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The study of thermal convection in porous media saturated by nanofluid and microorganisms is an important problem for many geophysical and engineering applications. The concept of a mixture of nanofluids and microorganisms has attracted the interest of many researchers due to its ability to improve thermal properties and, as a result, heat transfer rates. This property is actively used both in electronic cooling systems and biological applications. Thus, the purpose of this research is to study biothermal instability in a porous medium saturated by a water-based nanofluid containing gyrotactic microorganisms in the presence of a vertical magnetic field. Given the presence of an external magnetic field in both natural and technological situations, we were motivated to perform this theoretical research. Using the Darcy-Brinkman model, a linear analysis of the convective instability has been considered for both-free boundaries, taking into account the effects of Brownian diffusion and thermophoresis. The Galerkin method was used to perform this analytical study. We have established that heat transfer is accomplished by stationary convection without oscillatory movements. In stationary convection regimes, metal oxide nanofluids (Al2O3), metallic nanofluids (Cu, Ag), and semiconductor nanofluids (TiO2, SiO2) are analyzed. Increasing the Chandrasekhar and Darcy numbers improve system stability significantly, but increasing porosity and modified bioconvection Rayleigh-Darcy number speed up the beginning of instability. To determine the transient behavior of heat and mass transports, a non-linear theory based on the representation of the Fourier series method is applied. In small time intervals, the transitional Nusselt and Sherwood numbers exhibit an oscillatory character. The Sherwood numbers (mass transfer) in the time interval reach stationary values faster than the Nusselt numbers (heat transfer). This research might help with seawater convection in the oceanic crust as well as the construction of biosensors.

The efficiency of limiting quantities as a tool for describing physics at various spatio-temporal scales is shown. Due to its universality, limit values allow us to establish relationships between, at first glance, distant from each other's characteristics. The article discusses specific examples of the use of limit values to establish such relationships between quantities at different scales. Based on the principle of reaching the limiting values on the event horizons, a connection was obtained between the Planck values and the values of the Universe. The resulting relation can be attributed to relations of the Dirac type - the coincidence of large numbers that emerged from empirical observations. In the article, the relationships between large numbers of the Dirac type are established proceeding, in a certain sense, from physical principles - the existence of limiting values. It is shown that this ratio is observed throughout the evolution of the Universe. An alternative way of solving the problem of the cosmological constant using limiting values and its relation to the minimum spatial scale is discussed. In addition, a one-parameter family of masses was introduced, including the mass of the Universe, the Planck mass and the mass of the graviton, which also establish relationships between quantities differing by 120 orders of magnitude. It is shown that entropic forces also obey the same universal limiting constraints as ordinary forces. Thus, the existence of limiting values extends to informational limitations in the Universe. It is fundamentally important that on any event horizon, regardless of its scale (i.e., its gravitational radius), the universal value of limit force c4/4G is realized. This allows you to relate the characteristics of the Universe related to various stages of its evolution.

In this paper we studied the weakly nonlinear stage of stationary convective instability in a nonuniformly rotating layer of an electrically conductive fluid in an axial uniform magnetic field under the influence of: a) temperature modulation of the layer boundaries; b) gravitational modulation; c) modulation of the magnetic field; d) modulation of the angular velocity of rotation. As a result of applying the method of perturbation theory for the small parameter of supercriticality of the stationary Rayleigh number nonlinear non-autonomous Ginzburg-Landau equations for the above types of modulation were obtaned. By utilizing the solution of the Ginzburg-Landau equation, we determined the dynamics of unsteady heat transfer for various types of modulation of external fields and for different profiles of the angular velocity of the rotation of electrically conductive fluid.

In this paper, we investigated a new large-scale instability that arises in an obliquely rotating convective electrically conducting fluid in an external uniform magnetic field with a small-scale external force with zero helicity. This force excites small-scale velocity oscillations with a small Reynolds number. Using the method of multiscale asymptotic expansions, we obtain the nonlinear equations for vortex and magnetic disturbances in the third order of the Reynolds number. It is shown that the combined effects of the Coriolis force and the small external forces in a rotating conducting fluid possible large-scale instability. The linear stage of the magneto-vortex dynamo arising as a result of instabilities of -effect type is investigated. The mechanism of amplification of large-scale vortex disturbances due to the development of the hydrodynamic - effect taking into account the temperature stratification of the medium is studied. It was shown that a «weak» external magnetic field contributes to the generation of large-scale vortex and magnetic perturbations, while a «strong» external magnetic field suppresses the generation of magnetic-vortex perturbations. Numerical methods have been used to find stationary solutions of the equations of a nonlinear magneto-vortex dynamo in the form of localized chaotic structures in two cases when there is no external uniform magnetic field and when it is present.

Waste of the metalworking industry is analyzed from the point of view of their further processing. There is a lack of effective methods of processing and disposal of grinding sludge and, as a consequence, a negative impact on the environment. Existing methods of grinding sludge processing are analyzed. The expediency of applying the method of metallurgical remelting under the condition of special preparation of metal sludges of grinding machines is proved. It is established that briquettes for their further processing should have a certain density and purity. It is suggested to wash the sludge from the LCPM (lubricant-cooling process media) in special solutions using washing machines, briquettes and dry before using them in metallurgical remelting. In order to determine the technological parameters of the process of briquetting sludge grinding machines and drying of briquettes, the effect of pressing pressure, binder concentration and concentration of liquid (water) on the density of briquette was experimentally investigated. Appropriate mathematical dependencies and graphs of surfaces were obtained. It was found that the most significant factor influencing the density of the briquette is the pressure of the press, less significant – the concentration of liquid and binder. In the case of increasing water concentration, the density of the briquette decreases. It is recommended to prevent the briquette from spilling out after drying, to add a binder element of 3–5 % by weight of dry sludge. To dissolve the binder, water is added, the optimal concentration of which is 6–8 %. Technological pressing parameters are recommended.

In this paper the stability of the non-uniformly rotating cylindrical plasma in the axial uniform magnetic field with the vertical temperature gradient is investigated. In the approximation of geometrical optics a dispersion equation for small axisymmetric perturbations is obtained with the effects of viscosity, ohmic and heat conductive dissipation taken into account. The stability criteria for azimuthal plasma flows are obtained in the presence of the vertical temperature gradient and the constant magnetic field. The Rayleigh-Benard problem for stationary convection in the non-uniformly rotating layer of the electrically conducting fluid in the axial uniform magnetic field is considered. In the linear theory of stationary convection the critical value of the Rayleigh number subject to the profile of the inhomogeneous rotation (Rossby number) is obtained. It is shown that the negative values of the Rossby number have a destabilizing effect, since the critical Rayleigh number becomes smaller, than in the case of the uniform rotation , or of the rotation with positive Rossby numbers . To describe the nonlinear convective phenomena the local Cartesian coordinate system was used, where the inhomogeneous rotation of the fluid layer was represented as the rotation with a constant angular velocity and azimuthal shear with linear dependence on the coordinate. As a result of applying the method of perturbation theory for the small parameter of supercriticality of the stationary Rayleigh number a nonlinear Ginzburg-Landau equation was obtaned. This equation describes the evolution of the finite amplitude of perturbations by utilizing the solution of the Ginzburg-Landau equation. It is shown that the weakly nonlinear convection based on the equations of the six-mode Lorentz model transforms into the identical Ginzburg-Landau equation. By utilizing the solution of the Ginzburg-Landau equation, we determined the dynamics of unsteady heat transfer for various profiles of the angular velocity of the rotation of electrically conductive fluid.

In this work, a large-scale instability of the hydrodynamic -effect in an obliquely rotating stratified nanofluid taking into account the effects of Brownian diffusion and particle flux under the influence of a temperature gradient (thermophoresis) is obtained. The instability is caused by the action of an external small-scale non-spiral force, which excites small-scale velocity oscillations with zero helicity and a low Reynolds number. Nonlinear equations for large-scale motions are obtained using the method of multiscale asymptotic expansions by a small parameter (Reynolds number). A linear large-scale instability of hydrodynamic -effect is investigated depending on the parameters of rotation , temperature stratification , and concentration of nanoparticles . A new effect of the generation of large-scale vortex structures in nanofluid at is associated with an increase in the concentration of nanoparticles is obtained. The maximum instability increment is reached at inclination angles for the Prandtl numbers , and for the Prandtl numbers at inclination angles . It has been found that the frequency changing of the parametric impact will make it possible to control and track the generation of large-scale vortex structures. It is shown that circularly polarized Beltrami vortices appear in nanofluid as the result of new large-scale instability development. In this paper, the saturation regime of large-scale instability in an obliquely rotating stratified nanofluid with an external small-scale non-spiral force is investigated. In the stationary regime was obtained a dynamic system of equations for large-scale perturbations of the velocity field. Numerical solutions of this system of equations are obtained, which show the existence of localized vortex structures in the form of nonlinear Beltrami waves and kinks. The velocity profile of kink tends to be constant at large Z values.

We found a new large-scale instability, which arises in the rotating conductive fluid with small-scale turbulence. Turbulence is generated by small-scale external force with a low Reynolds number. The theory is built simply by the method of multiscale asymptotic expansions. Nonlinear equations for vortex and magnetic perturbations obtained in the third order for small Reynolds number. It is shown that the combined effects of the Coriolis force and the small external forces in a rotating conducting fluid possible large-scale instability. The large-scale increments of the instability, correspond to generation as the vortex and magnetic disturbances. This type of instability is classified as hydrodynamic and MHD alpha-effect. We studied the stationary regimes of nonlinear equations of magneto-vortex dynamo. In the limit of weakly conducting fluid found stationary solutions in the form of helical kinks. In the limit of high conductivity fluid was obtained stationary solutions in the form of nonlinear periodic waves and kinks.

The directed network of telephone subscribers is considered in the article. It can be described as a dynamic network with vertices that correspond to the subscribers of the telephone network and emerging directional edges that correspond to the connections between the respective subscribers. The position of the edge and its direction is determined by the incoming and outgoing calls from the corresponding vertices. The subject of the article is the statistical properties of the connections of a certain subset of telephone network subscribers. Such connections are dynamic in nature due to their appearance and disappearance. The number of outgoing (or incoming) connections occurred during a day at a selected vertex is used as the main characteristic. The distribution density of the number of outgoing (or incoming) connections (or calls) of such a network has been analyzed using the experimental data. It has been shown that such a distribution density over the number of calls obeys the lognormal distribution density, which depends on the two parameters. The values of two parameters, namely the mean value and the variance, determining the lognormal distribution density are established. The reasons for the appearance of a lognormal distribution density over the number of incoming (or outgoing) connections have been discussed. The statistical properties of other groups of subscribers have been considered as well. In particular, the group that makes a large number of outgoing calls to various subscribers of the telephone network has been selected for a separate study. The members of this group, who create and distribute spam can be called spammers. It has been shown that these groups, spammers for example, also obeys the lognormal distribution density over the number of calls but they are characterized by the different mean value and variance.

The survey covers a main achievements in the field of dynamo theory. Applications of the model of turbulent convective dynamo to the problem of generation of a large-scale vortexes and magnetic structures in the solar photosphere are discussed. Investigated are the new models of the vortex dynamo in a rotating fluid with small-scale external force. The main results in these models are obtained by the method of multiscale asymptotic expansions. The results of numerical analysis of nonlinear equations of a magnetovortex dynamo in a stationary mode are provided. Solutions are found in the form of spiral kinks, periodic nonlinear waves and solitons, which are also considered in the survey.

The review covers the main achievements in the field of the dynamics of strongly localized vortices in two-dimensional hydrodynamic media. The types of point vortices and their motion equations are discussed. The consideration is focused on dipole point vortices, a new type of point vortices. Investigated is the influence of the boundaries of the vortices on the character of their motion, and some new stationary fluid flows. The impact of potential waves on the interacting point vortices leads to new effects also considered in the review.

The majority of the existing testing systems provide access to test jobs by means of various software: password entry from the keypad, a voice in a microphone, scanning of fingerprints, the signature of the student or other devices. Thus the subsequent course of testing, as a rule, isn't traced that can be a basis for abuses. The system developed in Khmelnytsky national university of-line of testing with photo video fixing is integrated with the parameter assigned to each student – «a trust rating». Change of this parameter, changes testing procedure for the student: from self-test from any point of the world, to passing of this procedure on the remote information and communication center of university and up to testing under monitoring of the teacher at the central university. As a result of it the teacher-tutor receives the protocol of testing which contains the photos of all procedure of monitoring and results of responses of the student to each question taken through an accidental interval of time. Results of the protocol the teacher are claimed or void. Results of photo video fixing and responses to test jobs allow the teacher to receive information for the analysis of educational process of the student, an assessment of quality of tests, and opportunity with their help to evaluate the level of knowledge of the student.

The spectrum of emission of a composite particle with one degree of freedom in a constant electric field is obtained in the paper. The effectiveness of emission of such particle is compared with the structureless particle having the same parameters. The power of emission of composite particle is several digits more than that of a structureless particle. The dependence of the main characteristics of the emission spectrum on the parameters of the composite particle is discussed.

The features of the development of interactive virtual practical training courses for distance learning are examined in the article. The authors propose their own methods of development tools such disciplines as virtual simulation or video-on labs.

In recent times, the mechanical properties of the surface layer have changed in some areas of the surface of the grant. The mechanical properties of the soil along its thickness become discretely variable. The soil ceases to be monolithic. It becomes two-layered. The conditions for the construction of structures whose foundation height does not exceed the thickness of the surface layers should take into account the latter. The purpose of the work is to substantiate and formulate an algorithm for determining the parameters of the stress-strain state of the soil of a two-layer structure and to establish the dependence of soil surface deformations on the mechanical properties of the formed soil layers. The soil of the two-layer structure is considered as a two-layer body, of unlimited height, of limited dimensions in the orthogonal direction. An external normal load acts on the soil. Soil layers were considered linearly elastic, isotropic with excellent mechanical properties. It was taken into account that the contact surfaces of the layers deform together without the formation of gaps and overlapping. The interaction forces of the layers are equal and oppositely directed. The indicators of the flat stress-strain state of the layers were determined by the method of the classical linear theory of elasticity using the biharmonic Ery stress function. We took into account the load of the limited part of the outer surface of the first layer or its movement under the action of the structure and the conditions of compatibility of deformation of the layers. Formulated linear systems of algebraic equations. By solving it, the unknown coefficients of the stress function were determined. The dependences of the parameters of the stress-strain state of the layers of the two-layer soil were formulated. It was established that the change in the compression modulus of the surface layer of the soil significantly affects the deformation of the soil surface under the action of external normal load and is practically independent of other mechanical characteristics of the surface layer of the soil.

The paper defines a class of Hamiltonian systems whose phase flows are exact solutions of the two-dimensional hydrodynamics of an incompressible fluid. The properties of this class are considered. An example of a Lagrangian one-dimensional system is given, which after the transition to the Hamiltonian formalism leads to an unsteady flow, that is, to an exact solution of two-dimensional hydrodynamics. The connection between these formalisms is discussed and the Lagrangians that give rise to Lagrangian hydrodynamics are introduced. The obtained results make it possible to obtain accurate solutions, such as phase flows of special Hamiltonian systems.

In this paper, the influence of gravitational modulation on weakly nonlinear biothermal convection in a porous rotating layer is investigated. We consider a layer of porous medium saturated with Newtonian fluid, containing gyrotactic microorganisms, and subject to gravitational modulation, rotation, and internal heating. To analyze linear stability, it is sufficient to represent disturbances in the form of normal modes, while nonlinear analysis includes a truncated Fourier series containing a harmonic of the nonlinear interaction. A six-dimensional nonlinear Lorentz-type model is constructed, exhibiting both reflection symmetry and dissipation. We determined heat and mass transfer using a weakly nonlinear theory based on the representation of a truncated Fourier series. Additionally, the behavior of nonstationary Nusselt and Sherwood numbers was investigated by numerically solving finite amplitude equations. Applying the expansion of regular perturbations in a small parameter to a six-dimensional model of Lorentz equations with periodic coefficients, we obtained the Ginzburg-Landau (GL) equation. This equation describes the evolution of the finite amplitude of the onset of convection. The amplitude of convection in the unmodulated case is determined analytically and serves as a standard for comparison. The study examines the effect of various parameters on the system, including the Vadasz number, modified Rayleigh-Darcy number, Taylor number, cell eccentricity, and modulation parameters such as amplitude and frequency. By varying these parameters, in different cases, we analyzed heat and mass transfer, quantitatively expressed by the Nusselt and Sherwood numbers. It has been established that the modulation amplitude has a significant effect on the enhancement of heat and mass transfer, while the modulation frequency has a decreasing effect.

Despite the widespread use of the term "municipal solid waste" (MSW), the main regulatory and legislative documents of Ukraine use the term "household waste". International practice also does not have a clear definition of the "municipal solid waste" concept, however, there are a number of related terms. Municipal solid waste is defined as a waste that is generated in the course of human activity, accumulated in residential buildings and social institutions and considered as unsuitable for further use at places of its generation. As for the related terms used in foreign and national practice, the term “household waste”, i.e. waste generated directly by households, is more appropriate. Municipal solid waste is a heterogeneous mixture that has a complex waste composition and its quantitative and qualitative characteristics are not constant and depend on characteristics of a certain country, region, city or town where it was generated, season and other factors. Growing volumes of municipal solid waste is one of the components of growing anthropogenic load that poses a threat to environmental safety of the country's regions and public health and negatively affects the state of our environment. The main methods of such solid waste management in Ukraine include landfilling, incineration, recycling and recovery. Out of the total annual waste volume generated on the post-Soviet territories, 93% are taken to landfills or dumpsites, 4% – incinerated, and only about 3% – recycled. Therefore, creation and implementation of an effective system of solid waste management is an important task for ensuring environmental safety and sustainable development of the country's regions. Moreover, solid waste is a significant reserve for obtaining secondary material resources. According to the circular economy concept, almost all components of solid waste should be reused for production of new items. This will minimize negative impact on the environment and allow rational use of natural resources. The article analyses the current state of municipal solid waste management system in Odesa Region and assesses resource value of such waste. Secondary raw materials worth of almost UAH 1.4 million can be produced annually from the total flow of municipal solid waste in Odesa Region. And this figure does not take into account liquidity of food and other waste. After establishing an effective food and other organic waste management system, such amount may be significantly increased. Separation of resource-value components from the total solid waste flow and their subsequent use will help to reduce technogenic load on the environmental natural components and improve the overall environmental situation in Odesa Region.

This paper investigates the impact of gravity modulation on weakly nonlinear magnetoconvection in a nanofluid layer that is nonuniformly rotating. The fundamental equations are obtained for the Cartesian approximation of the Couette flow using the Boussinesq approximation and gravitational modulation. The weakly nonlinear regime is analyzed using the method of perturbations with respect to the small supercritical parameter of the Rayleigh number, considering the effects of Brownian motion and thermophoresis in the nanofluid layer. Heat and mass transfer are evaluated in terms of finite amplitudes and calculated from the Nusselt numbers for the fluid and the volume concentration of nanoparticles. The findings demonstrate that gravitational modulation, nonuniform rotation, and differences in the volume concentration of nanoparticles at the layer boundaries can effectively control heat and mass transfer. Additionally, the negative rotation profile has a destabilizing effect. The study shows that the modulated system conveys more heat and mass than the unmodulated system.

In this paper, the magnetohydrodynamic (MHD) flow of a ternary hybrid ferrofluid over a stretching/shrinking porous sheet in the presence of radiation and mass transpiration is studied. The ternary hybrid nanofluid is formed by suspending three types of nanoparticles for enhancing heat transfer. The nanoparticles of copper, (Cu) iron oxide (Fe3O4), and cobalt ferrite (CoFe2O4) are suspended in water in this study, producing in the combination Cu-Fe3O4-CoFe2O4-H2O. Brownian motion and thermophoresis are integrated into the ternary hybrid ferrofluid model. Similarity transformations convert the governing partial differential equations into ordinary differential equations. The boundary value problem (BVP) is used in the Maple computer software to solve transformed equations numerically. The computed results for relevant parameters such as velocity profile, temperature profile, skin friction coefficient, local Nusselt and Sherwood numbers are visually shown and explained in detail.

The review highlights the main achievements in the theory of the vortex dynamo in rotating media. Various models of a vortex dynamo in rotating media are discussed: a homogeneous viscous fluid, a temperature-stratified fluid, a moist atmosphere, and a stratified nanofluid. The main analytical and numerical results for these models obtained by the method of multiscale asymptotic expansions are presented. The main attention is paid to models with a non-spiral external force. For a rotating moist atmosphere, characteristic estimates of the spatial and temporal scales of the generated vortex structures are obtained. New effects of the vortex dynamo in a rotating stratified nanofluid, which arise due to thermophoresis and Brownian motion of nanoparticles, are shown. The results of the analysis of the nonlinear equations of the vortex dynamo in the stationary regime are presented in the form of spiral kinks, periodic nonlinear waves, and solitons.

Within the generalized prisoner's dilemma, the evolution of a population with a complete set of behavioral strategies limited only by memory depth has been examined. Evolution considers the pairing of strategies, in accordance with the iterated prisoner's dilemma. In doing so, each strategy interacts with each, including itself. Each subsequent generation of the population consistently loses the most profitable behavior strategies of the previous generation. Increasing population memory has been shown to be evolutionarily beneficial. The winners of evolutionary selection consistently are the agents with maximum memory. The concept of strategy complexity has been introduced. Collective variables are introduced to obtain the average of the family of strategies and their changes over time are studied. Strategies that succeed in natural selection have been shown to have maximum or near maximum complexity. An alternative evolution of a family of strategies limited only by memory depth is considered. In each generation, a strategy that maximizes the point of evolutionary benefits is removed from the family. Such an alternative evolution leads to significant changes in the family compared to the normal evolution. In some ways, alternative evolution maintains maximum memory depth and complexity even more than normal evolution. The main difference is the stationary strategies being absolute aggressive against each other. The stationary family is formed by the strategies being the most aggressive towards each other. Memory depth and complexity of strategies, as in normal evolution, are evolutionarily beneficial properties. The universal relation between the aggressiveness of the population and the number of points of evolutionary advantages that the strategy receives on average per turn is considered. On the whole, the universal link between average aggression and the number of strategy payoffs per turn is maintained.