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
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
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
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 study we consider the problem of determining
the motion and similarity parameter to the system of
worlds in a Riemannian space 112D with a common
field of gravity. Centrally symmetric metric,
depending on the 110 angle coordinates and the radial
coordinate and time was investigated. It is assumed
that there are intelligent beings in every world, striving
for self-knowledge. By virtue of the presence of the
world hierarchy in one of them there is a system of
complete identification of each characteristic of the
individual being with macroparameters his world. If
sentient beings in all the world to create a device to
simulate their own history in the form of a network of
computers using the available material and the
physical laws of his world, and the loss of information
when displaying one world to another is 1%, then 37-
th world played only 68.9449%. For Earthlings, it was
found that the average similarity parameter of
professional group in recognition by using
astronomical parameters is 68.75%. Therefore, we can
assume that the world system, including Earth,
contains 37 "floors." Assuming that each "floor" takes
three space dimensions, and all the "floors" connected
by a single time, we find here that the number of
dimensions of space-time of the whole system is 112.
In the article the angular motion in a Riemannian space
is considered. The effect of the separate worlds on
other worlds is simulated. It has been shown that the
physical laws in all worlds represent a single
movement covering the markers in the form of the
motion of atoms and elementary particles in a
gravitational field in the 112D
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 article deals with the solution of the NavierStokes
equations describing turbulent flows over
rough surfaces. 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. It is shown, that in threedimensional
flows over a rough surface turbulent
viscosity increases proportionally to the square of the
distance from the wall. The models of the flow,
taking into account the properties of the turbulent
environment are considered. A modification of the
continuity equation taking into account the limiting
magnitude of pressure fluctuations is proposed. It is
shown, that due to the pressure pulsation, the
incompressibility condition may be violated even for
flows with low Mach numbers. Modification of the
continuity equation taking into account turbulent
fluctuations leads to a system of nonlinear equations
of parabolic type. Modification of continuity equation
in the system of Navier-Stokes by the introduction of
turbulent viscosity allows the regularization of the
Navier-Stokes equations to solve the problems with
rapidly changing dynamic parameters. The main
result of which is obtained by numerical simulation of
the modified system of equations is the stability of the
numerical algorithm at a large Reynolds number,
which can be explained, first, a system of parabolic
type, and a large quantity of turbulent viscosity. A
numerical model of flow around plates with the rapid
change in angle of attack has been verified. We have
discovered the type of instability of the turbulent
boundary layer associated with the rapid changes in
dynamic parameters. It is shown, that the fluctuations
of the boundary layer to cause generation of sound at
a frequency of 100 Hz to 1 kHz
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 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
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
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