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
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
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
This work presents a new approach to the countries’
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 countries’ credit
rating estimation system called "7M"
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
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
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 hasn’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 – 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
Adequate and effective assessment of the efficiency, effectiveness and quality of scientific activities of specific scientists and research teams is crucial for the information society and society based on knowledge. The solution to this problem is the subject of scientometrics and its purpose. The current stage of development scientometrics differs greatly from its previous appearance in the open as well as paid on-line access to huge amount of detailed data on a large number of indicators on individual authors and on scientific organizations and universities. In the world, there are well-known bibliographic databases: Web of Science, Scopus, Astrophysics Data System, PubMed, MathSciNet, zbMATH, Chemical Abstracts, Springer, Agris, or GeoRef. In Russia, it is primarily the Russian scientific citing index (RSCI). RSCI is a national information-analytical system, accumulating more than 9 million publications of Russian scientists, as well as information about citation of these publications from more than 6,000 Russian journals. There is a lot of data, so-called "Big data". The main primary scientometric indicator (based on which we build all the rest, such as the h-index) is the number of citations of the author's works, placed in the bibliographic database. This number of citations is determined by the software of RSCI using so-called "binding" which is a grammatical analysis and search in databases for works of the author, for relevant links from references in the works of various authors. However, the problem is, as experience shows, that authors make a very large number of simply incorrect and incomplete references in the reference lists, very far from standard. Currently, the software that RSCI uses does not automatically bind these invalid references, and this requires human intervention. But, centrally, to do this is not possible by experts of RSCI because of the huge amount of work, and distributed work for a large number of specialists in the field still requires a centralized moderation. As a result, the work for binding references to the literary sources is very slow and a huge amount of links is unbound. This leads to an underestimation of nanomatrices indicators of both individual authors and research teams that cannot be considered acceptable. The solution to this problem is offered by applying the automated system-cognitive analysis (ASC-analysis) and its programmatic Toolkit – intellectual system called "Eidos". This work provides a numerical example of the intellectual anchor of the real incorrect references to the works of the author on the basis of a small amount of real scientific data that are publicly available free on-line access to the RSCI