Study of the meta-subject competencies cluster of teachers working with gifted children

The relevance of the studied problem is based on the insufficient information on the professional development of teachers working with gifted children and youth. It also comes from the low level of their meta-subject competencies formedness, which reduces the efficiency of their work.The purpose of this article is to substantiate and describe the cluster of meta-subject competencies of teachers working with gifted children, the research method for this cluster and the revealed deficiencies in its formation.The key approaches to studying this problem are competency-based and meta-subject. The main research method is a specially developed computer competence-oriented test containing a system of tasks aimed at identifying and assessing the range of working knowledge (experience, actions) and skills to apply competence in practice The study was conducted in a group of additional education teachers with a university degree who worked with gifted children (average age - 35 years). The main results of the research are: The substantiation of the cluster of meta-subject competencies of teachers working with gifted children and youth; comparative analysis of the formedness levels for different groups of meta-subject competencies; competence-oriented test; description of main deficiencies of the meta0subject competencies formedness; measures on eliminating these deficiencies.The paper may be used in conducting the research on revealing the deficiencies in the formation of meta-subject competencies of teachers working with gifted children, as well as and the development of these competencies in the teaching process or improving the teacher’s qualification in universities and institutions of additional professional education.Keywords: gifted children, teachers working with gifted children, teacher’s professional competencies, teacher's meta-subject competencies, cluster of professional competencies, teacher’s professional competencies assessment tools, competence-oriented test, case-study, test assignment, formedness level of meta-subject competencies, deficiencies in the formation of competencies, development of meta-subject competencie

Nonlinear electro-hydrodynamics of liquid crystals

We present nonlinear dynamic equations for nematic and smectic $A$ liquid crystals in the presence of an alternating electric field and explain their derivation in detail. The local electric field acting in any liquid-crystalline system is expressed as a sum of external electric field and the fields originating from feedback of liquid crystal order parameter, and a field, created by charged impurities. The system tends to decrease the total electric field, because it lowers the energy density. This basically nonlinear problem is not a pure academic interest. In the realm of liquid crystals and their applications, utilized nowadays modern experimental techniques have progressed to the point where even small deviations from the linear behavior can be observed and measured with a high accuracy. Hydrodynamics is the macroscopic description of condensed matter systems in the low frequency, long wavelength limit. Nonlinear hydrodynamic equations are well established to describe simple fluids. Similar approaches (with degrees of freedom related to the broken orientational or translational symmetry included) have been used also for liquid crystals. However to study behavior of strongly perturbed well above the thresholds of various electro-hydrodynamic instabilities of liquid crystals the nonlinear equations should include soft electromagnetic degrees of freedom as well. The self-consistent derivation of the complete set of the nonlinear electro-hydrodynamic equations for liquid crystals became an actual task. The aim of our work is to present these equations, which is a mandatory step to handle any nonlinear phenomenon in liquid crystals.Comment: 12 pages, no figure

Circulating Marangoni flows within droplets in smectic films

We present theoretical study and numerical simulation of Marangoni convection within ellipsoidal isotropic droplets embedded in free standing smectic films (FSSF). 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 still 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 were derived analytically. The temperature distribution in the ellipsoidal drop and the surrounding air was determined in the frames of the perturbation theory. As a result the analytical solutions for the stationary thermocapillary convection were derived 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 the drops were performed. Both the 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 persists. Thus, the thermocapillary convection within the ellipsoidal droplets in overheated FSSF is possible for the arbitrarily small Marangoni numbers

Marangoni instability in oblate droplets suspended on a circular frame

We study theoretically internal flows in a small oblate droplet suspended on the circular frame. Marangoni convection arises due to a vertical temperature gradient across the drop and is driven by the surface tension variations at the free drop interface. Using the analytical basis for the solutions of Stokes equation in coordinates of oblate spheroid we have derived the linearly independent stationary solutions for Marangoni convection in terms of Stokes stream functions. The numerical simulations of the thermocapillary motion in the drops are used to study the onset of the stationary regime. Both analytical and numerical calculations predict the axially-symmetric circulatory convection motion in the drop, the dynamics of which is determined by the magnitude of the temperature gradient across the drop. The analytical solutions for the critical temperature distribution and velocity fields are obtained for the large temperature gradients across the oblate drop. These solutions reveal the lateral separation of the critical and stationary motions within the drops. The critical vortices are localized near the central part of a drop, while the intensive stationary flow is located closer to its butt end. A crossover to the limit of the plane film is studied within the formalism of the stream functions by reducing the droplet ellipticity ratio to zero value. The initial stationary regime for the strongly oblate drops becomes unstable relative to the many-vortex perturbations in analogy with the plane fluid films with free boundaries

Increasing potato yield using foliar fertilization to boost growth

To date, the use of fertilizers has become firmly embedded in advanced crop cultivation technologies, as the main component of obtaining high and sustainable yields. The nutritional regime of plants cannot be optimized only with the help of macronutrients. They also need trace elements that can increase the resistance of plants to adverse growing conditions, diseases and pests. However, the high cost of such fertilizers makes it necessary to develop new more effective and less expensive drugs. Therefore, in modern potato cultivation technologies, much attention is paid to non-root top dressing. As a result of three-fold leaf treatments with the developed fertilizer, the yield increase of potato variety Gulliver was 0.4…5.2 t/ha, variety Vimpel 2.0…5.1 t/ha, variety Matushka 0.1…4.1 t/ha