Mathematical modeling of thermal stabilization of vertical wells on high performance computing systems

Temperature stabilization of oil and gas wells is used to ensure stability and prevent deformation of a subgrade estuary zone. In this work, we consider the numerical simulation of thermal stabilization using vertical seasonal freezing columns. A mathematical model of such problems is described by a time-dependent temperature equation with phase transitions from water to ice. The resulting equation is a standard nonlinear parabolic equation. Numerical implementation is based on the finite element method using the package Fenics. After standard purely implicit approximation in time and simple linearization, we obtain a system of linear algebraic equations. Because the size of freezing columns are substantially less than the size of the modeled area, we obtain mesh refinement near columns. Due to this, we get a large system of equations which are solved using high performance computing systems.Comment: 9 pages, 5 figure

Perception of Dynamic Social and Non-social Stimuli in Preterm and Full-term Children: Neurocognitive Correlates in Early Childhood

Preterm birth is the leading cause of newborn deaths in almost all countries around the world. Whilst survivors encounter severe motor, cognitive and behavioral impairments during infancy or later in their lives, the studies of the recent years have demonstrated that the social development serving a basis for learning and cognition of the environment in human infants can be severely affected even in normally developing preterm born children (gestational age < 37 weeks). The current article presents a discussion on the behavioral as well as the neuroimaging aspects of the social maturation in preterm and full-term children, depicting complexity of theimpairments and focusing on the involved brain structures. Further, authors perform the design of the longitudinal study of social and non-social perception in early childhood, implemented on the base of the Laboratory for Brain and Neurocognitive Development (Ural Federal University). Keywords: prematurity, social development, early childhood, neurocognitive correlate

An anomalous subauroral red arc on 4 August, 1972: comparison of ISIS-2 satellite data with numerical calculations

International audienceThis study compares the Isis II satellite measurements of the electron density and temperature, the integral airglow intensity and volume emission rate at 630 nm in the SAR arc region, observed at dusk on 4 August, 1972, in the Southern Hemisphere, during the main phase of the geomagnetic storm. The model results were obtained using the time dependent one-dimensional mathematical model of the Earth's ionosphere and plasmasphere (the IZMIRAN model). The major enhancement to the IZMIRAN model developed in this study to explain the two component 630 nm emission observed is the analytical yield spectrum approach to calculate the fluxes of precipitating electrons and the additional production rates of N+2, O+2, O+(4S), O+(2D), O?(2P), and O+(2P) ions, and O(1D) in the SAR arc regions in the Northern and Southern Hemispheres. In order to bring the measured and modelled electron temperatures into agreement, the additional heating electron rate of 1.05 eV cm?3 s?1 was added in the energy balance equation of electrons at altitudes above 5000 km during the main phase of the geomagnetic storm. This additional heating electron rate determines the thermally excited 630 nm emission observed. The IZMIRAN model calculates a 630 nm integral intensity above 350 km of 4.1 kR and a total 630 nm integral intensity of 8.1 kR, values which are slightly lower compared to the observed 4.7 kR and 10.6 kR. We conclude that the 630 nm emission observed can be explained considering both the soft energy electron excited component and the thermally excited component. It is found that the inclusion of N2(v > 0) and O2(v > 0) in the calculations of the O+(4S) loss rate improves the agreement between the calculated Ne and the data on 4 August, 1972. The N2(v > 0) and O2(v > 0) effects are enough to explain the electron density depression in the SAR arc F-region and above F2 peak altitude. Our calculations show that the increase in the O++N2 rate factor due to the vibrationally excited nitrogen produces the 5?19% reductions in the calculated quiet daytime peak density and the 16?24% decrease in NmF2 in the SAR arc region. The increase in the O++N2 loss rate due to vibrationally excited O2 produces the 7?26% decrease in the calculated quiet daytime peak density and the 12?26% decrease in NmF2 in the SAR arc region. We evaluated the role of the electron cooling rates by low-lying electronic excitation of O2(a1?g) and O2(b1?g+), and rotational excitation of O2, and found that the effect of these cooling rates on Te can be considered negligible during the quiet and geomagnetic storm period 3-4 August, 1972. The energy exchange between electron and ion gases, the cooling rate in collisions of O(3P) with thermal electrons with excitation of O(1D), and the electron cooling rates by vibrational excitation of O2 and N2 are the largest cooling rates above 200 km in the SAR arc region on 4 August, 1972. The enhanced IZMIRAN model calculates also number densities of N2(B3∏g+),N2(C3∏u), and N2(A3?u+) at several vibrational levels, O(1S), and the volume emission rate and integral intensity at 557.7 nm in the region between 120 and 1000 km. We found from the model that the integral intensity at 557.7 nm is much less than the integral intensity at 630 nm