Director distribution in periodically deformed planar nematic layers subjected to magnetic field

The periodic deformations induced by magnetic field in planar nematic layers, which can be observed as stripes, were studied numerically. Two types of deformations were distinguished corresponding to two directions of the field: (i) perpendicular to the layer, (ii) parallel to the layer but perpendicular to the initial director alignment. The rigid surface anchoring conditions were assumed. The calculations were performed for various magnetic field strength and elastic constants ratio. Sinusoidal form of the spatial dependence of the angles determining the director orientation, predicted in earlier theoretical works, was confirmed only for sufficiently small deformations. Quite different structure of the stripes was found at high field strengths. The deformation in each half of the stripe was nearly homogeneous. The deformations in neighbouring halves had opposite sense. The homogeneously deformed halves were separated by thin `walls' of highly distorted medium. The width of the stripes increased infinitely when the field approached to some critical value. This effect is equivalent to the transition from the periodic to the homogeneous deformations, since an uniformly deformed half of the stripe spreads over the whole layer.