A boundary value problem for a singularly perturbed system of two second order ODEs with different degrees of the small parameter at the second derivatives is considered. The peculiarity of the problem is that one of the two equations of the degenerate system has three disjoint roots, two of which are double, and the third is simple (single). It is proved that for sufficiently small values of a small parameter, the problem has a solution with a fast transition from one double root of the degenerate equation to another double root in a neighborhood of some interior point of the segment. A complete asymptotic expansion of this solution is constructed and substantiated. It differs qualitatively from the well-known expansion in the case when all the roots of the degenerate equation are simple. In particular, the expansion is carried out not in integer but in fractional powers of the small parameter, the boundary layer variables have a different scale, and the transition layer turns out to be eight-zone.
Chemical physics, physical kinetics, and plasma physics
I. K. Nesterenko, K. N. Kornev, A. A. Logunov, V. M. Shibkov
Memoirs of the Faculty of Physics 2021. N 2.
The paper considers the prospects of using a quasi-stationary pulsating discharge to control the process of supersonic combustion of hydrocarbon fuels. The discharge characteristics have been obtained experimentally under conditions of subsonic and supersonic air flow. Supersonic steady combustion of propane in expanding aerodynamic channels of various configurations has been implemented. The results obtained confirm the efficiency of using low-temperature plasma in supersonic plasma aerodynamics.
This work is devoted to the study of rheological, deformation and filtration properties of low-permeability rocks of Achimov deposits of the Urengoy gas condensate field using the directional unloading method. As part of the study, physical modeling of the real stresses in the vicinity of the well was carried out when implementing the directional unloading method. Experiments were conducted by using the unique facility, Triaxial Independent Load Test System of the Institute for Problems in Mechanics of the Russian Academy of Sciences. Modeling was carried out for two types of bottomhole design: an open hole and a perforation tip in a cased hole. The dependence of the filtration properties of rocks on the type of stress-strain state is shown; conclusions are drawn about the nature of creep. The values of pressure drawdown, which leads to an increase in the permeability, are determined. The results obtained indicate that the directional unloading method can be successfully applied to wells drilled in the Achimov deposits.
This article focuses on assessing the impact of wildfires and adverse weather conditions on air pollution in Moscow. The article examines in detail the case of aerosol pollution of the smoky atmosphere of the Moscow region in July 2016. The main indicators of wildfire investigated in this work are particulate matter PM10 and PM2.5. Calculations of the main statistical characteristics of PM10 and PM2.5 concentrations are presented: the average value, median and mode and pair correlation coefficients separately for PM10 and PM2.5 between different stations and between PM10 and PM2.5 at one station for the entire period of 2016 and 2018 as well as for the smoke period in July 2016 and the period with bad weather conditions in September 2018. The diurnal course under smoke is analyzed in comparison with the typical course in the warm period and in the bad weather conditions. Based on the intra-day dynamics of PM10 and PM2.5 concentrations in July 2016 and September 2018 the dependence of pollution on the thermal stratification of the atmospheric boundary layer is considered. The dependence of aerosol concentrations on the wind speed in the atmospheric boundary layer is analyzed.