Pattern Formation in Liquid Crystals --Symmetry of Fields and Nonequilibrium Macroscopic Fluctuation--

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In the current study, we_prepare electroconvective cells of initially two different symmetries using the surface treatment of the container. One is called the homeotropic alignment and the other the planar one. Both show nonequilibrium macroscopic fluctuations (spatiotemporal chaos) beyond certain thresholds of applied voltages. Below we describe typical properties of pattern dynamics observed in both systems depending on the symmetries.In the homeotropic alignment the system has continuously rotational symmetry, due to this symmetry the soft-mode turbulence (SMT) is obtained at first, and shows the following facts.(1)There observe strong interactions between convective and orientational fields related to the symmetries. One is normal rolls, and the other is oblique rolls. The transition between them appears when the frequency of applied voltages is changed. It may be regarded as the transition something similar to order-disorder one.(2)The correlation length ξ satisfies the relation ξ … More ∝ ε^<-1/2>. Here ε is an applied voltage normalized by the threshold for SMT.(3)In the one dimensional homeotropic system, the threshold of the soft-mode turbulence is shifted to higher value than that in two dimensional systems. It may be due to a finite size effect.(4)According to the relation between the dynamics of the soft-mode turbulence and the dimensionality of the system obtained from the temporal correlation of the fluctuations, dynamics is independent of the dimensionality of system.In the planar alignment, the system has initially broken the continuously rotational symmetry. In this case the defect lattice pattern is observed resulting from frozen macroscopic fluctuations as a periodic defect alignment.(1)The defect lattice forms due to superposition of two modes by abnormal rolls instability and skewed-varicose one.(2)The lattice structure partially collapses in space beyond a some threshold. The collapse area increases with the applied voltage. This is a typical spatiotemporal chaos, especially called spatiotemporal intermittency (STI). By further increase of applied voltages, the whole area becomes turbulence.(3)The lattice structure is reproduced in the collapse area by superimposing the modulation in the applied voltage at the same frequency as the lattice spontaneous oscillation. Thus STI can be controlled by small periodic perturbations, that is, the chaos control can be realized in systems with large spatial degrees of freedom. Less