Quasi two-dimensional pattern forming systems with spontaneously broken isotropy represent a novel symmetry class, that is experimentally accessible in electroconvection of homeotropically aligned liquid crystals. We present a weakly nonlinear analysis leading to amplitude equations which couple the short-wavelength patterning mode with the Goldstone mode resulting from the broken isotropy. The new coefficients in these equations are calculated from the hydrodynamics. Simulations exhibit a new type of spatio-temporal chaos at onset. The results are compared with experiments.61.30. Gd, 47.20.Ky, 47.20.Lz Ac driven electroconvection (EC) in nematic liquid crystal (NLC) layers is one of the richest systems for the study of pattern forming phenomena [1,2]. We consider the typical thin-layer geometry with the (slightly conducting) NLC sandwiched between glass plates coated with transparent electrodes. An ac voltage U is applied across the electrodes. By appropriate surface treatment of the glass plates the directorn (the preferred orientation of the NLC molecules) can be fixed at the boundaries. In particular the case of planar alignment (n in the plane of the layer) has been studied intensely. At onset one may then have normal rolls, where the wavevector is parallel to the undistorted director, or oblique ones.The case of homeotropic surface anchoring (n aligned perpendicularly to the boundaries) where the system is isotropic in the plane of the layer (= x-y plane) offers novel possibilities. Then, in the traditional EC materials with negative dielectric anisotropy, the voltage applied across the layer will first turn the director away from the layer normal (bend Freédericksz transition) leading to a quasi-planar director configuration (see e.g. [3]). The spontaneously chosen direction of the bend (i.e. direction of the projection ofn on the x-y plane) will be denoted byĉ =ĉ(r, t) ( |ĉ| = 1 ). Further increase of the voltage will eventually generate EC in close analogy to the planar case [4]; in fact nucleation to normal, oblique and traveling rolls has been observed [5]. The notable difference to the planar case is that the preferred axis (the in-plane directorĉ) is degenerate and not fixed externally (neglecting unavoidable inhomogeneities and in the absence of a planar magnetic field). Then oblique rolls are not expected to lead to a stable pattern because they will in general exert a torque onĉ which cannot be compensated. Even normal rolls, where a torque is absent because of symmetry, can be unstable because transverse modulations can be enhanced by the torque.Here we will investigate the situation by setting up a novel weakly nonlinear description that incorporates the critical convection mode together with the Goldstone mode resulting from the spontaneous breaking of the O(2) symmetry by the bend Freédericksz transition. The general form of the equations is derived from symmetry considerations. Analyzing the stability of rolls indicates that one may expect spatio-temporal chaos (STC) at onset under very g...

We calculate the threshold for electrohydrodynamic convection in homeotropically oriented nematic layers with negative dielectric anistropy that sets in after the bend-Fréedericksz transition to a quasi-planar alignment has taken place. Oblique rolls are found in a larger range than in the case of planar anchoring. The most interesting prediction is that in the weakly nonlinear analysis all roll solution are in fact unstable so that a direct transition to spatio-temporal chaos becomes possible. In the oblique-roll case this may be accompanied by a permanent local rotation of the director bend axis. Application of a planar magnetic field should stabilize the rolls

A homeotropically aligned nematic (MBBA) with negative dielectric anisotropy subjected to electric and magnetic fields has been investigated. If an electric field perpendicular to the nematic layer is applied, first the Frbedericksz transition takes place spontaneously breaking the rotational symmetry and subsequently the electrohydrodynamic instability (EHC) sets in. An additional magnetic field in the plane of the layer induces a preferred director orientation. The effects of the magnetic field on the EHC threshold voltage, on the critical wave vector and on the roll angle are examined as a function of the applied frequency. The data are compared with theoretical results. Furthermore, accompanying domain walls are characterized.

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We calculate the threshold of electrohydrodynamic convection (EHC) for nematic liquid crystals with negative dielectric anisotropy, where one allows for different director orientations at the upper and lower confining plates (hybrid cells). Besides the planar versus homeotropic case we present for the first time an analysis of continuous tilt at one plate. The predistorted ground state strongly influences the EHC character and the roll orientation. One observes a generic nonstationary behaviour and in particular the interesting scenario of drifting oblique rolls