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- Professor in Applied Mathematics, Fulbright Scholar (2014, University of Kentucky), International IT University (Kaza... moreProfessor in Applied Mathematics, Fulbright Scholar (2014, University of Kentucky), International IT University (Kazakhstan), more than 60 publications in the field of Mechanics of Deformable Solids, Mathematical Physics, Mathematical and Computer Modeling etcedit
We consider a homogeneous isotropic thermoelastic solid under axisymmetric conditions. We shall use following variables [6]: mass density ρ; thermoelastic constants γ, η, κ; Lame’s constants λ=νE/((1+ν)(1-2ν)) and μ=E/(2(1+ν)) ; E is... more
We consider a homogeneous isotropic thermoelastic solid under axisymmetric conditions. We shall use following variables [6]: mass density ρ; thermoelastic constants γ, η, κ; Lame’s constants λ=νE/((1+ν)(1-2ν)) and μ=E/(2(1+ν)) ; E is Young's modulus; and ν is Poisson's ratio; γ=(3λ+2μ)α_t is material constant [γ]=(N·К )/m^2 , where α_t is a coefficient of linear thermal expansion. Thermal diffusivity κ=λ_0 b_ε is a physical parameter characterizing the rate of temperature in a medium, []=m^2/sec; λ_0 is thermal conductivity and b_ε is the specific heat under constant strain. η=(γT_0)/λ_0 , []=К·sec/m^2 , where T_0 is the current absolute temperature of a medium in natural (initial) state measured in Kelvin degrees, [K]. All constants are positive: >0, >0, >0, >0, >0, >0.
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In operation, the solar sail is under influence of external forces, the most significant is the pressure of sunlight for motion. The influence of external forces causes vibrations of solar sail, which can affect flight of the spacecraft... more
In operation, the solar sail is under influence of external forces, the most significant is the pressure of sunlight for motion. The influence of external forces causes vibrations of solar sail, which can affect flight of the spacecraft and lead to damage of its structure. Here we consider three problems: (1) to obtain solar sail oscillation equation. This equation is derived for various forms of solar sail construction and various cases of loading; (2) to calculate thrust produced by deformed solar sail, since thrust will vary depending on the form of solar sail surface, the comparison with non-deformed solar sail will be made; (3) modeling of heliocentric motion of spacecraft with solar sail, taking into account deformation of the sail surface due to oscillations.
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The integration of the remote sending data and calculations of hydrodynamic models for estimation of mass transfer in dust storms are presented. It was shown, that the creation of a space-based monitoring of mathematical models and... more
The integration of the remote sending data and calculations of hydrodynamic models for estimation of mass transfer in dust storms are presented. It was shown, that the creation of a space-based monitoring of mathematical models and algorithms for research of the causes of dust storms in the area of Aral Sea.
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The heliocentric motion of the solar sail spacecraft (SSS) is described in classical Keplerian elements. The solar sail with an ideal reflection coefficient is considered. The spacecraft performs a non-coplanar motion with the sun gravity... more
The heliocentric motion of the solar sail spacecraft (SSS) is described in classical Keplerian elements. The solar sail with an ideal reflection coefficient is considered. The spacecraft performs a non-coplanar motion with the sun gravity and the light pressure. Disturbances of other celestial bodies gravity are not considered. To confirm the results correctness, we simulated the motion of solar sail spacecraft. The spacecraft's initial orbit coincides with the average Earth orbit relative to the Sun. Authors developed a program complex to simulate the planar heliocentric movement and obtained results for motion simulation of flights to Venus. The results were compared with the simulation results obtained using the Pontryagin maximum principle.
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In this paper authors consider changing of optical characteristics of the solar sail surface during the heliocentric flight. The sail surface is a multilayer epitaxial structure, which is physically a polyamide film covered with different... more
In this paper authors consider changing of optical characteristics of the solar sail surface during the heliocentric flight. The sail surface is a multilayer epitaxial structure, which is physically a polyamide film covered with different metals on the front and back sides. We calculate the optical characteristics of the multilayer film using the transition matrix method adapted for quantum-sized layers and taking into account the solar radiation spectrum. In order to analyse the influence of these characteristics variation on the spacecraft motion due to sail degradation we simulate the heliocentric Earth-Mercury flight.
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The given research presents the mathematical and computer modeling of flame attenuation in narrow channels for different fire extinguishing and explosion suppression compositions. The effect on the combustion reaction is possible with gas... more
The given research presents the mathematical and computer modeling of flame attenuation in narrow channels for different fire extinguishing and explosion suppression compositions. The effect on the combustion reaction is possible with gas mixture components concentration reducing, cooling the combustion zone and slowing down of chain reactions with the help of a phlegmatizing or inhibiting substances, of which the most universal and perspective are powder materials. Therefore, a necessary condition for solving the problems of developing effective flame arresters is to find common indicators and properties of substances that can become criteria for their phlegmatizing ability. The computer model in MatLab was created for methane allowing the choice of diameter and length of channel and velocity of explosion suppression composition, showing the dependence of temperature on length of channel.
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The work is devoted to one of the methods of the Earth’s protection from asteroid danger, namely, the use of the solar sail - a spacecraft, with the additional lighting the repels an asteroid from a dangerous orbit. The parameters of the... more
The work is devoted to one of the methods of the Earth’s protection from asteroid danger, namely, the use of the solar sail - a spacecraft, with the additional lighting the repels an asteroid from a dangerous orbit. The parameters of the near-Earth asteroids are revealed. Mathematical model of the control movement of all bodies (the Earth, the Sun, the asteroid, the solar sail), the control program and the software package (Delphi 7) for the simulation and visualization of the trajectories are designed.
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Research Interests:
Seismic processes under the influence of tectonic forces in the earth's crust generate shock waves, often leading to deep cracks, and, as a result, to catastrophic phenomena. A model of an elastic medium with a crack is often used for... more
Seismic processes under the influence of tectonic forces in the earth's crust generate shock waves, often leading to deep cracks, and, as a result, to catastrophic phenomena. A model of an elastic medium with a crack is often used for various contact conditions on its cracks. There is elastic medium (not thermoelastic) in connection with the complexity of solutions of the system of equations of motion of a thermoelastic medium, which belongs to systems of mixed hyperbolic-parabolic type. In this paper, a mathematical model of rock mass dynamics has been developed using a model of coupled thermoelasticity taking into account its thermoelastic properties with crack of an arbitrary geometry on its surface. Based on the method of generalized functions for elastic media with a crack of arbitrary shape, a generalized solution of the thermoelastic problem is constructed for given jumps of the relative velocity of displacements of the crack edges and stress jumps on the crack, its regular integral representation is given. The problem is solved in a 3D case in space of Laplace transforms in time.
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Generalized solutions of coupled thermoelastodynamics equations are considered. By use of generalized functions theory, the conditions on jumps of stresses, velocities, temperature gradients and energy density on their fronts are... more
Generalized solutions of coupled thermoelastodynamics equations are considered. By use of generalized functions theory, the conditions on jumps of stresses, velocities, temperature gradients and energy density on their fronts are received. The statements of four non-stationary boundary value problems of coupled thermoelasticity are given, for which uniqueness of decisions are proved by influence of shock thermoelastic waves.
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Research Interests:
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The propagation of transient, air-suspended solids in a vented explosion chamber is numerically investigated by a dynamic formulation for the Concentration Limit of Flame Propagation (CLFP) with the GUI MATLAB environment. The... more
The propagation of transient, air-suspended solids in a vented explosion chamber is numerically investigated by a dynamic formulation for the Concentration Limit of Flame Propagation (CLFP) with the GUI MATLAB environment. The geomechanics is modeled by a one-step overall reaction, which simulates the reaction of a stoichiometric propane– air-suspended solids. The CLFP modeling in the reaction rate model is numerically employed with mathematical models on basis Antoine's equation. This is based on an empirical correlation of the velocity fluctuations and implemented as interface with input-output data with graphic realization. The computer modeling show that the dynamic CLFP models provide superior results as general implementation of physical process of flame propagation and could be used for different rocks (f.e. granite, limestone, sandstone etc).
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The geomechanics of process is modeled by a one-step overall reaction, which simulates the reaction by burning of combustible gases. The Concentration Flame Limit Propagation (CFLP) modeling in the reaction rate model is numerically... more
The geomechanics of process is modeled by a one-step overall reaction, which simulates the reaction by burning of combustible gases. The Concentration Flame Limit Propagation (CFLP) modeling in the reaction rate model is numerically employed with mathematical models on basis Antoine's equation. The flame propagation of combustible gases is theoretically and numerically investigated by a dynamic formulation for the CFLP with the GUI MATLAB environment. This is based on an empirical correlation of the velocity fluctuations and implemented as interface with input-output data with graphic realization. The computer modeling show that the dynamic CFLP models provide superior results as general implementation of physical process of flame propagation and could be used for different media.
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The present paper represents the analytical calculation and computer simulation of motion of nanosatellite that in polar system of coordinates are structured. In particular, the paper asks whether possible to simulate the problem gets the... more
The present paper represents the analytical calculation and computer simulation of motion of nanosatellite that in polar system of coordinates are structured. In particular, the paper asks whether possible to simulate the problem gets the initial orbital altitude and eccentricity of trajectory. GUI in MATLAB designed to distinguish between these explanations are described. The results indicate that perigee distance, apogee distance, focal parameter, radius-vector, angle of true anomaly will change to describe trajectory of nanosatellite which is presented in 2D animation. These findings provide opportunity to calculate and model such type of problems using adapted user-friendly interface.
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The purpose of this paper is to present a fundamental tensor of tensions constructed via boundary integral equations (BIE) for unsteady value problems of coupled thermoelastodynamics. By BIEM implementation the following problems have... more
The purpose of this paper is to present a fundamental tensor of tensions constructed via boundary integral equations (BIE) for unsteady value problems of coupled thermoelastodynamics. By BIEM implementation the following problems have been solved: the thermoelastic statement of medium in 2-D and 3-D cases was considered under action of non-stationary concentrated mass forces and thermal sources; tensor of Green and fundamental tensor of tension were constructed in 2-D and 3-D cases (using dynamical functions), their properties were investigated, and their asymptotics were constructed; the dynamical analogues of formulas of Gauss and of Somigliana were constructed. The BIEM for the thermostress condition of medium was developed for the given non-stationary loadings and thermal flow on boundaries in 2-D and 3-D cases are presented.
The problem of the dynamics of a thermoelastic half-space under periodic surface forces and heat flows is solved using the model of coupled thermoelasticity. The Green’s tensor for one boundary value problem is constructed utilizing... more
The problem of the dynamics of a thermoelastic half-space under periodic surface forces and heat flows is solved using the model of coupled thermoelasticity. The Green’s tensor for one boundary value problem is constructed utilizing Fourier transformation. Analytical solutions for arbitrary surface forces and heat flow using the theory of generalized functions are constructed. To solve this boundary value problem, generalized function theory, tensor and differential algebra, the operator method, and integral transformations were used. The solutions obtained make it possible to investigate the thermal stress–strain state of an array with natural and artificial thermal sources and mass power forces acting at its surface.