ON A MATHEMATICAL MODEL DESCRIBING OPTIMAL PROCESSING MECHANISM OF DISPERSED GRANULAR MATERIALS IN GRAVITATIONAL FLOW WITH HORIZONTAL OR INCLINED VIBRATING SIEVE CLASSIFYING SCREENS

The investigation of motion and gravitational processing of disperse granular materials is very important for solution of a wide spectrum of technological processes, including the chemical technology of treatment (with or without the decoration-compression procedure) of granular mineral fertilizers and their drying and sorting/separation by means of vibrating sieve classifying screens, in particular. In this work, we have used the apparatus of the theory of continuous media for the mathematical modelling of dynamics of disperse granular materials, and by this we assume that a property of these materials is the distribution of a solid granular component inside of them. The elaborated mathematical model is based on the volume conservation law for granular components, on the momentum conservation law, as well as on the equations for stress tensor in the granular mineral fertilizers and equations for description of the Coulomb granular mineral fertilizers

TO THE ISSUE OF FINDING THE STOICHIOMETRIC COEFFICIENTS IN THE CHEMICAL REACTIONS

In the present paper, on the basis of the theory of inverse and ill-posed problems, an algorithm is proposed that allows to unambiguously determine the stoichiometric coefficients in the equations of chemical reactions of any type, including redox reactions and acid-base reactions, and, regardless of whether the constructed system of linear algebraic equations for the desired stoichiometric coefficients is underdetermined (i.e. there are fewer equations than unknowns) or overdetermined (i.e. there are more equations than unknowns). The proposed algorithm is a regularized algorithm (according to Tikhonov), which ensures that, in a computer implementation, possible computational errors will not make the comprised system of linear algebraic equations to be incapable of solving

SCIENTIFICALLY SUBSTANTIATED GUIDELINES FOR PHYSICO-MATHEMATICAL MODELLING OF LASER SURFACE-TREATMENT OF WEAR-RESISTANT IMPLANTS FOR HUMAN JOINT REPLACEMENTS

This paper presents the main results from a set of guidelines on the physico-mathematical modelling of laser surface-treatment of wear-resistant implants for human joint replacements. These guidelines contain synthesized and documented procedure, theoretical and practical recommendations, which are provided by researchers in the Nanomaterials Laboratory under the Institute of Fundamental Science and Innovative Technologies, Liepaja University. The present paper does not attempt to cover all aspects of physical and mathematical modelling, but draws together many key aspects concerning theoretical and practical difficulties, in the overcoming of what researchers of the Nanomaterials Laboratory, in particular, the authors of the present paper, have sufficient skills

Analytic-Numerical Modeling and Investigation of Nanostructures' Dynamics on Material Surfaces After Laser Irradiation

The work is devoted to modeling the formation and behavior of solid nano-sized particles on the surface of materials. In the simulation, it is assumed that the main processing technology of surface nanostructures is laser irradiation, which causes the Brownian motion of nanoparticles, due mainly to thermal fluctuations: if the temperature around the nanoparticles is uniformly distributed, the time average of the Brownian fluctuations is zero; however, if there is a temperature gradient around the nanoparticles, the thermal fluctuations affect the nanoparticle in different ways from different sides, and there is a force like the thermophoretic force, biasing the average position of the nanoparticle. When building a 1D model of the formation and flow behavior of nanoparticles, three important assumptions are introduced: the impact of nanoparticles on the process of irradiation is negligible; the impact of nanoparticles on each other as compared to the effect of laser irradiation on them is also negligible; and nanoparticles after laser irradiation can move both forward and backward and at every fixed period of time, moving the nanoparticles does not impose any steric constraints. Under the above assumptions, a 1D continuous model is built, implicit and explicit finite difference schemes to solve it are developed; their convergence and order of convergence are studied; an output condition ensuring the stability of the explicit difference scheme is obtained, the unconditional stability of implicit difference scheme is proven, and software for computer implementation of some of the obtained analytical and numerical results developed.

On one Mathematical Model for Dynamics of Propagation and Retention of Heat over New Fibre Insulation Coating

In circumstances, when it is important to replace insulation materials with high content of emissions during production it is necessary to create new heat and sound insulation material, which eliminates CO2 emissions, develop its production techniques and technological machinery – raw material chopper, pulp mixer, termopress, dryer chamber, formatting knifes, determine technical control parameters and control equipment, develop mathematical model of the material and calculation methods for design works. It is necessary to design, manufacture and experimentally test the respective technological equipment for insulation production pilot plant. To get exact physical parameters it is necessary design, manufacture and test unique laboratory equipment for determining the properties of insulation material. The mathematical model describing the dynamics of propagation and retention of heat over fibre insulation coating by taking "inner" specificities (graininess and porosity of layered structure of the considered fibre insulation) of heat insulator into account is proposed in the present paper

DETERMINATION OF SUBJECTS’ SIGNIFICANCE RATE AND OPTIMAL INFORMATION CONTROL IN SOCIAL NETWORKS

This paper examines social networks, where each agent is characterized by some dynamic parameters, the dynamics of which is resulting from the influence of other agents having their own objective functions and limiting factors, as well as from control/governing body with its own objective function. In this paper, referring to the type of social networks described above, the following two interrelated problems are investigated: the problem of determining the degree of information influence on social networks; the problem of finding optimal control in social networks.

MODELLING AND INVESTIGATION OF THE DEPENDENCE OF SUPERHYDROPHOBIC PROPERTIES OF NANOSURFACES ON THE TOPOLOGY OF MICROCHANNELS

In the Cassie-Baxter state anisotropic superhydrophobic surfaces have high lubricating properties. Such superhydrophobic surfaces are used in medical implants, aircraft industry, vortex bioreactors etc. In spite of the fact that quantitative understanding of fluid dynamics on anisotropic superhydrophobic surfaces has been broadened substantially for last several years, there still are some unsolved problems in this field. This work investigates dynamics of a liquid on unidirectional superhydrophobic surfaces in the Cassie-Baxter state, when surface texture is filled with gas and, consequently, the liquid virtually is located on some kind of an air cushion. Energy of the interphase boundary liquid-gas is much smaller than energy of the interphase boundary solid-liquid, that is why the contact angle at wetting such surfaces differs a lot from the Young contact angle and depends on contact area ratio of liquid-gas and liquid-solid in visible contact of liquid and surface. Considering difference in energy obtained if we slightly shift the three-phase contact line, expression for macroscopic equilibrium contact angle, which describes the Cassie-Baxter state, can be deduced. In the work the design formula for computing local-slip length profiles of liquid on the considered superhydrophobic surfaces is obtained

Mathematical Modelling of Aquatic Ecosystem

In present paper we consider the complete statements of initial-boundary problems for the modelling of various aspects of aqueous systems in Latvia. All the proposed models are the evolutionary models: all they are nonstationary and continuous qualitative models having the dynamic parameters and aimed at analysis, evaluation and forecast of aqueous systems (reservoirs, lakes and seas). In constructing these mathematical models as research tools classic apparatus of differential equations (both ODE and PDE) as well as apparatus of mathematical physics were used.

MODELLING OF URBAN TRAFFIC FLOW

In this paper non-deterministic motion of urban traffic is studied under certain assumptions. Based on those assumptions discrete and continuous mathematical models are developed: continuous model is written as the Cauchy initial-value problem for the integro-differential equation, whence among other things it is obtained the Fokker-Planck equation. Besides, the sufficient condition ensuring the mathematical legitimacy of the developed continuous model is formulated

ON THE GINZBURG-FEINBERG PROBLEM OF FREQUENCY ELECTROMAGNETIC SOUNDING FOR UNAMBIGUOUS DETERMINATION OF THE ELECTRON DENSITY IN THE IONOSPHERE

In the present work, we investigate an inverse problem of frequency electromagnetic sounding for unambiguous determination of the electron density in the ionosphere. Direct statement of this problem is known as the Ginzburg-Feinberg problem that has, in general case, an essential nonlinearity. Inverse statement of the Ginzburg-Feinberg problem has the boundary-value formulation relative to two functions: the sought-for electric-field strength and the distribution of the electron density (or rather two-argument function appearing in the additive decomposition formula for distribution of the electron density) in the ionosphere. In the present work, we prove the existence and uniqueness of the solution of the Ginzburg-Feinberg problem as well as we propose the analytical method, permitting: first, to reduce it to the problem of integral geometry, and, thereupon, having applied the adjusted variant of the Lavrentiev's theorem, to reduce the obtained problem of integral geometry to the first kind matrix integral equation of Volterra type with a weak singularit