Scientific Journal of KubSAU

The model of the motion of particles in the SternGerlach apparatus in the classical and quantum mechanics was developed. The data simulation of particle trajectories and distribution of silver atoms on the surface of the plate in their deposition are discussed. It was found that for the experimentally observed distribution of two-dimensional shapes of the atoms must be assumed that the atoms are not involved in the precession motion in a magnetic field, while maintaining the direction of the magnetic moment, for example, parallel to the induction vector of the magnetic field during the time of motion in the apparatus. To obtain a realistic picture of the figure of the scattering of atoms used a classical model of movement and expression of forces compatible with the quantum picture of the motion of particles with spin ½. The magnetic field is simulated based on the original Stern-Gerlach data describing the distribution of the gradient of the induction components related to the splitting of the beam. Quantum model of particle motion is based on the Pauli equation in the boundary layer approximation. It is found that in this model, depending on the initial polarization of the particle, beam is split into either two or is deflected towards the magnet blade or in the opposite direction. It is shown that if the initial conditions for the task are reproducing the geometric dimensions and the magnetic field in the Stern-Gerlach apparatus, the figure of the scattering particles in the shape of the outline is similar to the experimentally observed shape

In 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 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 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

Particle dynamics in metrics with logarithmic potential The work considers the problem of modeling the motion of particles in a unified field theory to 6D, in theory, supergravity in the 112D and metric galaxies. We have investigated a centrally symmetric metric in the 112-dimensional Riemannian space, which depends on the radial coordinate, time, and 110 angles. We present a system of equations describing the angular movement on a hypersphere of any dimension N. It is shown that the motion on the hypersphere depends on the 2 (N-1) of singular points. We have installed general nature of relativistic motion on a hypersphere when it is displayed on the plane and in three-dimensional space. It is shown that the motion determined by the reflection from the singular points that of motion on the plane in some cases leads to thickening of the trajectories in the neighborhood of sides of the rectangle. The 6D investigated metric describing the case of motion with two centers of symmetry. It is shown that in such a metric exists a class of exact solutions, logarithmically dependent on the gravity centers of origin. It is found that in this system there is a motion with condensation paths around the sides of the rectangle, due to scattering of test particles gravity sources. We set the general nature of angular motion on a hypersphere and radial movements in 6D in the metric of a logarithmic potential. It is proved that similar solutions with logarithmic potential exist in galaxies metric in the metric of Einstein's theory of gravity. The article also describes the connection of the solutions to the nonlinear electrodynamics, and with a theory of quark interactions and Yang-Mills theory

In this article, we investigate the restricted problem of many bodies with a logarithmic potential in the general theory of relativity. We consider the metric having axial symmetry and containing a logarithmic singularity. 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. The motion of relativistic particles in a logarithmic potential sources distributed on the surface of a torus simulated. It is shown that the trajectory of the particles in these systems form a torus covered with needles. It was found, that the Ricci flow in the general theory of relativity could be born three kinds of matter - positive and negative energy density, as well as the color of matter, the gravitational potential of which is complex. It has been shown that this type of material is associated with the manifestation of the quantummechanical properties, which is consistent with the hypothesis of the origin of Schrodinger quantum mechanics. It is assumed that the most likely candidate for the role of the color of matter is the system of quarks as to describe the dynamics of quarks using the logarithmic potential, and the quarks themselves are not observed in the free state

We consider numerical solutions of the Navier-Stokes equations describing laminar and turbulent flows in channels of various geometries and in the cavity at large Reynolds numbers. An original numerical algorithm for integrating a system of nonlinear partial differential equations is developed, based on the convergence of the sequence of solutions of the Dirichlet problem. Based on this algorithm, a numerical model is created for the fusion of two laminar flows in a T-shaped channel. A new mechanism of meandering is established, which consists in the fact that when the two streams merge, a jet is formed containing the zones of return flow. Vortex motion in a rectangular cavity is studied. It is established that the numerical solution of the problem with discontinuous boundary conditions loses stability at Reynolds number Re> 2340. The trajectories of passive impurity particles in a cylindrical cavity are investigated. An explanation of the behavior of tea leaves in a cup of tea in the formation of a toroidal vortex because of circular stirring is confirmed, which is confirms the wellknown hypothesis of Einstein. A numerical model of flow in an open channel with a bottom incline in a rotating system is developed. It is shown that in both laminar and turbulent flow under certain conditions a secondary vortex flow arises in the channel due to the Coriolis force, which explains the well-known Baer law and confirms the Einstein hypothesis

In this article, we investigate the problem of creation of matter in the collision of particles, presented by singularities of the gravitational field. A system of nonlinear parabolic equations describing the evolution of the axially symmetric metrics in the Ricci flow derived. A model describing the creation of matter in the collision and merger of the particles in the Ricci flow proposed. It is shown that the theory that describes the Ricci flow in the collision of black holes is consistent with EinsteinInfeld 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 which contains two singularities simulating particles of finite mass. It is shown that the static metric with two singularities corresponding to in Newton's theory of gravity two particles moving around the center of mass in circular orbits in a non-inertial frame of reference, rotating with a period of two-body system rotation. We have numerically investigated the change of the metric in the collision of particles with subsequent expansion. In numerical experiments, we have determined that the collision of the particles in the Ricci flow leads to the formation of two types of matter with positive and negative energy density, respectively. When moving singularities towards each other in the area between the particles the matter is formed with negative energy density, and in the region behind the particles - with positive density. In the recession of the singularities, the matter with positive energy density is formed in the area between the particles. The question of the nature of baryonic matter in the expanding universe is discussed

The article discusses various examples of dynamical systems in which the motion is determined by the logarithmic law - quark systems, hydrodynamic systems, galaxies. Set the general nature of angular motion on a hypersphere in a space of arbitrary dimension and radial movement 6D in the metric of a logarithmic potential. We investigate the 6D metric describing the case of motion with two centers of symmetry. It is shown that in such a metric exists a class of exact solutions, logarithmically dependent on the gravity center coordinates. It was established that in spiral galaxies the orbital motion is due to the logarithmic potential, which is the exact solution of the field equations of Einstein's theory of gravity. The most well-known and widespread in nature case is turbulent flow over a smooth or rough surface, in which the mean velocity depends logarithmically on the distance from the wall. We derivate the logarithmic velocity profile in turbulent flow from the NavierStokes equations. An analogy of the logarithmic velocity profile and the logarithmic law in the case of erosion of materials under impacts been proposed. In electrodynamics, Ampere's law, which describes the interaction of current-carrying conductors, is a consequence of the logarithmic dependence of the vector potential of the distance from the conductor axis. There is, however, an alternative derivation of Ampere law of the Riemann hypothesis about the currents due to the motion of charges

In this work, we investigate the problem of collisions of particles linked to the singularities of the gravitational field in the Ricci flow. A system of non-linear parabolic equations describing the evolution of the axially symmetric metrics proposed. We consider the metric having axial symmetry and comprising two singularities simulating particles of finite mass. There was numerically investigated the change of the metric in the collision of particles. Two formulations of the problem have been considered, one of which scatter particles after the collision, and the other as a result of the merger of two particles, a new stable static system, which can be interpreted as a new particle. 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 system. A model describing the emission of gravitational waves in the collision of particles in the Ricci flow proposed. 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

The article discusses a model of rocket motor of electromagnetic type, consisting of a source of electromagnetic radio frequency oscillations and the conical cavity, in which electromagnetic waves are excited. We have created a multi-dimensional transient numerical model describing the process of establishing electromagnetic oscillations in the resonator, taking into account the finite conductivity of the walls. Separately, the standing waves in the cavity with conducting walls have been simulated. It is shown that the oscillations mode in the conducting resonator different from that in an ideal resonator, both in a case of steady and unsteady waves. We have built a dynamic model taking into account the thermal conductivity and electrical conductivity of the walls, waves and particles emission and vacuum polarization. We have also developed a dynamic model enables to optimize a thrust force on a considerable number of parameters without the involvement of the hypotheses about the physics of the phenomenon. We run the optimization of the operating parameters of the device, namely by the excitation frequency, the frequency of the modulating signal, the magnitude of heat losses of electromagnetic energy by thermal radiation in the IR spectrum, the parameters of forced heat transfer and the temperature dependence of the resistance of the material of the cavity walls. It is found that the pulse modulation greatly improves the efficiency of conversion of electromagnetic energy into thrust. The mechanism of formation of traction, adjusting the metrics of space-time, the current contribution of elementary particles, the Yang-Mills and electromagnetic fields is proposed. It is shown that the contribution of the elementary particles in the thrust force is proportional to the electrical conductivity of the system multiplied by Abraham force

The 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 Navier-Stokes 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