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September  2012, 17(6): 1707-1728. doi: 10.3934/dcdsb.2012.17.1707

## Analysis and stability of bent-core liquid crystal fibers

 1 Department of Mathematics, Purdue University, West Lafayette, IN 47906, United States 2 Department of Mathematics, Purdue University, West Lafayette, IN 47907, United States

Received  February 2011 Revised  October 2011 Published  May 2012

In this paper we analyze a free-boundary model for free-standing fibers made from smectic layers of kinked (bent-core) liquid crystal molecules. In [1] a radial model was proposed to explain how fibers form (assuming radially symmetric configurations) based on the distinctive packing and ferroelectric properties of bent--core molecules. We develop this model further to include smectic energy terms so as to allow for non--circular cross--sections with non--radial configurations and fields. We show that the relative size of the energy's elasticity constants can be used to determine the stability (instability) of radially symmetric fibers with respect to non--radial perturbations.
Citation: Patricia Bauman, Daniel Phillips. Analysis and stability of bent-core liquid crystal fibers. Discrete & Continuous Dynamical Systems - B, 2012, 17 (6) : 1707-1728. doi: 10.3934/dcdsb.2012.17.1707
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##### References:
 [1] Tiziana Giorgi, Feras Yousef. Analysis of a model for bent-core liquid crystals columnar phases. Discrete & Continuous Dynamical Systems - B, 2015, 20 (7) : 2001-2026. doi: 10.3934/dcdsb.2015.20.2001 [2] Kyungkeun Kang, Jinhae Park. Partial regularity of minimum energy configurations in ferroelectric liquid crystals. Discrete & Continuous Dynamical Systems - A, 2013, 33 (4) : 1499-1511. doi: 10.3934/dcds.2013.33.1499 [3] Patricia Bauman, Daniel Phillips, Jinhae Park. Existence of solutions to boundary value problems for smectic liquid crystals. Discrete & Continuous Dynamical Systems - S, 2015, 8 (2) : 243-257. doi: 10.3934/dcdss.2015.8.243 [4] Jinhae Park, Feng Chen, Jie Shen. Modeling and simulation of switchings in ferroelectric liquid crystals. Discrete & Continuous Dynamical Systems - A, 2010, 26 (4) : 1419-1440. doi: 10.3934/dcds.2010.26.1419 [5] Carlos J. García-Cervera, Sookyung Joo. Reorientation of smectic a liquid crystals by magnetic fields. Discrete & Continuous Dynamical Systems - B, 2015, 20 (7) : 1983-2000. doi: 10.3934/dcdsb.2015.20.1983 [6] Marcelo M. Disconzi, Igor Kukavica. A priori estimates for the 3D compressible free-boundary Euler equations with surface tension in the case of a liquid. Evolution Equations & Control Theory, 2019, 8 (3) : 503-542. doi: 10.3934/eect.2019025 [7] Chun Liu. Dynamic theory for incompressible Smectic-A liquid crystals: Existence and regularity. Discrete & Continuous Dynamical Systems - A, 2000, 6 (3) : 591-608. doi: 10.3934/dcds.2000.6.591 [8] J. I. Díaz, J. F. Padial. On a free-boundary problem modeling the action of a limiter on a plasma. Conference Publications, 2007, 2007 (Special) : 313-322. doi: 10.3934/proc.2007.2007.313 [9] Panagiota Daskalopoulos, Eunjai Rhee. Free-boundary regularity for generalized porous medium equations. Communications on Pure & Applied Analysis, 2003, 2 (4) : 481-494. doi: 10.3934/cpaa.2003.2.481 [10] Geng Chen, Ping Zhang, Yuxi Zheng. Energy conservative solutions to a nonlinear wave system of nematic liquid crystals. Communications on Pure & Applied Analysis, 2013, 12 (3) : 1445-1468. doi: 10.3934/cpaa.2013.12.1445 [11] Qiumei Huang, Xiaofeng Yang, Xiaoming He. Numerical approximations for a smectic-A liquid crystal flow model: First-order, linear, decoupled and energy stable schemes. Discrete & Continuous Dynamical Systems - B, 2018, 23 (6) : 2177-2192. doi: 10.3934/dcdsb.2018230 [12] J. F. Padial. Existence and estimate of the location of the free-boundary for a non local inverse elliptic-parabolic problem arising in nuclear fusion. Conference Publications, 2011, 2011 (Special) : 1176-1185. doi: 10.3934/proc.2011.2011.1176 [13] Yuning Liu, Wei Wang. On the initial boundary value problem of a Navier-Stokes/$Q$-tensor model for liquid crystals. Discrete & Continuous Dynamical Systems - B, 2018, 23 (9) : 3879-3899. doi: 10.3934/dcdsb.2018115 [14] Wenya Ma, Yihang Hao, Xiangao Liu. Shape optimization in compressible liquid crystals. Communications on Pure & Applied Analysis, 2015, 14 (5) : 1623-1639. doi: 10.3934/cpaa.2015.14.1623 [15] Chun Liu, Jie Shen. On liquid crystal flows with free-slip boundary conditions. Discrete & Continuous Dynamical Systems - A, 2001, 7 (2) : 307-318. doi: 10.3934/dcds.2001.7.307 [16] Huijuan Song, Bei Hu, Zejia Wang. Stationary solutions of a free boundary problem modeling the growth of vascular tumors with a necrotic core. Discrete & Continuous Dynamical Systems - B, 2020  doi: 10.3934/dcdsb.2020084 [17] Yuming Chu, Yihang Hao, Xiangao Liu. Global weak solutions to a general liquid crystals system. Discrete & Continuous Dynamical Systems - A, 2013, 33 (7) : 2681-2710. doi: 10.3934/dcds.2013.33.2681 [18] Mauro Fabrizio, Claudio Giorgi, Angelo Morro. Isotropic-nematic phase transitions in liquid crystals. Discrete & Continuous Dynamical Systems - S, 2011, 4 (3) : 565-579. doi: 10.3934/dcdss.2011.4.565 [19] John Murrough Golden. Constructing free energies for materials with memory. Evolution Equations & Control Theory, 2014, 3 (3) : 447-483. doi: 10.3934/eect.2014.3.447 [20] Marco Cicalese, Antonio DeSimone, Caterina Ida Zeppieri. Discrete-to-continuum limits for strain-alignment-coupled systems: Magnetostrictive solids, ferroelectric crystals and nematic elastomers. Networks & Heterogeneous Media, 2009, 4 (4) : 667-708. doi: 10.3934/nhm.2009.4.667

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