Lagrangian formalism and Noether-type theorems for second-order delay ODEs

The Lagrangian formalism for variational problem for second-order delay ordinary differential equations (DODEs) is developed. The Noether-type operator identities and theorems for DODEs of second order are presented. Algebraic construction of integrals for DODEs based on symmetries are demonstrated by examples

Социальная поддержка современной модернизации в регионах Сибири

The article is devoted to the study of socio-economic, socio-demographic and socio-cultural characteristics of the economically active educated population of the regions of Siberian Federal District. The object of the study is residents of Siberia, who have high human capital and prospect of acting as a social support for contemporary modernization of their regions. Based on the analysis of official statistics and surveys of the population in the regions of Siberia, an assessment of the educational potential of internal migration and socio-cultural characteristics of potential agents of modernization in the population of these territories is made.Статья посвящена исследованию социально-экономических, социодемографических и социокультурных характеристик экономически активного образованного населения регионов Сибирского федерального округа. Объект исследования – резиденты Сибири, обладающие высоким человеческим капиталом и перспективой действия в качестве социальной поддержки современной модернизации их регионов. На основе анализа официальной статистики и изучения населения в регионах Сибири сделана оценка образовательного потенциала внутренней миграции и социокультурных характеристик потенциальных агентов модернизации среди населения этих территорий

One-dimensional MHD flows with cylindrical symmetry: Lie symmetries and conservation laws

A recent paper considered symmetries and conservation laws of the plane one-dimensional flows for magnetohydrodynamics in the mass Lagrangian coordinates. This paper analyses the one-dimensional magnetohydrodynamics flows with cylindrical symmetry in the mass Lagrangian coordinates. The medium is assumed inviscid and thermally non-conducting. It is modeled by a polytropic gas. Symmetries and conservation laws are found. The cases of finite and infinite electric conductivity need to be analyzed separately. For finite electric conductivity $\sigma (\rho,p)$ we perform Lie group classification, which identifies $\sigma (\rho,p)$ cases with additional symmetries. The conservation laws are found by direct computation. For cases with infinite electric conductivity variational formulations of the equations are considered. Lie group classifications are obtained with the entropy treated as an arbitrary element. A variational formulation allows to use the Noether theorem for computation of conservation laws. The conservation laws obtained for the variational equations are also presented in the original (physical) variables

Selection of numerical method for solving ordinary differential equation systems for a high-speed model of hydrocarbons steam cracking

Relevance. Caused by the need to increase production of light olefins. The use of advanced process control systems and Real–Time Optimization makes it possible to increase the efficiency of steam cracking plants, but requires a high-speed mathematical model of the process. Aim. To select a method for numerical solution of systems of ordinary differential equations, which provides the highest speed when calculating the reaction coil of a steam cracking furnace. Reducing the time spent on calculating each scenario will allow the proposed model to be used for real-time process optimization tasks. Object. Mathematical model of ethane steam cracking, numerical methods for ordinary differential equations systems solution. Methods. System analysis, mathematical modeling. To solve the ordinary differential equations systems, various explicit numerical methods were used, differing in approach to integration step determination. Results. The authors have developed and tested a steady-state model of ethane steam cracking. The developed model was used to compare the calculation time required for solving ordinary differential equations systems using different numerical methods. It was demonstrated, that the use of an adaptive integration step reduces calculation time by more than 20 times (from more than 11 hours to 34 minutes) while maintaining the accuracy of calculations. This is due to different reaction rates through the length of the reaction coil – in areas of high temperatures and high concentrations of reagents, a reduction in the integration step is required to obtain the desired accuracy. And in low reaction rates areas an increase in the step and reduction in the total calculated iterations are acceptable

Investigation of working processes in a flowing channel of ramjet engine

The technique and results of experimental-theoretical study of gas-dynamics, heat transfer and the structure of gas-flow in the flowing channel of a ramjet engine in Mach number range M = (5-7) are presented. The temperature distribution along the flowing channel of a ramjet engine was experimentally obtained. The temperature along the wall of the flowing channel of the axisymmetric model was measured using the developed thermoprobe. Distributions of Mach number and temperature along the symmetry axis of the flowing channel of the model are obtained numerically. Comparison of the numerical and experimentally obtained values of the Mach number showed their qualitative agreement

Cayley-Type Conditions for Billiards within kk Quadrics in RdR^d

The notions of reflection from outside, reflection from inside and signature of a billiard trajectory within a quadric are introduced. Cayley-type conditions for periodical trajectories for the billiard in the region bounded by $k$ quadrics in $R^d$ and for the billiard ordered game within $k$ ellipsoids in $R^d$ are derived. In a limit, the condition describing periodic trajectories of billiard systems on a quadric in $R^d$ is obtained.Comment: 10 pages, some corractions are made in Section