#### Name

Trunev Aleksandr Petrovich

#### Scholastic degree

•

#### Academic rank

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#### Honorary rank

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#### Organization, job position

A&E Trounev IT Consulting, Toronto, Canada

#### Web site url

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## Articles count: 125

Metric describing the accelerated and rotating reference system in general relativity in the case of an arbitrary dependence of acceleration and angular velocity on time has been proposed. It is established that the curvature tensor in such metrics is zero, which corresponds to movement in the flat spaces. It is shown that the motion of test bodies in the metric accelerated and rotating reference system in general relativity is similarly to the classical motion in non-inertial reference frame. Maxwell's equations and Yang-Mills theory are converted to the moving axes in metric describes the acceleration and rotating reference frame in the general relativity in the case of an arbitrary dependence of acceleration and angular velocity of the system from time. The article discusses the known effects associated with acceleration and (or) the rotation of the reference frame - the Sagnac effect, the effect of the Stewart-Tolman and other similar effects. The numerical model of wave propagation in non-inertial reference frames in the case when potential depending of one, two and three spatial dimensions has been developed. It has been shown in numerical experiment that the acceleration of the reference system leads to retardation effects, as well as to a violation of the symmetry of the wave front, indicating that there is local change of wave speed

In this study we investigate the dynamics of relativistic
particles in the axially symmetric metrics. We have built
metric having axial symmetry and contains two centers
of gravity and a logarithmic singularity. The application
received metrics to the movement of particles in galaxies
is described. It is established that there are stable orbit in
the metric with two centers of gravity, the particle
velocity at which reaches the value v/ c ≈ 7.0 . Orbit
radius varies widely, but remains substantially flat orbit.
Unstable same movements are completed so that the
particles leave the system. The hypothesis that this kind
of relativistic objects can serve as sources of the
magnetic fields of the planets, stars and galaxies has
been proposed. The question of the realization in the
galaxy metric of Einstein's hypothetical elevator in
which there is a uniform gravitational field, simulating
the accelerated movement of the elevator is described. A
homogeneous gravitational field in a limited region of
space was numerical simulated. It has been shown that
this kind of accelerated objects generate relativistic
effect in the form of a log potential, not diminishing with
distance from the center of the system. It is assumed that
such capabilities can be associated with the Higgs field
responsible for the occurrence of the inertial mass of the
elementary particles

The article discusses the dynamic model of the rocket
motor electromagnetic type, consisting of a source of
electromagnetic waves of radio frequency band and a
conical cavity in which electromagnetic waves are
excited. The processes of excitation of
electromagnetic oscillations in a cavity with
conducting walls, as well as the waves of the YangMills
field have been investigated. Multi-dimensional
transient numerical model describing the processes of
establishment of electromagnetic oscillations in a
cavity with the conducting wall was created
Separately, the case of standing waves in the cavity
with conducting walls been tested. It is shown that the
oscillation mode in the conducting resonator different
from that in an ideal resonator, both in the steady and
unsteady processes. The mechanism of formation of
traction for the changes in the space-time metric, the
contribution of particle currents, the Yang-Mills and
electromagnetic field proposed. It is shown that the
effect of the Yang-Mills field calls change the
dielectric properties of vacuum, which leads to a
change in capacitance of the resonator. Developed a
dynamic model, which enables optimal traction on a
significant number of parameters. It was found that
the thrust increases in the Yang-Mills field
parameters near the main resonance frequency. In the
presence of thermal fluctuations and the Yang-Mills
field as well the traction force changes sign,
indicating the presence of various oscillation modes

The article discusses the dynamic model of the rocket
motor electromagnetic type, consisting of a source of
electromagnetic waves of radio frequency band and a
conical cavity in which electromagnetic waves are
excited. The processes of excitation of
electromagnetic oscillations in a cavity with
conducting walls, as well as the waves of the YangMills
field are investigated. The multi-dimensional
transient numerical model describing the processes of
electromagnetic oscillations in a cavity with
conducting wall created. Separately, the case of
standing waves in the cavity with conducting walls
considered. It is shown that the oscillations mode in
the conducting resonator different from that in an
ideal resonator, both in steady and unsteady
processes. The mechanism of formation of traction
for the changes in the space-time metric, the
contribution of particle currents, the Yang-Mills and
electromagnetic field proposed. It is shown that the
Yang-Mills field calls the change of the dielectric
constant, which leads to a change in the capacitance
of the resonator. Thus, the parametric resonance
occurs in the system, which leads to a strengthening
of the Yang-Mills amplitude, and to the emergence of
traction. We have developed a dynamic model, which
enables optimal traction on a significant number of
parameters. It was found that the thrust increases in
the Yang-Mills field near the main resonance
frequency. A model describing the excitation and
emission of nonlinear waves of the Yang-Mills field
was proposed. It is shown that nonlinear waves of the
Yang-Mills field more effectively carry the
momentum from the system in comparison with
electromagnetic waves, and it explains the significant
increase by several orders of thrust in the engines of
the electromagnetic type, compared with the photon
rocket

A 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

In this work, we consider two types of vortex
currents-cyclones and anticyclones in the Northern
and Southern Hemispheres. Numerical modeling of
turbulent flows of these types uses the model of the
planetary boundary layer developed by the author.
The purpose of the study is to test hypotheses about
the influence of the Coriolis force on the formation of
cyclones and anticyclones in the northern and
southern latitudes. The first hypothesis on the
direction of circulation in cyclones was verified in the
case of axisymmetric radially converging and
vertically rising turbulent flows with a natural
Coriolis parameter and viscosity. From the obtained
data of numerical experiments, it follows that the
current in the northern latitudes circulates in a counter
clockwise direction, and in the south - in a clockwise
direction, in full accordance with the observational
data. Thus, we have shown that a cyclonic flow is
formed in a turbulent radially converging flow under
the influence of the Coriolis force. The second
hypothesis on the formation of anticyclones was
verified in the case of radially divergent and vertically
descending turbulent flows. Because of numerical
experiments, it was established that in this case, the
current in the northern latitudes circulates clockwise,
and in the south - in a counter clockwise direction,
which corresponds to observations for anticyclones.
To test the effect of the cyclone (anticyclone) center
velocity on circulation, a nonstationary 3D model of
turbulent flow was developed. Within the framework
of this model, flows in cyclones and anticyclones
moving at a constant speed, as well as in shear flow,
are studied. Some types of loop protuberances on the
Sun are explained by the presence of a vortex
turbulent flow starting in the bowels of the Sun and
encompassing the chromosphere

The paper deals with the problem of changing the
polarity of the geomagnetic field as a problem of a
unified field theory and supergravity in the 112D.
Investigated centrally symmetric metric depends on
the radial coordinate in the observable physical space
of one of the worlds. The equation that relates the
magnetic field of the planet with a gravitational field in
5D has been derived. The problem of changing the
polarity of the magnetic field of the Earth discussed.
The rapid change of the geomagnetic field polarity
detected on the basis of paleomagnetic data is modeled
as a movement on a hypersphere in the 112D, which
corresponds to 110 corners. The simplest example of
such a movement in the case of the three angles is the
Euler model that describes the rigid body rotation. In
this model, there are modes with a quick flip of the
body while conservation of the angular momentum. If
the body has a magnetic moment, when such a change
occurs flip of the magnetic field. It is assumed that the
central core of the earth is 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. The central core may sudden flip, as in the Euler
model. 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. We discuss Einstein's hypothesis about the
origin of the magnetic field when rotating the neutral
masses. It is shown that the motion on a hypersphere
in the 112D has the effect of a magnetic field due to
the interaction of nucleons in nuclei. Such magnetic
field is most evident for iron, cobalt and nickel -
elements are consisting of the Earth's core

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 the paper the problem of constructing a unified field
theory based on the theory of supergravity in the 112D
is discussed. It is assumed that in the 112-dimensional
Riemann space there are 37 three-dimensional worlds
coexist having a single time and associated gravity.
Investigated centrally symmetric metric depends on
the radial coordinate in the observable physical space
of one of the worlds. It is assumed that in the 112D
performed the wave equation of the general form,
describing the dynamics of the scalar field. From this
equation, the wave equation is displayed in the fourdimensional
space-time, containing terms describing
the contribution of extra dimensions. It is shown that
the quantum numbers of the problem allow us to
describe the structure of the atom and the atomic
nucleus on the assumption that given the total mass of
the central body. The problem on the dynamics of the
scalar field in the 112D in a centrally symmetric metric
has been described. Built of field quantization theory
in general, and in the particular case of metrics
depending on the Weierstrass elliptic functions. It is
shown that in this case there are bounded periodic
potentials and corresponding periodic solutions that
depend on the energy and angular momentum
projection, and on the invariants of the Weierstrass
function. It is found that in an excited state with a
sufficiently large magnitude of the angular momentum
of the projection portion of the radial wave function is
periodic in a limited range, while the ground state
allowed waves on all axes of the radial coordinate. The
connection of the solutions to the Yang-Mills theories
discussed

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