Google Scholar] [CrossRef] 
[11] Liu, H., Zhang, H. and Zhang, P. (2005) Axial Symmetry and Classi-fication of Stationary Solutions of Doi-Onsager Equation on the Sphere with Maier-Saupe Potential. Communications in Mathematical Sciences, 3, 201-218. [Google Scholar] [CrossRef] 
[12] Li, S., Wang, W. and Zhang, P. (2015) Local Well-Posedness and Small Deborah Limit of a Molecular-Based Q-Tensor System. Discrete and Continuous Dynamical Sys-tems—Series B, 20, 2611-2655. [Google Scholar] [CrossRef] 

为你推荐