name
Trunev Aleksandr Petrovich
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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

DYNAMICS OF RELATIVISTIC PARTICLES IN THE RING AND SPIRAL GALAXY METRIC
01.00.00 Physicalmathematical sciences
DescriptionIn this work, we examine the dynamics of relativistic particles in the ring or spiral galaxy metric in general relativity. On the basis of the solution of Einstein's equations we have derived metric having axial symmetry, comprising N centers of gravity and a logarithmic singularity. The application received metrics to describe the motion of particles in a spiral and ring galaxy. On the basis of Einstein's equations solutions for vacuum we are explained rotation of matter in spiral galaxies. An expression for gravitation potential in the inner region of spiral galaxies in agreement with experimental data on the rotation of the CO and hydrogen is described. It is established that in the metric with N centers of gravity which are distributed on the circumference, exist as a local motion near the center of gravity, and motion around N gravity center as well. The transition from one mode of motion to another is determined by the initial distance to the circle on which the distributed centers of gravity. A system of nonlinear parabolic equations describing the evolution of the metric in the Ricci flow proposed. The boundary problem for the gravitational potentials in the Ricci flow was formulated. There are applications of the theory to describe a spiral and ring galaxy

SIMULATION OF TURBULENT MHD FLOW IN A RECTANGULAR CAVITY IN A ROTATING MAGNETIC FIELD
01.00.00 Physicalmathematical sciences
DescriptionThe article deals with numerical solutions of MHD equations describing turbulent flow of a conducting fluid in a rectangular cavity in the rotating magnetic field at large values of the magnetic Taylor number, and Reynolds number. 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. The models based on the properties of currents of the turbulent environment proposed. A modification of the continuity equation taking into account the final magnitude of pressure fluctuations was considered. It is shown that due to pressure fluctuation the incompressibility condition can be violated even for flows with low Mach numbers. Modification of continuity in the system of NavierStokes equations by the introduction of turbulent viscosity allows the regularization of the NavierStokes equations to solve the problems with rapidly changing dynamic parameters, for example, in the case of a conducting fluid flow in a magnetic field rotating with a high frequency. 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 MHD flow in a rectangular cavity with rapid change in flow parameters was proposed. In numerical calculations revealed that under the influence of a rotating magnetic field in a conducting fluid there are forces occur, causing unsteady vortex flow, which is consistent with experimental data. We have discovered a type of large scale instability of the turbulent flow, connecting with the secondary flow in a form of vortices

SIMULATION OF HEXAGONAL TURBULENT FLOW IN THE NORTH POLAR REGION OF SATURN
01.00.00 Physicalmathematical sciences
DescriptionAs we know, currently, around the north pole of Saturn there is a largescale hexagonal flow, with characteristic scales of length and speed  120 m / s and 14,500 km respectively. This trend observed for more than 35 years, is the subject of many experimental and theoretical studies. In this study, we propose a model and discuss the numerical solutions of the equations describing turbulent flow in the planetary boundary layer around the north pole of Saturn. It has been shown that a small violation of the axial symmetry in geostrophic shear leads to the development of hexagonal patterns in a turbulent boundary layer. In addition, under the influence of Coriolis forces and turbulent eddy viscosity gradient in a turbulent boundary layer formed jet pressed to the bottom edge of the layer. These results are used to simulate the observed hexagonal flow around the north pole of Saturn. It is assumed that the small amplitude geostrophic flow is described by a sum of zero and the sixth current harmonic functions, which leads to the excitation current at the upper boundary of the planetary boundary layer. It is found that such excitation enhanced in the boundary layer and reaches a maximum in the jet pressed to the bottom border. This jet, circulating on the hexagon coincides with the region of origin of the cloud cover, which is registered in the experiments. This excitation mechanism hexagonal flow around the north pole of Saturn is confirmed by numerical calculations of threedimensional nonstationary planetary boundary layer

SIMULATION OF ATMOSPHERIC VORTEX FLOWS ON JUPIER AND SATURN
01.00.00 Physicalmathematical sciences
DescriptionAtmospheric currents on Jupiter and Saturn are characterized by turbulence and complex vortex structure, which is caused by a large angular speed of the gas giants. In this paper we consider two types of eddy currents  for hexagonal in the northern polar region of Saturn and the Great Red Spot in the equatorial region of Jupiter. For the numerical simulation of turbulent flows of this type the model of the planetary boundary layer was developed by the author. In both cases, the main strengthening mechanism is associated with geostrophic flow of small amplitude interacting with the planetary turbulent boundary layer. For hexagonal Saturn with its characteristic length scales and speed  120 m / s and 14,500 km, respectively, there are more than 35 years data of observation. We have found that a small axial symmetry violation geostrophic flow in the shear causes the development of a hexagonal pattern in a turbulent boundary layer. In addition, under the influence of the Coriolis force and the eddy viscosity gradient in the turbulent boundary layer there is the jet formed, pressed against the lower edge of the layer. Great Red Spot on Jupiter has the characteristic velocity and length scales  150 m / s, 14,000 km from north to south and 2400040000 km from west to east, there are already more than 350 years data. It identified another mechanism of formation of vortex flow, coupled with the strengthening of small amplitude zonal flow in a turbulent boundary layer with the eddy viscosity gradient and the volume turbulent viscosity on a rotating planet. Both mechanisms are confirmed by numerical calculations of nonstationary planetary boundary layer

01.00.00 Physicalmathematical sciences
DescriptionIn the present article, we investigate the metric of the crystal space in the general theory of relativity and in the YangMills theory. It is shown that the presence of a lattice of gravitational ether has observable macroscopic consequences. Earlier, the influence of the gravity of the celestial bodies of the solar system on the electrical conductivity, inductance, the rate of radioactive decay of atomic nuclei, on seismic activity, the magnetic field and the motion of the pole of our planet, and on the rate of biochemical reactions was established. In all cases, a similar behavior of the physicochemical characteristics of materials and processes is observed, depending on the universal parameters characterizing the seasonal variations of the gravitational field of the solar system. The relationship between lattice parameters and the properties of materials, elements, atomic nuclei, and elementary particles is discussed. Possible metrics of the crystal space are constructed: a metric that depends on the Weierstrass function, derived in the YangMills theory and analogous metrics found in Einstein's theory. Such metrics, which have a central symmetry, can be used to justify the structure of elementary particles, the properties of atomic nuclei, atoms and matter. Periodic metrics are constructed that admit an electromagnetic field, as well as metrics associated with the assumed structure of the crystal space. These metrics are of particular interest, since the properties of the substance are related to the metric parameters. We proposed the model of electron beam as a streamer of preons

PROPAGATION AND BRANCHING OF STRAIMERS IN CONDUCTING ENVIRONMENT
01.00.00 Physicalmathematical sciences
DescriptionIn this work, we develop a model describing the propagation and branching of a streamer in a conducting medium in external electric field. 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, the streamer model is formulated in the form of nonlinear equations of parabolic type. In the framework of the proposed model, the problem of the propagation of a streamer in the form of a traveling wave is considered, which leads to the emergence of SaffmanTaylor streamers. For streamers of this type, the branching problem is formulated, which has a unique solution. The dependence of the branch point on the parameters of the problemthe speed of the streamer, the diffusion coefficient of the electrons and the strength of the external electric field, is found. The branching mechanism of the streamer head by dividing it into two parts has been well studied and several alternative models have been formulated for its description. The novelty of the problem in question is that the streamer splits into two threedimensional channels that are symmetric with respect to the given plane. Numerical experiments also revealed the mechanism of branching of the streamer in the cathode region, connected with the separation of the main channel into several lateral branches. It is noted, that in nature both branching mechanisms are realized, whereas in theory the instability of the surface of the streamer head is investigated

SIMULATION OF PLASMOID AND STRAIMERS IN CONDUCTING ENVIRONMENT
01.00.00 Physicalmathematical sciences
DescriptionIn this work, a model is developed that describes the formation of a plasmoid and streamers 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, the streamer model is formulated in the form of a system of parabolictype nonlinear equations. As is known, in laboratories it is possible to create a plasmoid with a lifetime of 300 500 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 similarity of ball lightning and plasmoid is discussed. If this similarity is confirmed, then the number of theoretical hypotheses concerning the nature of ball lightning, currently more than 200, can be drastically reduced to one described in this article

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

SIMULATION OF A STEPPED LIGHTNING LEADER
01.00.00 Physicalmathematical sciences
DescriptionIn this work, a model is developed that describes the formation of a stepped lightning leader 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 and the lightning channel. Numerical simulation of the propagation of ionization waves in a region with a ratio of 1/100, 1/200 allows us to identify two types of stepped streamers in the form of waves of compression and rarefaction, respectively. It was previously 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 closing the space charge to the anode through the streamer system was observed. These branching mechanisms are also revealed when the leader is propagated. The obtained results, as well as the data of numerical experiments confirm the hypothesis of the universality of the minimal model of the streamer, as well as its expansion in the form proposed by the author. Known phenomena of nature associated with the electrical discharge  streamer, plasmoid, ball lightning and stepped leader can be described within the framework of the minimal model

SIMULATION OF A PLASMA CHANNEL AND TRACK IN MOTION OF PLASMA SOURCE IN CONDUCTIVE ENVIRONMENT
01.00.00 Physicalmathematical sciences
DescriptionA model is developed that describes the formation of the plasma channel and the trace when moving in a conducting medium of various objects that are sources of plasma  ball lightning, plasmoids, charged particles, and so on. To describe the contribution of conduction currents, we modified the standard electrostatic equation considering 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 the plasma channel and the track behind the moving object. In this formulation, the problem of the formation of the lightning channel in weak electric fields, characteristic for atmospheric discharges of cloudearth, is solved. Numerical simulation of the motion of plasma sources in a region with a ratio of the sizes 1/100, 1/200 makes it possible to find the shape of the channel and the total length of the track, as well as the branching regimes. It was previously established that there are three streamer branching mechanisms. The first mechanism is associated with the instability of the front, which leads to the separation of the head of the streamer into two parts. The second mechanism is related to 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. The third branching mechanism, observed in experiments, is associated with the closure of the space charge to the anode through the streamer system. These branching mechanisms are also revealed when the leader is spread. Numerical experiments have revealed a new channel branching mechanism and a trace behind a moving plasma object, caused by the conductivity of the medium