Defect Dynamics and Statistics of Defect Chaos in Electrohydrodynamic Convections in Nematics

Defect dynamics and chaos in electrohydrodynamic convections of nematic liquid crystals, which appear in the state slightly above the Williams domain convection (WD) occurring at a threshold voltage V are statistically investigated. The temporal change and ε-dependence of mean defect number are measured for two different aspect ratios Γ (ratio of the lateral dimension to the thickness of the layer) = 15 and 650 in the conduction regime, where ε = (V2 - V2c)/V2c. The power spectrum for the temporal change of the defect number is calculated. For small Γ = 15 the spectrum shows 1/f-type independently of ε. For large Γ = 650 defect turbulence called the fluctuating WD, appears at a voltage very close to V The spectrum shows white at relatively large ε and 1/f spectrum at very small ε. The probability distributions of defect numbers are rather well-fitted with Poisson distribution. The ε-dependence of mean defect number in the distribution clearly changes at identical ε where spectrum profile changes from 1/f to white. In the region indicating 1/f spectrum, the mean defect number is approximately proportional to ε2 whereas in the region with white spectrum, i.e. large ε, it is proportional to ε0.95. This cross-over is only observed in the cell with Γ = 650. But no change of the dependence is observed for Γ = 15. This probably suggests the possibility of two different dynamics for defect turbulence.