In the article we present a spatial structure of largescale
transport systems. The model of a transport
network can be presented in the form of a graph, with
a set of the nodes corresponding to elements of a
network and a set of edges – to sections of roads the
connecting these nodes. As the model of a card of
roads, it is offered to use prefractal graphs which
naturally reflect structure of communications when
reviewing a transport network in different scales (the
states, regions, areas). Prefractal graphs allow
describing structural dynamics of the studied system
in the discrete time. One of the most widespread
scenarios of structural dynamics is the growth of
structure. The statement of tasks of the organization
of transport routes contains requirements criteria to
finding of optimal solutions. Often these requirements
and criteria are contradicting each other. It leads to
appearance of a multicriteria problem definition.
The multicriteria problem definition on a class of
prefractal graphs is considered. The optimum
algorithm of separation of the greatest maximum
paths by the given criterion is constructed and
estimates by remaining criteria are given. In operation
computing complexity of the constructed algorithm of
separation of the greatest maximum paths on a
prefractal graph is calculated and advantage of
operation of algorithm on last before algorithm of
separation of the greatest maximum paths on normal
graphs is justified. The constructed algorithm on
prefractal graphs has polynomial complexity
The article presents the simulation of non-linear spatial-temporal color oscillations in Yang-Mills theory in the case of SU (2) and SU (3) symmetry. We examined three systems of equations derived from the Yang-Mills theory, which describes the transition to chaotic behaviour. These transitions are caused by nonlinear vibrations of colour, depending on the model parameters - the coupling constants and the initial wave amplitude. Such transitions to chaotic behaviour by increasing the parameters are characteristic of hydrodynamic turbulence. A model of spatial-temporal oscillations of the Yang-Mills theory in the case of three and eight colors. The results of numerical simulation show that the nonlinear interaction does not lead to a spatial mixing of colors as it might be in the case of turbulent diffusion. Depending on the system parameters there is a suppression of the amplitude of the oscillations the first three of five colors or vice versa - the first three five other colors. The kinetic energy fluctuations or shared equally between the color components, or dominated by the kinetic energy of repressed groups of colors. Note that the general property of physical systems described by nonlinear equations in the Yang-Mills theory and hydrodynamics is particularly strong in the formation of quark-gluon plasma and hadrons jets, when the Yang-Mills is involved in the formation of hydrodynamic flow. Note that there is a relationship between the Einstein and Yang-Mills theory, on the one hand, Einstein's equations and hydrodynamics - on the other. All of this points to the existence in the nature of a general mechanism of formation of a special type of turbulence - geometric turbulence
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
Article is devoted to the numerical analysis of regional problems for system of the equations of Nernst-Plank-Puasson (NPP), to application of these regional problems to modeling and studying of mass transfer in the channel desalting of electro dialysis device. Various mathematical models of the transfer of ions in potential static mode in the form of system of the quasilinear equations with private derivatives are offered. The basic rules of occurrence and development of a spatial charge in the channel desalting of electro dialysis device are revealed
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
The article deals with numerical solutions of MHD
equations describing turbulent flow of a conducting
fluid in a rectangular cavity in the rotating magnetic
field at large values of the magnetic Taylor number,
and Reynolds number. 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. The models based on the properties of
currents of the turbulent environment proposed. A
modification of the continuity equation taking into
account the final magnitude of pressure fluctuations
was considered. It is shown that due to pressure
fluctuation the incompressibility condition can be
violated even for flows with low Mach numbers.
Modification of continuity in the system of NavierStokes
equations by the introduction of turbulent
viscosity allows the regularization of the NavierStokes
equations to solve the problems with rapidly
changing dynamic parameters, for example, in the
case of a conducting fluid flow in a magnetic field
rotating with a high frequency. 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 MHD flow in a rectangular cavity
with rapid change in flow parameters was proposed.
In numerical calculations revealed that under the
influence of a rotating magnetic field in a conducting
fluid there are forces occur, causing unsteady vortex
flow, which is consistent with experimental data. We
have discovered a type of large scale instability of the
turbulent flow, connecting with the secondary flow in
a form of vortices
The completely closed model of wall turbulence was
derived directly from the Navier-Stokes equation. The
fundamental constants of wall turbulence including the
Karman constant have been calculated within a theory.
This model has been developed also for the accelerated
and non-isothermal turbulent boundary layer flows
over rough surface. Numerical solutions of equations
system of turbulent transport of admixtures in a surface
layer of the atmosphere for a large scale have
been studied
For a field task, we have shown the analytical solution of the control example by means of which the condi-tions of the correct application of a method of second-ary sources of a field. The numerical decision in the form of Fourier series of the same task, but with use of the method of secondary sources is found. The method of the registration of heterogeneity of the environment which enters secondary sources the way that bring together analytical and numerical solutions is offered
The article presents a theoretical substantiation, methods of numerical calculations and software implementation of the decision of problems of statistics, in particular the study of statistical distributions, methods of information theory. On the basis of empirical data by calculation we have determined the number of observations used for the analysis of statistical distributions. The proposed method of calculating the amount of information is not based on assumptions about the independence of observations and the normal distribution, i.e., is non-parametric and ensures the correct modeling of nonlinear systems, and also allows comparable to process heterogeneous (measured in scales of different types) data numeric and non-numeric nature that are measured in different units. Thus, ASC-analysis and "Eidos" system is a modern innovation (ready for implementation) technology solving problems of statistical methods of information theory. This article can be used as a description of the laboratory work in the disciplines of: intelligent systems; knowledge engineering and intelligent systems; intelligent technologies and knowledge representation; knowledge representation in intelligent systems; foundations of intelligent systems; introduction to neuromaturation and methods neural networks; fundamentals of artificial intelligence; intelligent technologies in science and education; knowledge management; automated system-cognitive analysis and "Eidos" intelligent system which the author is developing currently, but also in other disciplines associated with the transformation of data into information, and its transformation into knowledge and application of this knowledge to solve problems of identification, forecasting, decision making and research of the simulated subject area (which is virtually all subjects in all fields of science)