Name
Trunev Aleksandr Petrovich
Scholastic degree
•
Academic rank
—
Honorary rank
—
Organization, job position
A&E Trounev IT Consulting, Toronto, Canada
Web site url
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Articles count: 125
In 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 space-time. 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
space-time are discussed
The 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 Fermi-Dirac statistics and BoseEinstein-Maxwell-Boltzmann
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 centrally-symmetric 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
Atmospheric 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 24000-40000 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 non-stationary planetary boundary
layer
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
The article deals with the numerical solution of the
Navier-Stokes 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 Navier-Stokes
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 Navier-Stokes 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
In this article we consider the many-body 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 non-inertial 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
non-linear 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
The 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 10-13 satellites was run to
determine the period of constant polarity magnetic
field
We have studied the question of the electromagnetic
structure of a relativistic electron in connection with
the Yang-Mills 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 Yang-Mills 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 wave-particle, 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
In the present article, we investigate the metric of the
crystal space in the general theory of relativity and in the
Yang-Mills 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 Yang-Mills
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
In this article, the restricted problem of three and more
bodies in the Ricci flow in the general theory of
relativity considered. A system of non-linear 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 many-body problem is consistent with the
Einstein-Infeld 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