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

We propose an approach to the modeling of stressstrain
state of lithospheric structures near faults by
modeling them as Kirchhoff plates on threedimensional
elastic foundation. We describe an
efficient method of solving problems for plates with
rectilinear fractures, based on the transformation of
the differential operator, which allows us to analyze
the solutions obtained for different contact conditions
in the area of the fracture. The method is presented
on the example of the vibration problem of two
elongated plates on the surface of the elastic layer
under the effect of concentrated surface load. The
results of numerical implementation of the developed
algorithm make it possible to identify the influence of
the substrate properties, characteristics of the plates
and the nature of their border interactions on the
picture of wave process in the test structure. At the
same time obtained configurations of the harmonic
signal passage through the fracture can serve as an
indicator of its type. The proposed approach should
be used to determine the presence and type of
fractures based on measurements of signals from
vibration sources in cases when geophysical
environment can be modeled by the previously
described structure. The problems of studying objects
we reviewed in this paper also occur in various areas
of technology, and, therefore we can apply the
proposed method for their solution

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

This work presents a new approach to the countriesâ€™
credit rating definition, based on the advanced mathematical
models, such as neural network model, multiple
regression, cluster analysis and discriminant analysis.
A range of the analyses such as discriminant, cluster,
multiple regression models and a neural network
were performed on the following economic figures:
GDP per capita, GDP value, annual growth rate of
GDP, FDI - foreign investment, rate of unemployment,
consumer price inflation index, the size of government
debt in percentage of GDP. The results, obtained for
each model were combined in the countriesâ€™ credit
rating estimation system called "7M"

The influence of dissociation / recombination of water
molecules is important for understanding
electroconvection processes, as some authors believe
that the emergence of new carriers + H and − OH , and
can lead to a reduction in the space-charge and,
consequently, to electroconvection disappearance.
However, as shown in [5], the dissociation of water
molecules, although it reduces the space charge and
increases the threshold fall potential jump at which
begins electroconvection, yet it persists and effectively
mixes the solution. This article is devoted to
mathematical modeling of electrodiffusion of four
types of ions at the same time (two salt ions as well as
+ H and − OH ions) in the diffusion layer in electromembrane
systems with perfectly selective membrane
under the joint influence of violation of electrical neutrality, and the reaction of dissociation /
recombination of water molecules, development of
mathematical models of these processes, building
efficient algorithms asymptotic and numerical analysis
for different types of electrolytes. The work proposes a
new mathematical model of the process of transfer of
salt ions in view of the space charge and the
dissociation / recombination of water in the form of a
boundary value problem for a system of ordinary
differential equations. This system is reduced to a form
convenient for numerical solution. We have calculated
the required additional boundary conditions for the
electric field. Numerical and asymptotic solution of the
boundary value problem and physico-chemical
analysis of the influence of dissociation /
recombination on the transfer of salt ions is expected
to devote the next part of the work

Specially formed mixtures of isotopes of chemical
elements have better consumer properties than their
natural counterparts. Therefore, the development of
methods for increasing the efficiency of the known
methods for producing of isotope materials is relevant. It
is known that the chemical bond is formed only in the singlet state of the spins of valence electrons of the
reagents. On the basis of the known representations
about dispersion of spin projections on the coordinate
axes and the molecular-kinetic theory of gases was
obtained an expression for the constant of the chemical
reaction between the radicals occurring in the magnetic
field. This expression allows calculating the reactivity of
the isotopic modifications of radicals. Plasma allows to
transfer many of the compounds in the gas phase. It is
known that a significant part of particles in low
temperature plasma is in a radical form. The equations of
chemical kinetics for describing the process of oxidation
of the carbon isotopes in argon-oxygen plasma occurring
in an external permanent magnetic field were written in
the work. It was shown that the efficiency of plasma
process of isotopes separation can be increased only
under insufficient oxygen relative to the stoichiometric
value. These equations of chemical kinetics of processes
occurring in the plasma process of incomplete oxidation
of carbon isotopes needed to find experimental
conditions that provide the maximum isotope effect in a
magnetic field

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

The article is devoted to the solution of the problem which is the fact that on the one hand, the rating of Russian universities is in demand and on the other hand it hasnâ€™t been created yet. The proposed idea of solving the problem consists in the application of domestic licensing of innovative intelligent technologies for these purposes: we have suggested using an automated system-cognitive analysis (ASC-analysis) and its software tools â€“ the intelligent system called "Eidos". These methods are described in detail in this context. It is proposed to consider the possibility of applying these tools on the example of the Guardian University ranking. The article discusses its private criteria (indicators of universities). We specify the sources of data and the methods of their preparation for processing in "Eidos" system. In accordance with ASC-analysis methodology the article describes the installation of "Eidos", the data input into it, and the formalization of the subject area, synthesis and verification of models, their display and use to solve problems of assessment of the Guardian rating for Russian universities and research object modeling. It also discusses the prospects and ways of development of the integrated rating of Russian universities and operation of rating in adaptive mode. We have also specified the limitations of the proposed approach and the prospects of its development