Comment on "On the threshold characteristics of the flexoelectric domains arising in a homogeneous electric field: the case of anisotropic elasticity" by Y.G. Marinov and H.P. Hinov.

It is demonstrated that the key findings of the paper by Y.G. Marinov and H.P. Hinov, Eur. Phys. J. E 31, 179-189 (2010), are in direct conflict with the general physical background of flexoelectric domains. This is caused by a methodological error in the theoretical analysis of the paper.

Direct transition to electroconvection in a homeotropic nematic liquid crystal.

We present an experimental and theoretical investigation of a variant of electroconvection using an unusual nematic liquid crystal in an isotropic configuration (homeotropic alignment). The significance of the system is a direct transition to the convecting state due to the negative conductivity anisotropy and positive dielectric anisotropy. We observe at onset rolls or squares depending on the frequency and amplitude of the applied ac voltage with a strong signature of the zigzag instability. Good agreement with calculations based on the underlying hydrodynamic theory is found. We also construct an extended Swift-Hohenberg model which allows us to capture complex patterns like squares with a quasiperiodic modulation.

Isotropic convection scenarios in an anisotropic fluid.

We study a new variant of electroconvection using a homeotropically aligned nematic liquid crystal. The novelty of this system is a direct transition to roll- or square-type patterns controlled by the frequency of the applied voltage with a rich crossover scenario and strong influence of the zigzag instability even at onset. From the weakly nonlinear theory and simulations of an adapted Swift-Hohenberg model one can understand essential features of the phase diagram. In particular we find a quasiperiodic pattern with square symmetry.

Electroconvection in nematic liquid crystals with positive dielectric and negative conductivity anisotropy.

Electroconvection in an unusual nematic compound with strongly positive dielectric anisotropy and negative anisotropy of the conductivity is investigated. For homeotropic alignment, where one has a direct transition to rolls or squares depending on the frequency of the applied voltage, we present a quantitative theory. From the comparison we infer values for some viscosities, which are rather unusual, but not unreasonable in view of the vicinity of the nematic-smectic transition. For planar alignment, electroconvection sets in above a splay Freedericksz transition with "parallel rolls," which is also captured by the theory.

Periodic forcing in viscous fingering of a nematic liquid crystal.

Viscous fingering of an air-nematic interface in a radial Hele-Shaw cell is studied when periodically switching on and off an electric field, which reorients the nematic and thus changes its viscosity, as well as the surface tension and its anisotropy (mainly enforced by a single groove in the cell). Undulations at the sides of the fingers are observed that correlate with the switching frequency and with tip oscillations that give maximal velocity to smallest curvatures. These lateral undulations appear to be decoupled from spontaneous (noise induced) side branching. It is concluded that the lateral undulations are generated by successive relaxations between two limiting finger widths. The change between these two selected pattern scales is mainly due to the change in the anisotropy. This scenario is confirmed by numerical simulations in the channel geometry, using a phase-field model for anisotropic viscous fingering.

Director precession and nonlinear waves in nematic liquid crystals under elliptic shear

Elliptic shear applied to a homeotropically oriented nematic above the electric bend Freedericks transition (FT) generates slow precession of the director. The character of the accompanying nonlinear waves changes from diffusive phase waves to dispersive ones exhibiting spirals and spatiotemporal chaos as the FT is approached from above. An exact solution of the flow alignment equations captures the observed precession and predicts its reversal for non-flow-aligning materials. The FT transforms into a Hopf bifurcation opening the way to understand the wave phenomena.

Abnormal rolls and regular arrays of disclinations in homeotropic electroconvection

We present the first quantitative verification of an amplitude description for systems with (nearly) spontaneously broken isotropy, in particular for the recently discovered abnormal-roll states. We also obtain a conclusive picture of the three-dimensional director configuration in a spatial period doubling phenomenon involving disclination loops. The first observation of two Lifshitz frequencies in electroconvection is reported.

Regular dendritic patterns induced by nonlocal time-periodic forcing

The dynamic response of dendritic solidification to spatially homogeneous time-periodic forcing has been studied. Phase-field calculations performed in two dimensions (2D) and experiments on thin (quasi-2D) liquid-crystal layers show that the frequency of dendritic side branching can be tuned by oscillatory pressure or heating. The sensitivity of this phenomenon to the relevant parameters, the frequency and amplitude of the modulation, the initial undercooling and the anisotropies of the interfacial free energy, and molecule attachment kinetics, has been explored. It has been demonstrated that in addition the side-branching mode synchronous with external forcing as emerging from the linear Wentzel-Kramers-Brillouin analysis, modes that oscillate with higher harmonic frequencies are also present with perceptible amplitudes.