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Many theoretical and experimental studies indicate that a propagation block represents an important factor in spiral wave initiation in excitable media. The analytical and numerical results we obtained for a generic two-component reaction-diffusion system demonstrate quantitative conditions for the propagation block in a one-dimensional and a two-dimensional medium due to a sharp spatial increase of the medium's excitability or the coupling strength above a certain critical value. Here, we prove that this critical value strongly depends on the medium parameters and the geometry of the inhomogeneity. For an exemplary two-dimensional medium, we show how the propagation block can be used to initiate spiral waves by a specific choice of the size and shape of the medium's inhomogeneity.

The spatiotemporal dynamics of oscillating electroconvective structures appearing in a nematic liquid crystal (NLC) under the combined action of applied alternating (ac) and direct (dc) electric voltages has been experimentally studied. It is established that an increase in the dc component of the applied voltage leads to synchronization of the hydrodynamic mode with the orientational twist mode of the NLC director. The synchronization parameter and the phase shift of the modes are determined as function of the applied dc voltage. The results confirm the flexoelectric mechanism of synchronization.

Electroconvection in twisted nematics has been studied experimentally and theoretically. The frequency dependence of the threshold voltage and rolls period for the different twist angles as well as the Lifshitz point versus the twist angle have been measured. The experimental results agree well with the predictions of linear stability analysis. Various types of secondary instabilities were found above the roll instability depending on the twist angle. The transition from 1D structure to the 2D domain pattern was investigated.

The temperature behaviour of the anchoring energy of nematic liquid crystal MBBA at the substrates with oblique SiO evaporation and director orientation at the interface have been studied by means of magnetic Freedericksz transition technique. The temperature dependence of the coefficients in the phenomenological model of surface anchoring energy has been determined.

We consider planarly oriented nematic liquid crystal subjected to plane, rectilinear, oscillatory Couette or Poiseuille flow in the case, when the director is initially perpendicular to the flow plane. Using the Galerkin method we found the critical amplitude of the flow at which the homogeneous instability develops. The analytical approximations for the frequency dependence of the critical amplitude for different types of flow are obtained. The results are compared with experimental data.

The optical response of the nematic liquid crystal confined between plates with strong homeotropic and weak planar anchoring (hybrid geometry) under the oscillatory shear has been investigated. Critical shear amplitude above that the director deviates from the planar orientation at the substrate with weak anchoring was found and the dependence of the tilt angle on the displacement amplitude was obtained. The anchoring strength and surface viscosity for the SiO-evaporated substrate was estimated.

~Received 19 March 1998! The response of a homeotropically aligned nematic liquid crystal layer to oscillatory rectilinear shear ~Couette flow ! was investigated for frequencies f between 0.01 and 200 Hz and layer thickness d between 10 and 130 mm. Below the onset of instability the cell was placed between crossed polars and light transmission was studied using a parallel light beam. The experimental results for the transmitted light intensity agree quantitatively with numerical solutions of the nematodynamic equations for different cell thicknesses, oscillation frequencies, and amplitudes. For frequencies between 25 and 150 Hz the critical oscillation amplitude for the onset of a spatial pattern, observed in polarized white light, could be reached. The pattern consisted of stationary rolls perpendicular to the direction of the oscillation. The experimentally obtained frequency dependence of the critical shear amplitude for the roll instability for different cell thicknesses is compared with an existing theory and the results of numerical calculations. @S1063-651X~98!09411-2# Nematic liquid crystals ~NLCs! exhibit interesting flow phenomena due to the coupling between the local molecular orientation ~director n ˆ! and the velocity field v. The flow properties of NLCs are characterized by Leslie viscosity coefficients a 1 ,...,a6 , two of which a 2(,0) and a 3 are important in describing the coupling between flow and director orientation @1‐4#. In the case of steady, plane, parallel shear flow, e.g., along the x axis with a velocity field v x(z )( v y 5 v z 50) and in the absence of other torques, the director will tend to align in the flow plane ( x-z plane! at a fixed angle u fl 56arctan(a3 /a2) 1/2 with the x axis if a 3,0 ~the 6

Pattern forming instabilities induced by ultralow frequency sinusoidal voltages were studied in a rodlike nematic liquid crystal by microscopic observations and simultaneous electric current measurements. Two pattern morphologies, electroconvection (EC) and flexodomains (FD), were distinguished, both appearing as time separated flashes within each half period of driving. A correlation was found between the time instants of the EC flashes and those of the nonlinear current response. The voltage dependence of the pattern contrast $C(U)$ for EC has a different character than that for the FD. The flattening of $C(U)$ at reducing the frequency was described in terms of an imperfect bifurcation model. Analyzing the threshold characteristics of FD, the temperature dependence of the difference $|{e}_{1}\ensuremath{-}{e}_{3}|$ of the flexoelectric coefficients was also determined by considering elastic anisotropy.

Optical methods are most convenient to analyze spatially periodic patterns with wavevector $\bm q$ in a thin layer of a nematic liquid crystal. In the standard experimental setup a beam of parallel light with a 'short' wavelength $\lambda \ll 2 \pi/q$ passes the nematic layer. Recording the transmitted light the patterns are either directly visualized by shadowgraphy or characterized more indirectly by the diffraction fringes due to the optical grating effects of the pattern. In this work we present a systematic short-wavelength analysis of these methods for the commonly used planar orientation of the optical axis of liquid crystal at the confining surfaces. Our approach covers general 3D experimental geometries with respect to the relative orientation of $\bm q$ and of the wavevector $\bm k$ of the incident light. In particular the importance of phase grating effects is emphasized, which are not accessible in a pure geometric optics approach. Finally, as a byproduct we present also an optical analysis of convection rolls in Rayleigh-B\'enard convection, where the refraction index of the fluid is isotropic in contrast to its uniaxial symmetry in nematic liquid crystals. Our analysis is in excellent agreement with an earlier physical optics approach by Trainoff and Cannell [Physics of Fluids {\bf 14}, 1340 (2002)], which is restricted to a 2D geometry and technically much more demanding., Comment: 22 pages

We calculate the threshold of electrohydrodynamic convection (EHC) for nematic liquid crystals with negative dielectric anisotropy, where one allows for different director orientations at the upper and lower confining plates (hybrid cells). Besides the planar versus homeotropic case we present for the first time an analysis of continuous tilt at one plate. The predistorted ground state strongly influences the EHC character and the roll orientation. One observes a generic nonstationary behaviour and in particular the interesting scenario of drifting oblique rolls.

We present some experiments on electrohydrodynamic convection (EHC) in nematic liquid crystals with a planar, but twisted configuration (MBBA). The threshold voltage is shown to depend only weakly on the twist angle. A theoretical analysis of the onset behaviour agrees well with the experiments. More sensitive is a secondary transition to modulation structures, which are not easily observed in untwisted geometries. A rough estimate of the secondary instability based on the behaviour of the most rapidly growing modulation mode seems to account well for the observations. Additional theoretical investigations for materials with positive dielectric anisotropy concerning the competition between the Freedericksz transition and EHC are included. We predict the existence of a crossover codimension-2 point, which could easily be tested by variation of the twist angle

Using a simple averaging method we show that under plane oscillatory shear a net torque acts on the director of a nematic liquid crystal leading to unexpected flow alignment. Under quite general conditions the usual flow-alignment orientations are unstable, and the ori- entation parallel to the shear (perpendicular to the velocity) becomes most stable within the shear plane. The effect drops out exactly under (unrealistic) linear shear unless the director has a nontrivial space dependence. An explicit application to plane Poiseuifle flow is presented. Pre- liminary experimental data are shown which demonstrate a transition under planar oscillatory shear from a homeotropically aligned nematic to a spatially homogeneously deformed state.

The experimental investigation of surface polarization by modulation spectroscopy of electro-reflection from the nematic liquid crystal-semiconductor interface and capacitance modulation spectroscopy of direct piezoeffect in nematics has been carried out. The models of surface polarization with induced polar order parameter have been suggested.

Novel behavior in electroconvection (EC) has been detected in nematic liquid crystals (NLCs) under the condition of comparable timescales of the director relaxation and the period of the driving ac voltage. The studied NLCs exhibit standard EC (s-EC) at the onset of the instability, except one compound in which nonstandard EC (ns-EC) has been detected. In the relevant frequency region, the threshold voltage for conductive s-EC bends down considerably, while for dielectric s-EC it bends up strongly with the decrease of the driving frequency. We show that inclusion of the flexoelectric effect into the theoretical description of conductive s-EC leads to quantitative agreement, while for dielectric s-EC a qualitative agreement is achieved. The frequency dependence of the threshold voltage for ns-EC strongly resembles that of the dielectric s-EC., Comment: 13 pages, 14 figures, submitted

The problem of disclinations streamlining by the flow of nematic liquid crystal (NLC) was investigated theoretically. Distributions of the flow velocity for defects with different topological indices were found numerically.

For many years it has been commonly accepted that electroconvection (EC) as primary instability in nematic liquid crystals for the "classical" planar geometry requires a positive anisotropy of the electric conductivity, sigma(a), and a slightly negative dielectric anisotropy, epsilon(a). This firm belief was supported by many experimental and theoretical studies. Recent experiments, which have surprisingly revealed EC patterns at negative conduction anisotropy as well, have motivated the theoretical studies in this paper. It will be demonstrated that extending the common hydrodynamic description of nematics by the usually neglected flexoelectric effect allows for a simple explanation of EC in the "nonstandard" case sigma(a)

We have determined the diffusion, thermal diffusion, and Soret coefficients of a poly(dimethyl siloxane)/poly(ethyl-methyl siloxane) (PDMS/PEMS) polymer blend as a function of composition and temperature within the homogeneous phase. The critical slowing down of the diffusion and the corresponding critical divergence of the Soret coefficient are described within the pseudospinodal concept both for critical and off-critical compositions. These data are used to model in detail the channel-like structures that form due to the Soret effect when a focused laser beam is scanned across a polymer film of $100\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}\mathrm{m}$ thickness. A moderate vertical asymmetry is attributed to solutal convection. Although heat rapidly diffuses away from the laser focus, the composition distribution in the early stage resembles the sharp profile of the laser beam. PDMS accumulates within the center of the structures, whereas a thin PEMS-rich layer is formed that isolates the central core from the windows. Experimentally, the structures are analyzed by means of phase contrast microscopy. Possible applications as rewritable optical waveguides or tunable phase plates are briefly discussed.

Motivated by Lehmann-like rotation phenomena in cholesteric drops we study the transverse drift of two types of cholesteric fingers, which form rotating spirals in thin layers of cholesteric liquid crystal in an ac or dc electric field. We show that electrohydrodynamic effects induced by Carr-Helfrich charge separation or flexoelectric charge generation can describe the drift of cholesteric fingers. We argue that the observed Lehmann-like phenomena can be understood on the same basis., 4 pages, 4 figures, submitted to PRL

The stability of the equilibrium configurations of a nematic liquid crystal confined between two coaxial cylinders is analysed when a radial electric field is applied and the flexoelectric effect is taken into account. The threshold for perturbations depending only on the radius r in the cylindrical coordinate system and strong boundary conditions is studied. A new type of orientational transition caused by pure flexoelectric effect is found., 8 pages, 3 figures. To appear in Mol. Cryst. Liq. Cryst. (2001)

It has been confirmed that the flexoelectric polarization model can provide an adequate interpretation of the temperature behavior of the electrical response of homeotropically oriented samples of n-methoxybenzylidene-n-butylaniline nematic liquid crystals at twice the excitation frequency. The temperature dependence of samples with different director orientations has been investigated experimentally.

We report experimental and theoretical results on the flexoelectric instability and crossover between flexoelectric domains and electroconvection in a hybrid aligned nematic MBBA under d.c. voltage. At threshold a spatially periodic flexoelectric deformation in the form of longitudinal domains (along the planar director) was observed. With increasing voltage the director deviation out of the initial plane becomes clearly detectable. Observations of tracers show that hydrodynamic flow develops inside the flexoelectric stripe pattern in the form of circular orbits perpendicular to the domain stripes. With further increasing d.c. voltage electroconvection sets in in the form of drifting oblique rolls inside the flexoelectric domains., Comment: 8 pages, 4 figures. To Appear in Mol. Cryst. Liq. Cryst. (2001)