Circulating Marangoni flows within droplets in smectic films.

We present a theoretical study and numerical simulation of Marangoni convection within ellipsoidal isotropic droplets embedded in free-standing smectic films (FSSFs). The thermocapillary flows are analyzed for both isotropic droplets spontaneously formed in FSSF overheated above the bulk smectic-isotropic transition and oil lenses deposited on the surface of the smectic film. The realistic model for which the upper drop interface is free from the smectic layers, while at the lower drop surface the smectic layering persists is considered in detail. For isotropic droplets and oil lenses this leads effectively to a sticking of fluid motion at the border with a smectic shell. The above mentioned asymmetric configuration is realized experimentally when the temperature of the upper side of the film is higher than at the lower one. The full set of stationary solutions for Stokes stream functions describing the Marangoni convection flows within the ellipsoidal drops are derived analytically. The temperature distribution in the ellipsoidal drop and the surrounding air is determined in the frame of the perturbation theory. As a result, the analytical solutions for the stationary thermocapillary convection are obtained for different droplet ellipticity ratios and the heat conductivity of the liquid crystal and air. In parallel, the numerical hydrodynamic calculations of the thermocapillary motion in drops are made. Both analytical and numerical simulations predict the axially symmetric circulatory convection motion determined by the Marangoni effect at the droplet-free surface. Due to a curvature of the drop interface a temperature gradient along its free surface always exists. Thus, the thermocapillary convection within the ellipsoidal droplets in overheated FSSF is possible for the arbitrarily small Marangoni numbers. Possible experimental observations enabling the checking of our predictions are proposed.

Coexistence of spiral magnetic state and weak ferromagnetism in a multiferroic, cross-controlled by external magnetic and electric fields.

The influence of external magnetic and electric fields on the properties of a multiferroic with a helical magnetic structure is described. Thermodynamics of the phase transition from the antiferromagnetic ferroelectric to the new magnetic state is described for a multiferroic with a perovskite-type structure. In this magnetic state a spiral spin structure and weak ferromagnetism can exist simultaneously. Such a state is a result of the first-order phase transition at a certain temperature below T(N) when, due to the Dzyaloshinskii-Moriya effect, a helical magnetic structure occurs. In this state the vectors of electrical polarization and the helicoid of magnetic moments in perovskites are mutually perpendicular and lie in the basic (ab) plane perpendicular to the main c axis. In this case an additional electrical polarization proportional to the square of magnetization appears in the (ab) plane which reduces the common polarization of the ferroelectric. It is shown that a weak ferromagnetic moment m occurs along the c axis in an applied magnetic field in addition to a modulated magnetic structure appearing in the (ab) plane. The dependence of these phenomena on the applied electric field is considered. It is shown that a sign-alternating electric field causes a linear-in-the-field variation of the magnetic moment opposite in sign to the electric field variation (i.e., the greater is the electric field, the smaller is the magnetic moment m). The observed hysteresis phenomena determining the temperature ranges of overheating and overcooling of each phase under applied magnetic and electrical fields are explained.

"Thresholdless" hysteresis-free switching as an apparent phenomenon of surface stabilized ferroelectric liquid crystal cells.

The thresholdless, hysteresis-free V-shape electro-optical switching in surface-stabilized ferroelectric liquid crystals, observed usually with a triangular voltage form, has been shown to be rather an apparent and not a real effect. Strictly speaking, it is observed only at one characteristic frequency f(i) and is accompanied by an inversion of the electro-optical hysteresis direction from the normal to the abnormal one. The switching of the director in a liquid crystal layer at f(i), in reality, has a threshold and a normal hysteresis. Even the optical transmittance shows a hysteresis at f(i) when it is plotted as a function of the voltage on the liquid crystal layer and not as a function of the total voltage on the liquid crystal cell which always includes the inner insulating layers. Due to these layers, a voltage divider is formed which includes the capacitance of the insulating layers and the dynamic impedance (capacitance and resistance) of the ferroelectric liquid crystal layer. The new explanation has been confirmed by experiments with different ferroelectric liquid crystal cells combined with external resistors and capacitors and by measurements of a strong dependence of f(i) on the liquid crystal resistance which was varied over three orders of magnitude. A theoretical analysis of the problem has also been made using certain approximations for material parameters and the space dependence of the sine form of the electric field in the liquid crystal layer. The conclusions are qualitatively consistent with the experimental results. Finally, the dynamic problem has been solved numerically by taking into account of all the relevant parameters (in the absence of flow and irregularities in the cell plane) and the obtained results are in excellent correspondence with the experiment. This has been demonstrated for sets of material and cell parameters providing the best V-shape performance.