Scientific Journal of KubSAU

In this study, we investigate the problem of the emission of gravitational waves produced in collisions of particles submitted to the singularities of the gravitational field. A system of non-linear parabolic equations describing the evolution of the axially symmetric metrics in the Ricci flow derived. A model describing the emission of gravitational waves in the collision and merger of the particles in the Ricci flow proposed. It is shown that the theory of the Ricci flow describes the problem of black holes merge, consistent with Einstein-Infeld theory, which describes the dynamics of the material particles provided by the singularities of the gravitational field. As an example, we consider the metric having axial symmetry and comprising two singularities simulating particles of finite mass. We have numerically investigated the change of the metric in the collision and merger of the particles. The initial and boundary conditions using the exact solution of the static problem, so the collision persist particularly metrics caused by the presence of particles. In numerical experiments determined that the collision of the particles in the Ricci flow leads to the formation of gravitational waves, similar in structure to the waves, registered in the LIGO experiment. Consequently, we can assume that the observed gravity waves caused mainly by transients associated with the change in the metric of a system. The influence of the parameters of the problem - the speed and mass of the particles, on the amplitude and intensity of the emission of gravitational waves was numerically simulated. We have found chaotic behavior of gravitational potentials at the merger of the singularities in the Ricci flow

As we know, currently, around the north pole of Saturn there is a large-scale 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 three-dimensional non-stationary planetary boundary layer

In 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 problem-the 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 three-dimensional 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

In 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 parabolic-type nonlinear equations is formulated that describes the formation of streamers, plasma long-lived formations and ball lightning. As is known, in laboratories it is possible to create a plasmoid with a lifetime of 300-500 ms and a diameter of 10-20 cm, which is interpreted as a ball lightning. With high-speed 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 long-lived 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

In 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 parabolic-type 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

The article presents the simulation of non-linear spatial-temporal color oscillations in Yang-Mills theory in the case of SU (2) and SU (3) symmetry. We examined three systems of equations derived from the Yang-Mills theory, which describes the transition to chaotic behaviour. These transitions are caused by nonlinear vibrations of colour, depending on the model parameters - the coupling constants and the initial wave amplitude. Such transitions to chaotic behaviour by increasing the parameters are characteristic of hydrodynamic turbulence. A model of spatial-temporal oscillations of the Yang-Mills theory in the case of three and eight colors. The results of numerical simulation show that the nonlinear interaction does not lead to a spatial mixing of colors as it might be in the case of turbulent diffusion. Depending on the system parameters there is a suppression of the amplitude of the oscillations the first three of five colors or vice versa - the first three five other colors. The kinetic energy fluctuations or shared equally between the color components, or dominated by the kinetic energy of repressed groups of colors. Note that the general property of physical systems described by nonlinear equations in the Yang-Mills theory and hydrodynamics is particularly strong in the formation of quark-gluon plasma and hadrons jets, when the Yang-Mills is involved in the formation of hydrodynamic flow. Note that there is a relationship between the Einstein and Yang-Mills theory, on the one hand, Einstein's equations and hydrodynamics - on the other. All of this points to the existence in the nature of a general mechanism of formation of a special type of turbulence - geometric turbulence

The article presents the theory of the electromagnetic type of rocket motor. The apparatus consists of a magnetron and a conical cavity in which electromagnetic oscillations are excited. We explain the mechanism of trust in such a device based on Maxwell's theory and the Abraham force. We built a dynamic model of the motor and calculated the optimal parameters. It is shown, that the laws of conservation of momentum and energy for the rocket motor of electromagnetic type are true, taking into account the gravitational field. In simulation, the movement used the theory of relativity. The source of the motion in an electromagnetic drive is the mass conversion in various kinds of radiation. The optimization of the operating parameters of the device is done, namely by the excitation frequency, the magnitude of heat losses of electromagnetic energy by thermal radiation in the IR spectrum, the parameters of heat transfer and forced from the temperature dependence of the resistance of the material of the cavity walls. It was found that the effective conversion of electromagnetic energy in the trust force necessary to minimize the deviation of the excitation frequency of the primary resonance frequency of the cavity. The mechanism of formation of trust under change the metrics of space-time, taking into account the contribution of the Yang-Mills theory and electromagnetic field tensor of energymomentum has been proposed

A number of information and semantic models has been developed using artificial intelligence system AIDOS-X. The similarity between the movement of the elements of the lunar orbit and the dynamics of the instantaneous pole of the Earth, as well as violations of the global atmospheric circulation and water, leading to the emergence of episodes of El Niño and La Niña are justified. We have explored a possibility of semantic information models equatorial regions of the Pacific for prediction of global climatic disturbances in the tropical latitudes. We made a forecast about breaking of global ocean circulation, or the occurrence of El Niño episode of the classical type in 2015

The question of construction of electrodynamics in the framework of the metric theory of gravitation is discussed. It is shown that the energy-momentum tensor of the electromagnetic field creates a space in which Faraday's law of induction is true. In such a space the scalar curvature vanishes identically, although space contains matter in the form of an electromagnetic field. It is proposed to call such space Faraday's magnetic universe as historically Faraday first established experimentally that "empty space is a magnet." We consider the metric of the expanding universe and metrics that describe the local gravitational field in the Newtonian theory. It was established that the field equations in spaces containing matter only in the form of an electromagnetic field in these metrics are reduced to hyperbolic equations describing the propagation of waves at the speed of light. However, in the field containing matter, the field equations are the equations of parabolic type, which describe diffusion or probability waves of Schrödinger quantum theory type. It is assumed that the potentials of the two metrics are connected, as with the potentials of the electromagnetic field, and the potentials of the Yang-Mills theory. Hence, the total output for all interactions law establishing the primacy of the gravitational field as the fundamental interaction, generating other interactions

In this article we consider the Yang-Mills theory in connection with the Einstein and Maxwell equations. The model of a metric satisfying the basic requirements of particle physics and cosmology is proposed. Firstly we consider the example of a purely temporary solution of the Yang-Mills equations in the space of torsion-free and the basic equations of the model of the cosmological scale. Some exact solutions and numerical model in a case, when density of baryonic matter and electromagnetic energy density remains constant over time been investigated. We obtained the solution combines the properties of Einstein's model, and Friedman’s model as well, describes the universe as a time-dependent metric, and with a constant density distribution of baryonic matter and electromagnetic field. Secondly, the model of the proton scale proposed. We proved that the metric of the observable universe is associated with a metric of the periodic lattice, given by the Weierstrass function. We find that there may be a spherical particle, which expand in sync with the space of the universe. Therefore, from the point of view of the outside observer they seem having static form like protons.