name
Trunev Aleksandr Petrovich
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•
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• A&E Trounev IT Consulting, Toronto, Canada
директор
Research interests
Математическое моделирование социальноэкономических и природных процессов
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Articles count: 125
Сформировать список работ, опубликованных в Научном журнале КубГАУ

SIMULATION OF TURBULENT FLOW IN A CAVITY ON THE NAVIERSTOKES EQUATIONS
01.00.00 Physicalmathematical sciences
DescriptionThe article deals with the numerical solution of the NavierStokes equations describing turbulent flow in a rectangle cavity or in a cuboid with one open face at high Reynolds numbers. It is known, that there is a mechanism of turbulent mixing in natural systems, leading to an increase in the viscosity of the continuous medium. In this regard, we suggest methods of regularization of the NavierStokes equations, similar to the natural mechanisms of mixing. We proposed the models based on the properties of the turbulent environment. For this we modified the continuity equation taking into account the pressure fluctuations. It is shown that the incompressibility condition is can be violated due to pressure fluctuation even for flows with low Mach numbers. Modification of continuity equation by the introduction of turbulent viscosity allows the regularization of the NavierStokes equations to solve the problems with rapidly changing dynamic parameters. It was shown that the modification of the continuity equation taking into account turbulent fluctuations leads to a system of nonlinear equations of parabolic type. A numerical model of turbulent flow in the cavity with the rapid change in the parameters of the main flow developed. Discovered type of instability of the turbulent flow associated with the rapid changes in the main flow velocity. In numerical simulations found that due to the acceleration of the main flow there is the unsteady vortex flow in the cavity, which is characterized by the integral of energy not vanishing with time, vibrations that have a certain period, depending on the turbulent viscosity

SIMULATION OF BALL LIGHTNING IN CONDUCTING ENVIRONMENT
01.00.00 Physicalmathematical sciences
DescriptionIn this work, a model is developed to describe the formation of streamers, plasmoid, and ball lightning in a conducting medium. To describe the contribution of the conductivity currents, we modified the standard electrostatic equation taking into account the vortex component of the electric field. As a result of this generalization, a system of parabolictype nonlinear equations is formulated that describes the formation of streamers, plasma longlived formations and ball lightning. As is known, in laboratories it is possible to create a plasmoid with a lifetime of 300500 ms and a diameter of 1020 cm, which is interpreted as a ball lightning. With highspeed photography, a complex structure is detected, consisting of a plasmoid and surrounding streamers. Within the framework of the proposed model, problems are posed about the formation of a plasmoid and the propagation of streamers in an external electric field. In this model, the plasmoid is considered to be a longlived streamer. The range of parameters in which a plasmoid of spherical shape is formed is indicated. It is established that there are three streamer branching mechanisms. The first mechanism is related to the instability of the front, which leads to the separation of the head of the streamer into two parts. The second mechanism is associated with the instability of the streamer in the base region, which leads to the branching of the streamer with the formation of a large number of lateral streamers closing the main channel of the streamer to the cathode. In numerical experiments, the third branching mechanism observed in experiments connected with the branching of the plasmoid in the cathode region with the closure of the space charge to the anode through the streamer system was observed. The results of modeling the evolution of globular clusters in a scale of hundreds of milliseconds are given. Plasma exchange recharge modes leading to the formation of a positive or negative charge of the system are found

01.00.00 Physicalmathematical sciences
DescriptionMovement of geographical and magnetic poles versus celestial bodies’ positions is examined on the basis of the special and general relativity theory.

THE INTERACTION OF LIGHT AND PARTICLES WITH GRAVITATIONAL WAVES
01.00.00 Physicalmathematical sciences
DescriptionIn this article we consider a model of the structure of matter, in which elementary particles, atoms and molecules are composed of gravitational waves. A model of interaction of light and particle beams with macroscopic gravitational waves has been proposed. The protocols of experiments to test the theory are considered

EXITATION OF ELECTROMAGNETIC RADIATION, NUCLEAR REACTION AND PARTICLES DECAY BY THE ACCELERATION
01.00.00 Physicalmathematical sciences
DescriptionThe article discusses the excitation of electromagnetic radiation, nuclear reactions and decays of particles by the acceleration of charges, atomic nuclei and the macroscopic volumes of matter. The motion of charged particles in a magnetic trap used for plasma confinement was computed. We propose a model of the electromagnetic radiation of a charge moving in a noninertial reference frame in general relativity. We have also constructed a theory of perturbation with using a wave equation with small parameters, taking into account a characteristic radius of the trajectory of the electrons as they move in a magnetic field. It was found that in the first approximation, the radiation backreaction force depends on the acceleration of the charge. For the simulating of processes in hadrons and nuclei we used YangMills theory and the metric, describes the acceleration and rotating reference frame in general relativity. We consider the scalar glueball model for an arbitrary dependence of acceleration and angular velocity of the system on time. The numerical model of wave propagation in noninertial reference frame for the geometry of system of one, two or three spatial dimensions was tested. In the numerical experiments shown that the acceleration of the system leads to instability, leading to an unlimited increase in the amplitude of waves, which is interpreted as a decay of system. It was found that there are critical values of acceleration above which the instability develops

REPRESENTATION OF THE SOLUTIONS OF THE NAVIERSTOKES IN GENERAL RELATIVITY
01.00.00 Physicalmathematical sciences
DescriptionIn this paper, we investigated solutions of the NavierStokes equations associated with the solutions of Einstein's equations for empty space. There exists a metric in which the NavierStokes equations are integrated exactly. We demonstrate that the solution of the NavierStokes equations of general form consistent metrics describing in general relativity space with nonzero curvature

THE ORIGIN OF INERTIAL MASS OBSEVABLE MATTER
01.00.00 Physicalmathematical sciences
DescriptionWe consider the hypothesis of the origin of mass of the observed matter from electromagnetic field interacting with streams of preons. The interaction between preons and the scalar and vector potentials of the electromagnetic fields acquire mass, which leads to a massive scalar and vector bosons. The described mechanism of mass generation is different from the wellknown Higgs mechanism associated with the spontaneous breaking of the electroweak symmetry, for which at the moment is finding a suitable scalar boson

GENERAL RELATIVITY AND GALACTIC METRICS
01.00.00 Physicalmathematical sciences
DescriptionIt is shown that the metric of the galaxy should be universal, depending only on the fundamental constants. There are examples of universal metrics obtained in Einstein's theory of gravitation and YangMills theory. The axialsymmetric solutions of Einstein’s equations for a vacuum are applied to explain the rotation of matter in spiral galaxies

GENERAL RELATIVITY AND METRICS OF INHOMOGENEOUS ROTATING UNIVERSE
01.00.00 Physicalmathematical sciences
DescriptionThe metric of inhomogeneous rotating Universe is discussed. There are examples of universal metrics obtained in Einstein's theory of gravitation. On the basis of solutions of Einstein’s equation we have proposed universal metric describing the properties of galaxies, groups and clusters of galaxies in inhomogeneous rotating Universe

RESTRICTED MANYBODY PROBLEM IN THE RICCI FLOWS IN GENERAL RELATIVITY
01.00.00 Physicalmathematical sciences
DescriptionIn this article, the restricted problem of three and more bodies in the Ricci flow in the general theory of relativity considered. A system of nonlinear parabolic equations describing the evolution of the axially symmetric metrics in the Ricci flow proposed. A model describing the motion of particles in the Ricci flow derived. It is shown that the theory describing the Ricci flow in the manybody problem is consistent with the EinsteinInfeld theory, which describes the dynamics of the material particles provided by the singularities of the gravitational field. As an example, consider the metric having axial symmetry and contains two singularities simulating particles of finite mass. It is shown that the static metric with two singularities corresponds to Newton's theory of the two centers of gravity, moving around the center of mass in circular orbits in a noninertial frame of reference, rotating with a period of bodies. We consider the statement of the problem of many bodies distributed at the initial time on the axis of symmetry of the system. In numerical calculations, we studied the properties of the gravitational potential in the problem of establishing a static condition in which multiple singularities retain the initial position on the axis of the system. This is achieved due to relativistic effects, which have no analogues in Newton's theory of gravitation. Using the properties of relativistic potentials we have justified transition from the relativistic motion of the particles to the dynamic equations in the classic theory