The complex systems

In the paper, flows of an inhomogeneous medium consisting of gas and dispersed inclusions are simulated. The research objective is aerosols, i.e. solid particles or liquid droplets suspended in gas. The mathematical model of the complex medium flow consists of the dynamics equations for the carrier component, i.e. gas, and the dynamics equations for the dispersed component. The system of equations describing the motion of each mixture component includes continuity equations of mass, momentum and energy. The continuity of momentum for the carrier phase is described by the one-dimensional Navier-Stokes equation. The interphase interaction was defined by relations known from the literature. The mixture dynamics was simulated in one-dimensional approximation. The mathematical model equations were integrated using an explicit finite-difference method. To suppress numerical oscillations, a nonlinear grid function correction scheme was applied to the obtained solution.

The three-dimensional representation of the solution for the ordinary differential equations system (ODE) describing convective flow is a Lorentz attractor. This system of equations is the basic deterministic system with which the development of chaos theory began. In order to derive the characteristics of this complex system, the development of a modern accessible and easy to use software product is necessary.
The aim of the work was to create a program for investigating the Lorentz attractor in Python using special command libraries. Particular attention is paid to ways of solving the system of ordinary differential equations by different numerical methods and to the clarity of the presented results.
The code blocks of the developed software are described; it is used to calculate the Lorentz attractor by varying the numerical methods for solving the ordinary differential equations and system parameters. Conclusions are drawn from the results of the calculation.

The paper еtheorizes the relationship between a redshift in the electromagnetic spectrum of space objects and their gravity and demonstrates it with computational experiments. Redshift, in this case, is a consequence of deceleration of the photons emitted from the surface of objects, which is caused by the gravity of these objects. The photon speed reduction due to the attraction of space gravitating object (GO) is defined as ΔC = C-C ‘, where C’ is a photon speed changed by the time the receiver records it. Then, at photon speed variation between a stationary source and a receiver, the redshift factor is determined as Z = (C-C ‘)/C’. Computational experiments have determined the gravitational redshift of the Earth, the Sun, a neutron star, and a quasar. The graph of the relationship between the redshift and the ratio of sizes to the mass of any space GOs washas been obtained. The findings indicate that the distance to space objects does not depend on the redshift of these objects.

This paper proposes a version of the brain mechanism for emergence and formation of perceptual and mental images. The initial event of perceptual image emergence is the result of interaction on thalamic relay neurons between chaotic sensory impulse flow and also impulse flow organized in trains and coming from reticular structures. The subsequent step is the formation of a metastable dynamic association of excited allocortex columns. The role played by the functional association of allocortex columns and the intrafusal muscular reception in the activation of distributed brain systems and in the formation of a perceptual image is considered. This image is seen as a meta-stable state of synergistic processes in neuromuscular structures. The rationale for the imperceivableness of a perceptual image is given. It is assumed that a mental image is based on the perceived effects of Newtonian forces caused by muscle contractions. Properties of perceptual and mental images, their difference and conjugacy, and also the role of a mental image in interaction with conscious images are discussed.

The paper deals with the philosophical and methodological aspects of the geosystems, or geographical systems, doctrine evolution. Attention is drawn to undesirable tendencies in this evolution, manifested in giving some aspects of the doctrine the appearance of fundamental principles. It shows general scientific dialectic base of the classical variant of the geosystem doctrine as it was developed by its founder academician V. B. Sochava. It emphasizes the inconsistency of particular principles of the doctrine on geosystems as a metascientific paradigm developed later and being developed at present, the relative fundamentality and viability of the classical and widely interpreted, “imperfect” concepts, allowing to operate them in a wide range of aspects of geographical (and not only) knowledge, in particular, using the example of the geosystem doctrine.