Amplitude equations for the electrohydrodynamic instability in nematic liquid crystals

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Abstract
We study the near-threshold behavior of electrohydrodynamic convection (EHC) in planarly aligned nematic liquid crystals in the (low-frequency) conduction regime. The investigations are based on a rigorous and systematic weakly nonlinear analysis of the standard hydrodynamic equations leading to a reduced description in terms of order-parameter equations. The typical experimental stability regimes in control parameter and wave-number space are identified for normal rolls near threshold. In particular, the decisive role of mean-flow effects in triggering the typical secondary zigzag instability leading to oblique rolls is emphasized. Subsequently, a set of coupled amplitude equations is derived directly from the basic equations that includes the mean-flow effects and higher-order gradient terms important at least in EHC. Simulations of the amplitude equations point to the possible existence of more than one attractor beyond the zigzag destabilization line, which might explain the sometimes conflicting experimental results. The scenario of ‘‘weak turbulence’’ (sometimes called ‘‘defect turbulence’’) is well accounted for by the theory.