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Journal articles on the topic 'Ericksen–Leslie equations'

Author: Grafiati

Published: 4 June 2021

Last updated: 13 February 2022

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1

Mottram, N. J., J. T. Pinto, and G. McKay. "Decoupling of the Ericksen–Leslie equations." Liquid Crystals 40, no. 6 (2013): 787–98. http://dx.doi.org/10.1080/02678292.2013.783134.

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2

Véron, Alain R., and Assis F. Martins. "Tensorial Form of Leslie-Ericksen Equations and Applications." Molecular Crystals and Liquid Crystals 508, no. 1 (2009): 309/[671]—336/[698]. http://dx.doi.org/10.1080/15421400903065796.

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3

Chechkin, Gregory A., Tudor S. Ratiu, Maxim S. Romanov, and Vyacheslav N. Samokhin. "Existence and uniqueness theorems for the full three-dimensional Ericksen–Leslie system." Mathematical Models and Methods in Applied Sciences 27, no. 05 (2017): 807–43. http://dx.doi.org/10.1142/s0218202517500178.

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In this paper, we study the three-dimensional Ericksen–Leslie equations for the nematodynamics of liquid crystals. We prove short time existence and uniqueness of strong solutions for the initial value problem for the periodic case and in bounded domains with both Dirichlet- and Neumann-type boundary conditions.

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4

Jiang, Ning, Yi-Long Luo, and Shaojun Tang. "On well-posedness of Ericksen–Leslie’s parabolic–hyperbolic liquid crystal model in compressible flow." Mathematical Models and Methods in Applied Sciences 29, no. 01 (2019): 121–83. http://dx.doi.org/10.1142/s0218202519500052.

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We study the well-posedness of the Ericksen–Leslie’s parabolic–hyperbolic liquid crystal model in compressible flow. Inspired by our study for incompressible case [N. Jiang and Y.-L. Luo, On well-posedness of Ericsen–Leslie’s hyperbolic incompressible liquid crystal model, preprint (2017), arXiv:1709.06370v1 ] and some techniques from compressible Navier–Stokes equations, we first prove the local-in-time existence of the classical solution to the system with finite initial energy, under some natural constraints on the Leslie coefficients which ensure that the basic energy law is dissipative. F

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5

Hieber, Matthias, and Jan Prüss. "Dynamics of the Ericksen–Leslie Equations with General Leslie Stress II: The Compressible Isotropic Case." Archive for Rational Mechanics and Analysis 233, no. 3 (2019): 1441–68. http://dx.doi.org/10.1007/s00205-019-01382-9.

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6

Hieber, Matthias, and Jan Prüss. "Dynamics of the Ericksen–Leslie equations with general Leslie stress I: the incompressible isotropic case." Mathematische Annalen 369, no. 3-4 (2016): 977–96. http://dx.doi.org/10.1007/s00208-016-1453-7.

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7

Güler, Marifi. "Symbolic evaluation of the Ericksen-Leslie equations in the computation domain." Journal of Non-Newtonian Fluid Mechanics 52, no. 3 (1994): 309–21. http://dx.doi.org/10.1016/0377-0257(94)85027-5.

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8

Hieber, Matthias. "On operator semigroups arising in the study of incompressible viscous fluid flows." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 378, no. 2185 (2020): 20190618. http://dx.doi.org/10.1098/rsta.2019.0618.

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This article concentrates on various operator semigroups arising in the study of viscous and incompressible flows. Of particular concern are the classical Stokes semigroup, the hydrostatic Stokes semigroup, the Oldroyd as well as the Ericksen–Leslie semigroup. Besides their intrinsic interest, the properties of these semigroups play an important role in the investigation of the associated nonlinear equations. This article is part of the theme issue ‘Semigroup applications everywhere’.

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9

Brzeźniak, Zdzisław, Erika Hausenblas, and Paul André Razafimandimby. "A note on the stochastic Ericksen-Leslie equations for nematic liquid crystals." Discrete & Continuous Dynamical Systems - B 22, no. 11 (2017): 1–18. http://dx.doi.org/10.3934/dcdsb.2019106.

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10

Cabrales, R. C., F. Guillén-González, and J. V. Gutiérrez-Santacreu. "A Time-Splitting Finite-Element Stable Approximation for the Ericksen--Leslie Equations." SIAM Journal on Scientific Computing 37, no. 2 (2015): B261—B282. http://dx.doi.org/10.1137/140960979.

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11

Ryskin, G. "One modification of the Ericksen-Leslie equations in a two-dimensional motion." Journal of Non-Newtonian Fluid Mechanics 39, no. 2 (1991): 207–10. http://dx.doi.org/10.1016/0377-0257(91)80012-9.

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12

SRINIVASARAO, MOHAN. "RHEOLOGY AND RHEO-OPTICS OF POLYMER LIQUID CRYSTALS." International Journal of Modern Physics B 09, no. 18n19 (1995): 2515–72. http://dx.doi.org/10.1142/s0217979295000951.

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The rheological and rheo-optical properties of nematic solutions of rodlike polymers are discussed. Magnetic field induced instability in the twist geometry is discussed in terms of the flow properties of these solutions. The rheological properties of these nematic solutions are compared to isotropic solutions of the same polymer. The behavior in shear flow of nematic solutions is discussed in terms of the Ericksen-Leslie equations. Deviations from those solutions are also discussed in context to polymeric nematics.

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13

Walkington, Noel J. "Numerical approximation of nematic liquid crystal flows governed by the Ericksen-Leslie equations." ESAIM: Mathematical Modelling and Numerical Analysis 45, no. 3 (2010): 523–40. http://dx.doi.org/10.1051/m2an/2010065.

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14

Muschik, Wolfgang, Harald Ehrentraut, and Christina Papenfuss. "The Connection Between Ericksen-Leslie Equations and the Balances of Mesoscopic Theory of Liquid Crystals." Molecular Crystals and Liquid Crystals Science and Technology. Section A. Molecular Crystals and Liquid Crystals 262, no. 1 (1995): 417–23. http://dx.doi.org/10.1080/10587259508033544.

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15

Cruz, Pedro A., Murilo F. Tomé, Iain W. Stewart, and Sean McKee. "Numerical solution of the Ericksen–Leslie dynamic equations for two-dimensional nematic liquid crystal flows." Journal of Computational Physics 247 (August 2013): 109–36. http://dx.doi.org/10.1016/j.jcp.2013.03.061.

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16

Geng, Jinbo. "Remarks on regularity criteria for an Ericksen–Leslie system and the viscous Camassa–Holm equations." Applied Mathematics Letters 23, no. 10 (2010): 1193–97. http://dx.doi.org/10.1016/j.aml.2010.05.010.

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17

Mondal, Kartick, Abir Ghosh, Joydip Chaudhuri, and Dipankar Bandyopadhyay. "Electric-field-mediated instability modes and Fréedericksz transition of thin nematic films." Journal of Fluid Mechanics 834 (November 17, 2017): 464–509. http://dx.doi.org/10.1017/jfm.2017.727.

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Instabilities at the deformable free surface of a thin nematic liquid crystal film can develop interesting patterns when exposed to an external electrostatic field. A general linear stability analysis is performed involving the Ericksen–Leslie governing equations for the dynamics of the nematic film coupled with the anisotropic Maxwell stresses for the electric field to uncover the salient features of these instabilities. The study reveals the coexistence of twin instability modes: (i) long-wave interfacial mode – stimulated when the sole destabilizing influence of the electric field overcomes

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18

Martins, Assis F., Alexandre E. Gomes, Laura Orian, and Antonino Polimeno. "Simulations of Flow-Induced Director Patterns in Nematic Liquid Crystals Through Leslie-Ericksen Equations in Two Dimensions." Molecular Crystals and Liquid Crystals Science and Technology. Section A. Molecular Crystals and Liquid Crystals 351, no. 1 (2000): 135–43. http://dx.doi.org/10.1080/10587250008023262.

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19

Polimeno, Antonino, Laura Orian, Assis F. Martins, and Alexandre E. Gomes. "Simulations of flow-induced director structures in nematic liquid crystals through Leslie-Ericksen equations. I. Computational methodology in two dimensions." Physical Review E 62, no. 2 (2000): 2288–300. http://dx.doi.org/10.1103/physreve.62.2288.

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20

Guan. "Performance Analysis of a Microfluidic Pump Based on Combined Actuation of the Piezoelectric Effect and Liquid Crystal Backflow Effect." Micromachines 10, no. 9 (2019): 584. http://dx.doi.org/10.3390/mi10090584.

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A novel combined actuation method based on the piezoelectric effect and liquid crystal backflow effect is proposed in this paper. The coupling mechanism of a piezoelectric transducer (PZT) and liquid crystal (LC) in a combined driving mode is analyzed, and the governing equations of electromechanical coupling based on inverse piezoelectric effect and the classical Leslie–Ericksen backflow equation are modified under combined driving method. The new multifield coupling dynamic equations for numerical analysis is established. Experimentally, a sandwiched micropump was manufactured and sealed wit

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21

Cruz, Pedro A., Murilo F. Tomé, Iain W. Stewart, and Sean McKee. "A numerical method for solving the dynamic three-dimensional Ericksen–Leslie equations for nematic liquid crystals subject to a strong magnetic field." Journal of Non-Newtonian Fluid Mechanics 165, no. 3-4 (2010): 143–57. http://dx.doi.org/10.1016/j.jnnfm.2009.10.007.

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22

Martins, Assis F., Alexandre E. Gomes, Antonino Polimeno, and Laura Orian. "Simulations of flow-induced director structures in nematic liquid crystals through Leslie-Ericksen equations. II. Interpretation of NMR experiments in liquid crystal polymers." Physical Review E 62, no. 2 (2000): 2301–9. http://dx.doi.org/10.1103/physreve.62.2301.

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23

Srinivasarao, Mohan, Raul O. Garay, H. Henning Winter, and Richard S. Stein. "Rheo-Optics of an Augned Thermotropic Liquid Crystalline Polymer." MRS Proceedings 248 (1991). http://dx.doi.org/10.1557/proc-248-197.

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AbstractRheo-optical studies on aligned and unaligned melts of a main chain thermotropic polyester with flexible spacers are discussed in terms of the predictions of the Ericksen-Leslie equations. It is shown, using conoscopy, that the director is flowaligning at temperatures close to TNI and nonflow-aligning close to a smectic to nematic (TSN) phase transition. The implications of these results are discussed in terms of the change in sign of one of the Leslie viscosity coefficients and interpreted in the framework of the Ericksen-Leslie Theory.

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24

Kortum, Joshua. "Concentration-cancellation in the Ericksen–Leslie model." Calculus of Variations and Partial Differential Equations 59, no. 6 (2020). http://dx.doi.org/10.1007/s00526-020-01849-8.

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AbstractWe establish the subconvergence of weak solutions to the Ginzburg–Landau approximation to global-in-time weak solutions of the Ericksen–Leslie model for nematic liquid crystals on the torus $${\mathbb {T}^2}$$ T 2 . The key argument is a variation of concentration-cancellation methods originally introduced by DiPerna and Majda to investigate the weak stability of solutions to the (steady-state) Euler equations.

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25

Brzeźniak, Zdzislaw, Gabriel Deugoué, and Paul André Razafimandimby. "On the 2D Ericksen–Leslie equations with anisotropic energy and external forces." Journal of Evolution Equations, May 18, 2021. http://dx.doi.org/10.1007/s00028-021-00710-5.

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AbstractIn this paper we consider the 2D Ericksen–Leslie equations which describe the hydrodynamics of nematic liquid crystal with external body forces and anisotropic energy modeling the energy of applied external control such as magnetic or electric field. Under general assumptions on the initial data, the external data and the anisotropic energy, we prove the existence and uniqueness of global weak solutions with finitely many singular times. If the initial data and the external forces are sufficiently small, then we establish that the global weak solution does not have any singular times a

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26

Rey, Alejandro D. "Radial Creeping Flow Between Parallel Disks of Rod-like Nematic Liquid Crystals: Textures and Instabilities." MRS Proceedings 177 (1989). http://dx.doi.org/10.1557/proc-177-317.

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ABSTRACTFour solutions to the Leslie-Ericksen equations for nematic liquid crystals are obtained for pressure-driven radial out-flow between concentric parallel disks and homeotropic director wall anchoring. At low pressure drops the in-plane mode is stable; the centerline director orientation is normal to the flow direction. For each radial distance from the entrance hole there is a critical pressure drop at which the elongational torque twist the director out-ofthe- plane of flow ; left and right rotations are possible. The transition results in the appearance of secondary flows in the azimu

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27

Metzger, Stefan. "A convergent finite element scheme for a fourth-order liquid crystal model." IMA Journal of Numerical Analysis, October 23, 2020. http://dx.doi.org/10.1093/imanum/draa069.

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Abstract In this manuscript we propose and analyse a fully discrete, unconditionally stable finite element scheme for a recently developed director model for liquid crystalline flows (Metzger, S. (2020) On a novel approach for modeling liquid crystalline flows. Commun. Math. Sci., 18, 359–378). The model consists of nonlinear fourth-order partial differential equations describing the evolution of the director field and Navier–Stokes equations governing the velocity field. We employ a stable splitting approach to reduce the computational complexity by decoupling the update of the director field

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28

Walton, Joshua, Geoffrey McKay, Michael Grinfeld, and Nigel J. Mottram. "Pressure-driven changes to spontaneous flow in active nematic liquid crystals." European Physical Journal E 43, no. 8 (2020). http://dx.doi.org/10.1140/epje/i2020-11973-8.

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Abstract. We consider the effects of a pressure gradient on the spontaneous flow of an active nematic liquid crystal in a channel, subject to planar anchoring and no-slip conditions on the boundaries of the channel. We employ a model based on the Ericksen-Leslie theory of nematics, with an additional active stress accounting for the activity of the fluid. By directly solving the flow equation, we consider an asymptotic solution for the director angle equation for large activity parameter values and predict the possible values of the director angle in the bulk of the channel. Through a numerica

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