A&E Trounev IT Consulting, Toronto, Canada
Author list of organization
List of articles written by the authors of the organization

LOGARITHMIC LAW AND EMERGENCE PARAMETER OF CLASSICAL AND QUANTUM SYSTEMS
01.00.00 Physicalmathematical sciences
DescriptionThe work discusses various examples of physical systems which state is determined by the logarithmic law  quantum and classical statistical systems and relativistic motion in multidimensional spaces. It was established that the FermiDirac statistics and BoseEinsteinMaxwellBoltzmann distribution could be described by a single equation, which follows from Einstein's equations for systems with central symmetry. We have built the rate of emergence of classical and quantum systems. The interrelation between statistical and dynamic parameters in supergravity theory in spaces of arbitrary dimension was established. It is shown that the description of the motion of a large number of particles can be reduced to the problem of motion on a hypersphere. Radial motion in this model is reduced to the known distributions of quantum and classical statistics. The model of angular movement is reduced to a system of nonlinear equations describing the interaction of a test particle with sources logarithmic type. The HamiltonJacobi equation was integrated under the most general assumptions in the case of centrallysymmetric metric. The dependence of actions on the system parameters and metrics was found out. It is shown that in the case of fermions the action reaches extremum in fourdimensional space. In the case of bosons there is a local extremum of action in spaces of any dimension

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

THEORY OF PHYSICAL CONSTANTS AND SUPERGRAVITY IN 112D
01.00.00 Physicalmathematical sciences
DescriptionIn this article we discuss a version of the metric theory of the fundamental interactions in which it is assumed that the physical constants due to the presence of extra dimensions of spacetime. The estimation of the number of physical constants based on the theory of supergravity in 112D is that the minimum number of constants is equal to 222, and the maximum number  1404928. At present, the number of parameters that characterize the elementary particles, isotopes and chemical elements is about 150920. This number is 9.3 less than the maximum possible number of parameters that indicate still great potential of modern science. Functions describing the area and volume of a unit hypersphere, embedded in a Riemannian space of arbitrary dimension, were used to find the fundamental physical constants. A satisfactory agreement with a relative error of 0.03% calculated and experimental values of the fine structure constant found out. For the ratio of the average mass of a nucleon to the electron mass is obtained coincidence with the experimental value with an accuracy of 0.002%. The proposed theory of physical constants different from that Bartini theory that established the optimal dimension of the space is a hypersphere 5 and 7, rather than 6 as in Bartini theory. The problems of the compactification of extra dimensions in describing the motion in fourdimensional spacetime are discussed

DYNAMICS OF THE GEOMAGNETIC FIELD AND REVERSALS IN THE SATELLITE MODEL
01.00.00 Physicalmathematical sciences
DescriptionThe article deals with the problem of changing the polarity of the geomagnetic field in the satellite model. It is assumed that the central core of the earth magnetized and surrounded by a number of satellites, each of which has a magnetic moment. Satellites interact with a central core and one another by means of gravity and through a magnetic field. It is shown that satellites distributed in orbit around a central core in such a system. It displays two models, one of which on the outer orbit satellites interact with each other and with a central body  the core and satellites, located on the inner orbit. The central body can make sudden upheavals in the fall at the core of one or more satellites, which leads to the excitation of vibrations in the satellite system, located on the outer orbit. It is shown that the duration of phase with constant polarity and upheaval time depends on the magnitude of the disturbance torque and core asymmetry. The second model contains two magnets subsystems and the central core. The rapid change of the geomagnetic field polarity detected on the basis of paleomagnetic data is modeled based on the Euler theory describing the rigid body rotation. In this model, there are modes with a quick flip of the body while maintaining the angular momentum. If the body has a magnetic moment, when there is a change coup magnetic field polarity. This leads to the excitation of vibrations in the satellite subsystems that are on the inner and outer orbits. Numerical simulation of the dynamics of the system consisting of the core and 1013 satellites was run to determine the period of constant polarity magnetic field

MANYBODY PROBLEM IN THE METRIC OF CIRCULAR DISTRIBUTED SOURSES
01.00.00 Physicalmathematical sciences
DescriptionIn this article we consider the manybody problem in general relativity in the case of the distribution of N singularities on the circle. It specifies the exact solution of the problem for an arbitrary distribution of singularities. It is shown that the static metric of N singularities corresponds to Newton's theory of N centers of gravity, moving around the central body in a circular orbit in a noninertial frame of reference, rotating with a period of bodies revolving. We consider the statement of the problem of many bodies distributed at the initial time on the circle. 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 circle. This is achieved due to relativistic effects, which have no analogues in Newton's theory of gravitation. Using the properties of relativistic potentials justified transition from the relativistic motion of the particles to the dynamic equations in the classical theory. A system of nonlinear parabolic equations describing the evolution of the metric in the Ricci flow proposed. The problem of the calculation of the potentials in the Ricci flow formulated. The application of the theory to describe the ring galaxy, planetary rings and the asteroid belt considered

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

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

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

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

ELECTRON STRUCTURE AND THE YANGMILLS THEORY
01.00.00 Physicalmathematical sciences
DescriptionWe have studied the question of the electromagnetic structure of a relativistic electron in connection with the YangMills theory. From the Lorentz electrodynamics equations of and Dirac electron theory derived an equation describing nonlinear waves of the scalar potential. It is shown that this equation is similar to the equation describing the dynamics of the condensate in the YangMills theory. There is also the connection to the Schrödinger equation: the scalar potential is a complex function, similar to the wave function in the Schrödinger theory. The model discussed electron is a solitary wave that occurs in the electromagnetic field. This wave has the properties of charged particles, able to interact with the external electric and magnetic field. An analytical solution describing solitary electromagnetic waves traveling at a speed less than the speed of light has been obtained. The existence of solitary electromagnetic waves consistent with the Hertz's hypothesis that suggested that cathode rays are a form of wave motion in an electromagnetic field. The proposed model of the electromagnetic structure of the electron thus solves the problem of duality waveparticle, which historically arose in the interpretation of experiments with cathode rays. Numerical modeling of electromagnetic electron structure shows that the initial state such as a spherical shell is unstable and disintegrates into a pair of nonlinear waves that leave the system with the speed of light. In the decay of the initial state concentrated in the neighborhood of the origin, waves of complex part of potential disappear with time, but a real part of the potential it tends to equilibrium