### Abstract

We numerically investigate the Fréedericksz transition for steady state plane shear flow of nematic liquid crystals between two parallel plates in the presence of external magnetic fields. Three typical configurations with the external field in the plane of the flow and perpendicular to it, in the plane and along the flow, and where it is perpendicular to the plane of the flow are considered. In each case, the Fréedericksz transition is studied as a bifurcation problem. Beginning with a steady state shear flow, solutions corresponding to slowly increasing magnetic fields and those corresponding to fields which are suddenly turned on at a given intensity are studied. For a typical idealized nematic, we show that the symmetric pitchfork bifurcation in the absence of shear becomes a transcritical bifurcation from the trivial solution in one configuration while in another it resembles a disconnected pitchfork where the turning point of the disconnected branch is a generic singularity in the absence of symmetry or a trivial solution.

Original language | English |
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Article number | 021703 |

Journal | Physical Review E - Statistical, Nonlinear, and Soft Matter Physics |

Volume | 71 |

Issue number | 2 |

DOIs | |

State | Published - 1 Feb 2005 |

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*Physical Review E - Statistical, Nonlinear, and Soft Matter Physics*, vol. 71, no. 2, 021703. https://doi.org/10.1103/PhysRevE.71.021703

**Shear flow in nematic liquid crystals : Fréedericksz transition as a bifurcation.** / Mukherjee, Arup; Mukherjee, Bagisa.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Shear flow in nematic liquid crystals

T2 - Fréedericksz transition as a bifurcation

AU - Mukherjee, Arup

AU - Mukherjee, Bagisa

PY - 2005/2/1

Y1 - 2005/2/1

N2 - We numerically investigate the Fréedericksz transition for steady state plane shear flow of nematic liquid crystals between two parallel plates in the presence of external magnetic fields. Three typical configurations with the external field in the plane of the flow and perpendicular to it, in the plane and along the flow, and where it is perpendicular to the plane of the flow are considered. In each case, the Fréedericksz transition is studied as a bifurcation problem. Beginning with a steady state shear flow, solutions corresponding to slowly increasing magnetic fields and those corresponding to fields which are suddenly turned on at a given intensity are studied. For a typical idealized nematic, we show that the symmetric pitchfork bifurcation in the absence of shear becomes a transcritical bifurcation from the trivial solution in one configuration while in another it resembles a disconnected pitchfork where the turning point of the disconnected branch is a generic singularity in the absence of symmetry or a trivial solution.

AB - We numerically investigate the Fréedericksz transition for steady state plane shear flow of nematic liquid crystals between two parallel plates in the presence of external magnetic fields. Three typical configurations with the external field in the plane of the flow and perpendicular to it, in the plane and along the flow, and where it is perpendicular to the plane of the flow are considered. In each case, the Fréedericksz transition is studied as a bifurcation problem. Beginning with a steady state shear flow, solutions corresponding to slowly increasing magnetic fields and those corresponding to fields which are suddenly turned on at a given intensity are studied. For a typical idealized nematic, we show that the symmetric pitchfork bifurcation in the absence of shear becomes a transcritical bifurcation from the trivial solution in one configuration while in another it resembles a disconnected pitchfork where the turning point of the disconnected branch is a generic singularity in the absence of symmetry or a trivial solution.

UR - http://www.scopus.com/inward/record.url?scp=41349098139&partnerID=8YFLogxK

U2 - 10.1103/PhysRevE.71.021703

DO - 10.1103/PhysRevE.71.021703

M3 - Article

AN - SCOPUS:41349098139

VL - 71

JO - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

JF - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

SN - 1539-3755

IS - 2

M1 - 021703

ER -