OBLIQUE ROLLS IN NEMATIC LIQUID-CRYSTALS DRIVEN BY STOCHASTIC FIELDS - ONE-DIMENSIONAL THEORY INCLUDING THE FLEXOEFFECT AND 3-DIMENSIONAL THEORY

The formation of oblique rolls in nematic liquid crystals driven by di chotomous stochastic fields is investigated in the frame of a one-dime nsional 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 c alculated and the angle of the oblique rolls is determined by mode sel ection. It is shown that in certain parameter ranges oblique rolls hav e lower thresholds than normal rolls. As for deterministic excitation, with increasing flexoeffect the formation of oblique rolls is favoure d. 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 a nd the two wave numbers which give the angle of the oblique rolls are determined by mode selection. The appearance of oblique rolls is studi ed for different parameters of the driving stochastic field. The resul ts are compared with those of the one-dimensional model without the fl exoeffect.