Oblique rolls in nematic liquid crystals driven by stochastic fields: One-dimensional theory including the flexoeffect and three-dimensional theory

The formation of oblique rolls in nematic liquid crystals driven by dichotomous stochastic fields is investigated in the frame of a one-dimensional linear theory including the flexoeffect, and in the frame of a three-dimensional linear theory with free boundary conditions. In the first model the threshold for the stability of the first moments is calculated and the angle of the oblique rolls is determined by mode selection. It is shown that in certain parameter ranges oblique rolls have lower thresholds than normal rolls. As for deterministic excitation, with increasing flexoeffect the formation of oblique rolls is favoured. It is observed that at full strength the flexoeffect alone is able to trigger the formation of rolls. In the three-dimensional model the threshold for the stability of the first moments is calculated again and the two wave numbers which give the angle of the oblique rolls are determined by mode selection. The appearance of oblique rolls is studied for different parameters of the driving stochastic field. The results are compared with those of the one-dimensional model without the flexoeffect.