Abstract
We report on a new mode interaction found in electroconvection experiments on the nematic liquid crystal mixture Phase V in planar geometry. The mode interaction (codimension two) point occurs at a critical value of the frequency of the driving AC voltage. For frequencies below this value the primary pattern-forming instability at the onset voltage is an oblique stationary instability involving oblique rolls, and above this value it is an oscillatory instability giving rise to normal traveling rolls (oriented perpendicular to and traveling in the director direction). The transition has been confirmed by measuring the roll angle and the dominant frequency of the time series, as both quantities exhibit a discontinuous jump across zero when the AC frequency is varied near threshold. The globally coupled system of Ginzburg–Landau equations that qualitatively describe this mode interaction is constructed, and the resulting normal form, in which slow spatial variations of the mode amplitudes are ignored, is analyzed. This analysis shows that the Ginzburg–Landau system provides the adequate theoretical description for the experimentally observed phenomenon. The experimentally observed patterns at and higher above the onset allow us to narrow down the range of the parameters in the normal form.
Highlights
Electroconvection in nematic liquid crystals is a physical system that serves as a testing ground for experimental studies and theoretical predictions of pattern formation in spatially extended anisotropic systems [1,2,3,4,5]
In this paper we have presented and analyzed the first reported occurrence of near-onset patterns dominated by the interaction of steady oblique rolls and normal traveling rolls in nematic elctroconvection experiments
The results described in this paper confirm that nematic electroconvection is a multi-parameter physical system that naturally exhibits this kind of mode interaction
Summary
Electroconvection in nematic liquid crystals is a physical system that serves as a testing ground for experimental studies and theoretical predictions of pattern formation in spatially extended anisotropic systems [1,2,3,4,5]. A number of experimental and analytical studies of steady-oscillatory (Hopf) mode interactions in isotropic pattern forming systems, like Taylor–Couette flow, Rayleigh–Bénard convection, and convection in binary mixtures have been reported in the literature (see, e.g., [17,18,19,20,21] and references therein). In this paper we report and analyze complex spatiotemporal patterns recorded in the electroconvection of the nematic mixture Phase V for AC voltages slightly above the onset value, which are dominated by normal oscillatory/oblique steady-state mode interaction. Ginzburg–Landau amplitude equations that captures near-onset patterns in the neighborhood of the mode interaction point, and perform a bifurcation analysis of the associated normal form.
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