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The vertical profiles of the O 3 , CO, CO 2 and CH 4 concentrations measured onboard the Optik Tu-134 aircraft laboratory and retrieved from data obtained with an IASI Fourier transform spectrometer operating aboard a MetOp satellite (European Space Agency) have been compared. This comparison shows that absolute differences between aircraft satellite ozone concentrations may vary from 55 to 15 ppb at the land surface and within the lower boundary layer and from 30 to −15 ppb at a height of 7000 m. Their relative differences range within 60 to 30% at a height of 500 m and 30 to −35% at a height of 7000 m. Absolute differences between aircraft and satellite carbon-monoxide concentrations may vary from 80 to 2300 ppb, while their relative differences range within −140 to 98%. For methane, the mean difference is maximal within the atmospheric boundary layer (90 ppb). According to the data on all profiles, the maximum and minimum differences reach 220 and 8 ppb, respectively, within the atmospheric boundary layer. Minimum differences range from zero at the land surface to −100 ppb in the upper troposphere. For carbon dioxide, the mean difference between the results of aircraft and satellite measurements ranges from −2 to −9 ppm. In the free troposphere, at a height of more than 3000 m, this difference is almost constant and amounts to −6 ppm. Over all flights, the maximum and minimum differences between aircraft and satellite CO 2 concentrations range from 14 to −4 ppm and from −7 to −16 ppm, respectively, within the atmospheric boundary layer. In this case, the maximum and minimum relative deviations over all flights amount to 3.4 and −4.2%, respectively, within the atmospheric boundary layer. These differences are significantly larger than those found earlier for the background conditions. It is necessary to improve the vertical gas distribution models used in the algorithms of satellite-data processing.

We consider the results of remote spectrophotometric and lidar measurements of the total ozone and nitrogen dioxide contents and temperature, obtained at the Siberian Lidar Station (SLS) of V.E. Zuev Institute of Atmospheric Optics, Siberian Branch, Russian Academy of Sciences (Tomsk: 56.5°N; 85.0°E) in comparison with the results of analogous satellite measurements. The ground-based measurements of the total ozone (TO) content are performed with the help of М-124 ozonometer; and the measurements of the nitrogen dioxide (NO2) content are carried out with automatic spectrophotometer. The groundbased lidar measurements of temperature are conducted on the basis of SLS measurement complex. These measurements are compared with data of balloon-sonde and satellite measurements. The satellite measurements are performed by the TOMS and IASI instrumentation.

Modeling systems with piecewise constant parameters imposes special requirements on the computational algorithms used. In places where the parameters are discontinuous, the model variables may experience discontinuities or smoothness disturbances. In this case, the conditions for matching the values of the variables on both sides of the discontinuity boundary, reflecting the physical conditions at this boundary, must be satisfied. The paper proposes computational algorithms for modeling these systems, based on the formulation of the initial initial-boundary value problem in the form of a system of partial differential equations for generalized functions. In this case, the initial conditions, conditions on the external and internal boundaries are included in these equations in a weak form. The latter circumstance makes it possible to avoid the need to subordinate the basis functions, according to which the desired solution is expanded, to the conditions on the outer and inner boundaries, which is an important circumstance, especially for problems with many spatial variables. The paper presents a solution to the generalized Riemann problem with conditions on the outer or inner boundary for a differential equation with second-order derivatives with respect to spatial variables. The solution to the Riemann problem is based on the formulation of the problem in the form of a partial differential equation for generalized functions and the construction of a fundamental solution to the problem operator. When constructing a computational algorithm, the solution of the generalized Riemann problem is used on the inner and outer boundaries. The proposed technique allows, by using high-degree polynomials as basis functions, to build computational algorithms of a high order of approximation.

The work is devoted to the construction of effective computational algorithms for modeling vibrations of elastically supported load-bearing systems. An approach is developed based on the representation of a mathematical model in the form of partial differential equations for generalized functions. With this approach, the presence of elements with a very high stiffness in the design made it necessary to carry out the calculation with a very small time step. To build a computational algorithm, a fundamental solution to the problem operator is used, which allows one to obtain a solution at the next time step for each point of the spatial grid independently. The need to carry out the calculation with a very small time step arises only in nodes that coincide with the location of structural elements with very high stiffness. The proposed approach allows simulating impact forces and instantaneous change of boundary conditions. The possibility of using the model with an absolutely rigid restraining support as a limit transition from a model of elastic bond of high rigidity was researched on.

An approximation of matrix Green's function for a hyperbolic system of linear differential equations of the first order has been created. An algorithm for an approximate solution of the generalized Riemann problem of discontinuity decay in the presence of additional conditions at the boundaries has been proposed. A computational algorithm for the approximate solution of boundary value problems for hyperbolic systems of equations has been set up on the basis of these solutions. The algorithm is implemented for a system of equations describing the propagation of elastic waves in a block-fractured medium. The results of the numerical experiments aimed at studying the possible mechanisms of propagation of elastic waves to a considerable depth without scattering have been presented.

The method of modeling oscillations of an elastically supported strained bar with movement limiters at the ends under the action of a moving variable load is being improved and developed. Two models of limiting support are used. A computational algorithm was constructed. The model is formulated in terms of generalized functions, which makes it possible to effectively model pointwise in space and instantaneous in time forces. When solving partial differential equations, the boundary conditions are included in the original equations. To solve the differential equation, piecewise linear basis functions are used. They remain constant during the calculation. Numerical studies of the behavior of a dynamic system depending on the variation of a wide range of parameters using a computer program in Matlab have been performed. The developed method will allow analyzing the dynamic behavior of a number of structurally nonlinear technical systems.

We proposed mathematical models for the electrocardiogram and photoplethysmogram signals with functionality to preset the pattern of synchronization between the phases of the low-frequency oscillations, which are related to the sympathetic neuronal control of circulation. The simulated phase difference reproduced the statistical and spectral characteristics of the experimental data, including the alternating horizontal and sloped sections, corresponding to the intervals of synchronous and asynchronous behavior. Using the proposed model, we tested and tuned an algorithm for detection of the phase synchronization between the parts of the sympathetic control of circulation, improving both sensitivity and specificity of the algorithm.

We propose a mathematical model of the human cardiovascular and respiratory systems. The cardiovascular segment of the model simulates the main heart rate, oscillating blood pressure, peripheral vascular resistance, and nonlinear dynamics of the autonomic control of circulation, namely α- and β- sympathetic and parasympathetic control. The respiratory part includes central pattern generator, lungs, and a control loop sensitive to the concentration of CO 2 and O 2 in the arterial blood. Both parts of the model are linked in a physiological manner. The adequacy of the model is demonstrated by comparing the simulated time series to the experimental records of healthy subjects from the SIESTA database using spectral analysis, statistical analysis, and nonlinear measures of directional coupling. The proposed model can become a useful tool for investigation of the cardiovascular dynamics during sleep.

Metals and alloys in amorphous state are promising for the use as structural and functional materials due to their superior properties related to the absence of such defects as grain boundaries and dislocations. Obtaining the amorphous state requires quenching from liquid state with a high cooling rate. In conventional technologies, this is the reason for a considerable size limitation hindering application of amorphous alloys. Additive manufacturing (AM) is free of the size limitation. The so-called bulk metallic glass (BMG) alloys have extremely low critical cooling rates and can be used in AM. Recent studies on AM from Zr-based BMGs by selective laser melting (SLM) has proved the possibility of attaining the amorphous state and revealed partial crystallization to be the principal drawback of this process. The present work aims to analyze the conditions for partial crystallization and attempts to control it by optimizing the process parameters. A comprehensive parametric analysis is accomplished in single-track SLM experiments with Zr-based BMG alloy Vit 106. The observed microstructures are related to the temperature fields and thermal cycles estimated by an analytic heat-transfer model in the laser-impact zone. In the cross section of a laser track, a central bright domain is identified as the remelted zone. An annular darker crystallization zone encircles the remelted zone. The model fits the experimentally obtained dependencies of the remelted zone size versus laser power and scanning speed and indicates that 43 ± 2% of the incident laser energy is transferred into the substrate thermal energy. The principal energy losses are reflection of the incident laser radiation and material evaporation. Primary crystalline inclusions existing in the substrate before laser processing dissolve at the laser melting. The mean cooling rate in the remelted zone is up to 4 orders of magnitude greater than the critical cooling rate. Therefore, homogeneous nucleation is not expected. Nevertheless, the theoretically estimated crystallization times are sufficient for a considerable crystal growth in the heat-affected zone where primary crystalline inclusions and nuclei are not completely dissolved.