On the theory of Rayleigh-Bénard convection in homeotropic nematic liquid crystals

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Abstract
A rigorous linear and weakly nonlinear analysis of Rayleigh-Bénard convection in homeotropically aligned nematic liquid crystals is presented for both adverse convection (heating from above) and normal convection (heating from below) allowing for th presence of magnetic fields. In adverse convection we find a transition from forward to backward bifurcation with increasing vertical (stabilizing) field. The stability analysis of roll solutions explains the experimentally observed transition between roll and square patterns for weak horizontal (destabilizing) fields. In a range of high vertical magnetic fields two steady convective modes with different wavelengths and symmetries become critical at nearly the same threshold giving rise to competition and resonant interaction. For the oscillatory instability in normal convection the nature of the bifurcation for both traveling and standing rolls is determined. Comparison with previous theories and with experiments is made wherever possible

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