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 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

ON A 3D INITIAL-BOUNDARY VALUE PROBLEM FOR DETERMINING THE DYNAMICS OF IMPURITIES CONCENTRATION IN A HORIZONTAL LAYERED FINE-PORE MEDIUM

In the present paper, we propose an analytical approach for solving the 3D unsteady-state boundary-value problem for the second-order parabolic equation with the second and third types boundary conditions in two-layer rectangular parallelepipedic domain

DETERMINING COUNTRIES' POTENTIALS FOR SUCCESSFUL EXPORT OF LUXURIOUS AND BANKING SERVICES

Country's economic potential implies joint capability of the country's economy, its branches and enterprises to carry out production and economic activity, to create goods and services, to supply the demand of the population, to stimulate production and consumption development. Country's economic potential is defined by estimating different economic, social, ecological, scientific and technical, political and other criteria, which, as a rule, are interconnected and correlated. Each of these criteria includes heterogeneous set of economic, financial, social, political, juridical, educational, scientific and innovational, ecological, cultural and other factors, every single of which can consist of independent or indirectly correlated subfactors called indices or indicators. In this work we investigate the problem of estimating economic potentials of groups of countries according to their measurable economic, financial, social and other indicators in order to export bank and other luxurious services. The approach to solving the problem offered in this work is based on the apparat of the theory of inverse and ill-posed problems

3D MATHEMATICAL MODEL CHARACTERIZING THE DYNAMICS OF THE TEMPERATURE FIELD OF A WALL STRUCTURE WITH A DOUBLE-SIDED FACING FROM A SAPROPEL-HEMP COMPOSITE MATERIAL

In this paper, a 3D mathematical model is proposed to determine the dynamics of the temperature field in a three-layer composite sapropel-hemp slab. The proposed model consists of a system of three initial-boundary value problems with respect to the temperature function for each layer, respectively, and one initial-boundary value problem with respect to the unknown velocity of heat propagation along the thickness dimension of the composite sapropel-hemp slab.

ON THE ISSUE OF PLANNING SOWING AGRICULTURAL CROPS WITH THE MINIMUM RISK UNDER THE PRESENCE OF VARIOUS AGROCLIMATIC CONDITIONS

The present paper deals with one problem of quantitative controlling the seeding of the sown area by agricultural crops in different agroclimatic conditions. The considered problem is studied from the standpoint of three strategies: from the seeding planning perspective aiming at minimal risk associated with possible unfavourable agroclimatic conditions (a probabilistic approach is used); from the perspective of obtaining the maximum crops sales profit (a deterministic approach is used); from the perspective of obtaining the maximum crops harvest. For the considered problem, mathematical models are constructed (one probabilistic model and two deterministic models, respectively), their analytical solutions are found, and then, using a specific example, the application of the constructed and solved mathematical models is illustrated as well as the obtained numerical results are analysed.