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P.G. de Gennes and J. Prost, The Physics of Liquid Crystals, 2nd ed. (Clarendon Press, Oxford, 1993);, S. Chandrasekhar, Liquid Crystals, 2nd ed. (Cambridge University Press, Cambridge, 1992)
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P.G. de Gennes and J. Prost, The Physics of Liquid Crystals, 2nd ed. (Clarendon Press, Oxford, 1993);S. Chandrasekhar, Liquid Crystals, 2nd ed. (Cambridge University Press, Cambridge, 1992).
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Mesquita, O.N.4
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Shashidhar, R.5
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85037189402
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A.N. Beris and B.J. Edwards, Thermodynamics of Flowing Systems (Oxford University Press, Oxford, 1994)
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A.N. Beris and B.J. Edwards, Thermodynamics of Flowing Systems (Oxford University Press, Oxford, 1994)
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85037181759
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M. Doi and S. Edwards, The Theory of Polymer Dynamics (Clarendon Press, Oxford, 1989)
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M. Doi and S. Edwards, The Theory of Polymer Dynamics (Clarendon Press, Oxford, 1989).
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85037251336
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A.A. Sonin, The Surface Physics of Liquid Crystals (Gordon and Breach, Amsterdam, 1995)
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A.A. Sonin, The Surface Physics of Liquid Crystals (Gordon and Breach, Amsterdam, 1995)
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0000163491
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G. Barbero and G. Durand, in Liquid Crystals in Complex Geometries, edited by G. P. Crawford and S. Zumer (Taylor and Francis, London, 1996), p. 21
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A.K. Sen and D.E. Sullivan, Phys. Rev. A 35, 1391 (1987);G. Barbero and G. Durand, in Liquid Crystals in Complex Geometries, edited by G. P. Crawford and S. Zumer (Taylor and Francis, London, 1996), p. 21.
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Sen, A.K.1
Sullivan, D.E.2
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26
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85037207813
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Simulations were performed on a (Formula presented) lattice with (Formula presented) (Formula presented) (Formula presented) (Formula presented) (Formula presented) (Formula presented) (Formula presented) (Formula presented) (Formula presented) and (Formula presented) The magnitude of order (Formula presented) is then (Formula presented) in the bulk. Periodic boundary conditions were used in the x direction and free boundaries were used in the y direction with (Formula presented) symmetric surface tilt. Given suitable pressure, length, and time scales these parameters can be mapped to a lattice size (Formula presented) (Formula presented) (Formula presented) The Frank elastic constants are (Formula presented) and Miesowicz viscosities 0.02 Pa s to (Formula presented) s. The material parameter values chosen are close to those of 5CB
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Simulations were performed on a (Formula presented) lattice with (Formula presented) (Formula presented) (Formula presented) (Formula presented) (Formula presented) (Formula presented) (Formula presented) (Formula presented) (Formula presented) and (Formula presented) The magnitude of order (Formula presented) is then (Formula presented) in the bulk. Periodic boundary conditions were used in the x direction and free boundaries were used in the y direction with (Formula presented) symmetric surface tilt. Given suitable pressure, length, and time scales these parameters can be mapped to a lattice size (Formula presented) (Formula presented) (Formula presented) The Frank elastic constants are (Formula presented) and Miesowicz viscosities 0.02 Pa s to (Formula presented) s. The material parameter values chosen are close to those of 5CB.
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27
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85037254084
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The distance between the defects is always much larger than (Formula presented) in the simulations, thus the surface effects dominate the defect-defect interaction
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The distance between the defects is always much larger than (Formula presented) in the simulations, thus the surface effects dominate the defect-defect interaction.
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28
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85037183502
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If (Formula presented) and the director is confined to the (Formula presented) plane, the Frank elastic free energy density (assuming uniaxiality and constant magnitude of order) can be written as (Formula presented) where (Formula presented) is the angle of the director to the horizontal axis and (Formula presented) The dynamics of the medium, (Formula presented) are invariant under mirroring on the x axis. Moreover, given (Formula presented) and (Formula presented) correspond to the same dynamics as (Formula presented) and (Formula presented) (Note that there is no speed anisotropy in the latter case with the purely relaxational dynamics for the tensor order parameter.) For defects this equivalence is only approximate due to the biaxiality and the change in the magnitude of order in the core
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If (Formula presented) and the director is confined to the (Formula presented) plane, the Frank elastic free energy density (assuming uniaxiality and constant magnitude of order) can be written as (Formula presented) where (Formula presented) is the angle of the director to the horizontal axis and (Formula presented) The dynamics of the medium, (Formula presented) are invariant under mirroring on the x axis. Moreover, given (Formula presented) and (Formula presented) correspond to the same dynamics as (Formula presented) and (Formula presented) (Note that there is no speed anisotropy in the latter case with the purely relaxational dynamics for the tensor order parameter.) For defects this equivalence is only approximate due to the biaxiality and the change in the magnitude of order in the core.
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29
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0030906651
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V.K. Gupta and N.L. Abbott, Science (Washington, DC, U.S.) 276, 1533 (1997).
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, pp. 1533
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Gupta, V.K.1
Abbott, N.L.2
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30
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0037175910
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A. Bogi, P. Martinot-Lagarde, I. Dozov, and M. Nobili, Phys. Rev. Lett. 89, 225501 (2002).
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(2002)
Phys. Rev. Lett.
, vol.89
, pp. 225501
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Bogi, A.1
Martinot-Lagarde, P.2
Dozov, I.3
Nobili, M.4
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