diffusion

The purpose of this research is to suggest and analyze a spatiotemporal of an IS-LM model with two delays, interest rate, liquidity preference and general investment function.  The first delay into the proposed model refers to the time delay between the decision of investment and his implementation.  However, the second one represents the delay in investment production.  The well posedness of the model is proved.  The stability analysis and the existence of Hopf bifurcation are obtained.  Furthermore, numerical examples that confirm the analytical results are shown.

The migration of highly concentrated pesticide solutions in the soil has been experimentally studied. A mathematical model of the diffusion process in the soil environment has been developed. Based on the mathematical model, a system of equations for calculating the duration and intensity of the process depending on environmental parameters was obtained. The dependence of the process velocity on the direction of the diffusion front is determined, and the diffusion coefficients, kinetic coefficients of the diffusion process and the diffusion front velocity were calculated.

In this paper, we investigate the population dynamics of phytoplankton–zooplankton–nanoparticle model with diffusion and density dependent death rate of predator.  The functional response of predator in this model is considered as Beddington–DeAngelis type.  The stability analysis of the equilibrium points is observed by applying the Routh–Hurwitz criterion.  Numerical simulations are given to illustrate the theoretical results.

The process of saturation of sucrose particles of pumpkin fruits is considered. An experimental setup for saturation of fruit particles with sugar under conditions of intensive pneumatic mixing was developed. The kinetic dependences of the saturation of candied fruits and changes in the concentration of sugar syrup under various temperatures were obtained. The saturation conditions are compared for various ratios of «candied fruit: syrup». A mathematical generalization confirms the ratio “candied fruit: syrup” selected by the authors of the article.

In the current conditions of globalization and European integration, the need for the development of innovative economy and activation of export activity, innovation capacity is one of the key drivers of export diversification towards science-intensive products. An important prerequisite for starting and developing export activity is not only the availability of sufficient innovation potential, but also the willingness, need and feasibility of introducing and commercializing innovative products in foreign markets.

The article presents the results of theoretical and experimental studies on the determination of the coefficients of internal diffusion of moisture from capillary-porous materials of plant origin during filtration drying, in particular, beet pulp, a by-product of sugar production.  A model based on the solution of the internal diffusion differential equation with the corresponding initial and boundary conditions were used to find the internal diffusion coefficient. 

Processes of self-assembly were studied in the magnetic polymer carbon nanocomposites doped with cobalt nanoclusters. These processes proceed due to the diffusion of magnetic nanoparticles stimulated by a combined effect of an outer steady magnetic fields and heating. The obtained polymer composites are promising for practical applications.

The structure of an emulsion formed in wastewater from edible oils production has been investigated. The type of emulsifier has been determined and the method of emulsion destruction has been proposed, providing further quality treatment of wastewater via liquid-extraction method. The resulting equilibrium and operating lines of the process were received. The number of transfer stages has been determined. The mathematical model of liquid-extraction wastewater treatment was built.

The effect of light wave length on the rate of carbon dioxide absorption by microalgae has been studied. The mechanism of transfer of carbon dioxide from the air into the internal environment of the cells of microalgae has been described. The coefficient of microalgae growth based on the mathematical model has been determined. The analytical dependence of the mentioned coefficient on the light wave length has been obtained. The optimum length of light wave has been determined to design the flow chart for eliminating carbon dioxide from industrial gas emissions by the biological method.