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...

No abstract

For over 25 years it is known that the roll structure of electroconvection (EC) in the dielectric regime in planarly aligned nematic liquid crystals has, after a transition to defect chaos, the tendency to form chevron structures. We show, with the help of a coarse-grained model, that this effect can generally be expected for systems with spontaneously broken isotropy, that is lifted by a small external perturbation. The linearized model as well as a nonlinear extension are compared to simulations of a system of coupled amplitude equations which generate chevrons out of defect chaos. The mechanism of chevron formation is similar to the development of Turing patterns in reaction diffusion systems.

No abstract