Thermal gravity-driven convection of near-critical helium in enclosures

The results of numerical simulation of Rayleigh-Benard convection in ³He near the thermodynamic critical point are presented. The mathematical model including the full Navier-Stokes equations with two-scale splitting of the pressure and the van der Waals equation of state is applied. The known experimental data on ³He are used in simulations. On the basis of the calibration laws the "real" Rayleigh and Prandtl numbers are estimated. It is shown that one should agree these "real" criteria of similarity in the model and physical media to approach results of simulations to experiments. The Rayleigh number characterising the convection onset is defined from obtained numerical data. This number is shown to be in a good agreement with known experimental and theoretical values

Didactic potential of using mobile technologies in the development of mathematical thinking

© 2020 by the authors. The relevance of the research is due to additional opportunities to improve the quality of teaching mathematics in a digital school, support professional orientation and self-determination of young people through the inclusion of mobile services and platforms in mathematical activities. The research problem is determined by the following contradictions: 1) between the capabilities of modern digital technologies in terms of improving the quality of mathematical training, the formation of universal skills required by the economy of the future, and the model implemented by educational institutions; 2) between the need to provide resources for solving problems of a socio-economic nature in the conditions of the fourth industrial revolution and the insufficient level of mathematical literacy of graduates. The purpose of this research is to study the didactic potential of mobile technologies to support mathematical education in a digital school while preparing specialists of the future. Moreover, the research offers a methodological approach to organize project activities of developing applications in terms of increasing the effectiveness of teaching mathematics and vocational guidance. The article clarifies the concepts "mathematical thinking", "mathematical literacy" for a digital school and describes the didactic principles of incorporating mobile resources into the educational space which increase the efficiency of training engineers of the future, support vocational guidance and self-determination. The author offers methodological methods and recommendations for organizing creative interdisciplinary project activities in order to develop mobile applications that contribute to the formation of qualities and skills forming the basis of mathematical thinking. The materials of the article can be used: firstly, to ensure the personalization of mathematical training in the course of creative, interdisciplinary, cognitive research activities of students while developing mobile applications, social integration and vocational guidance; secondly, to change the concept of mathematical education at school; thirdly, to improve the implemented model of education based on the traditional trajectory "preschool education-school-university-additional education" in the context of the new requirements of business, society, and the state for the training of highly qualified professionals in the professions of the future