Extended weakly nonlinear theory of planar nematic convection

Plaut, Emmanuel; Pesch, Werner

doi:10.1103/physreve.59.1747

Cited by 48 publications

(64 citation statements)

References 41 publications

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“…In the case of finite γ c i the calculation can be refined along the lines presented by Plaut & Pesch (1999). The stability of weakly nonlinear roll and hexagon patterns is determined by a linear stability analysis of the various solutions of Eq.…”

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confidence: 99%

Re-entrant hexagons in non-Boussinesq convection

2006

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While non-Boussinesq hexagonal convection patterns are well known to be stable close to threshold (i.e. for Rayleigh numbers R ≈ R c ), it has often been assumed that they are always unstable to rolls already for slightly higher Rayleigh numbers. Using the incompressible Navier-Stokes equations for parameters corresponding to water as a working fluid, we perform full numerical stability analyses of hexagons in the strongly nonlinear regime (ǫ ≡ R − R c /R c = O(1)). We find 'reentrant' behavior of the hexagons, i.e. as ǫ is increased they can lose and regain stability. This can occur for values of ǫ as low as ǫ = 0.2. We identify two factors contributing to the reentrance: i) the hexagons can make contact with a hexagon attractor that has been identified recently in the nonlinear regime even in Boussinesq convection (Assenheimer & Steinberg (1996);Clever & Busse (1996)) and ii) the non-Boussinesq effects increase with ǫ. Using direct simulations for circular containers we show that the reentrant hexagons can prevail even for side-wall conditions that favor convection in the form of the competing stable rolls. For sufficiently strong non-Boussinesq effects hexagons become stable even over the whole ǫ-range considered, 0 ≤ ǫ ≤ 1.5.

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confidence: 99%

Re-entrant hexagons in non-Boussinesq convection

2006

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“…Figures 4(a)and4(b) show the quantitative comparison of the dependence of the experimental data obtained at 80°C ͑T ‫ء‬ = 0.86͒ on frequency of the threshold voltage U c and that of the critical wave number ͉q c ͉ = ͱ q x 2 + q y 2 with the results of the linear stability analysis of the standard nematohydrodynamic description evaluated by a numerical Galerkin procedure[25]. The quantities used in the figures are =2f and the charge relaxation time 0 = ⑀ 0 ͑⑀ Ќ / Ќ ͒.…”

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confidence: 99%

Electroconvection with and without the Carr-Helfrich effect in a series of nematic liquid crystals

et al. 2004

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Experimental electroconvection (EC) investigations on four homologs with negative dielectric anisotropy epsilona and conductivity anisotropies sigmaa of various signs (the relative sigma; a=sigmaa/sigma(perpendicular) ranges from -0.6 to +0.3 ) are reported. The homolog with positive conductivity anisotropy follows the predictions of the standard theoretical model, while the homolog with negative sigmaa shows a phenomenon, i.e., nonstandard electroconvection, not described by the Carr-Helfrich mechanism but manifesting in forms of stripes mainly parallel to the initial director, thus having a morphological similarity to the rolls of the standard EC. The remaining two homologs change the sign of their conductivity anisotropy with temperature that leads to a twofold character by crossing over from standard to nonstandard electroconvection. The patterns of both the standard and nonstandard EC have been characterized and compared.

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“…With increasing applied ac voltage, the following sequence of transitions takes place: zigzag instability accompanied by the formation of oblique rolls transition to "abnormal" rolls "varicose" instability. This scenario of transitions was predicted using extended nonlinear analysis of the standard model of NLC electrohydrodynamics, which takes into account activation of the homogeneous twist mode [18,19]. In contrast to a number of earlier studies [18,22,31], we observed for the first time the complete sequence of secondary instabilities.…”

Section: Resultsmentioning

confidence: 47%

“…It has been established that an increase in the applied ac voltage to a value above the electroconvec tion threshold in a planar layer of an NLC leads to excitation of the twist mode and is accompanied by the formation of so called abnormal rolls [18,20,21]. In addition, the interaction of the twist mode with con vective modes of rolls in an ac electric field may lead to the evolution of local oscillations between two degen erate states of oblique rolls (so called zigzag rolls) [19]. The dynamics of such oscillations represents typ ical patterns of spatiotemporal chaos [22].…”

Section: Introductionmentioning

confidence: 99%

“…A characteristic feature of elec troconvection in NLCs above the threshold for the formation of convective rolls is a large variety of sec ondary instabilities and scenarios of the evolution of nonequilibrium structures due to various nonlinear interactions of hydrodynamic and orientational modes. One of the most important mechanisms deter mining the evolution of secondary instabilities in the supercritical region is the excitation of a homogeneous (in the plane of the layer) twist mode of the director [18,19]. It has been established that an increase in the applied ac voltage to a value above the electroconvec tion threshold in a planar layer of an NLC leads to excitation of the twist mode and is accompanied by the formation of so called abnormal rolls [18,20,21].…”

Section: Introductionmentioning

confidence: 99%

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On the role of flexoeffect in synchronization of electroconvective roll oscillations in nematics

Batyrshin

Krekhov

Scaldin

et al. 2012

J. Exp. Theor. Phys.

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We describe the dynamics of zigzag oscillations in a system of convective rolls in a nematic liquid crystal above the electroconvection threshold under the action of an ac voltage with a biased position of the mean value. It is found that an increase in the contribution from the constant component leads to a substantial increase in the spatiotemporal ordering of zigzag rolls and their synchronization with the homogeneous twist mode. The results confirm the flexoelectric mechanism of locking.

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Extended weakly nonlinear theory of planar nematic convection

Cited by 48 publications

References 41 publications

Re-entrant hexagons in non-Boussinesq convection

Re-entrant hexagons in non-Boussinesq convection

Electroconvection with and without the Carr-Helfrich effect in a series of nematic liquid crystals

On the role of flexoeffect in synchronization of electroconvective roll oscillations in nematics

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