diffusion

Kinetic coefficients of ion transport in a porous medium based on the Enskog–Landau kinetic equation

Normal solutions of the Enskog–Vlasov–Landau kinetic equation were obtained within the model of positively and negatively charged solid spheres for the system ion solution – porous medium.  The Chapman–Enskog method was applied.  Analytical expressions for coefficients of viscosity, thermal conductivity, diffusion of ions in the system ionic solution – porous medium were derived by constructing the equations of hydrodynamics on the basis of normal solutions of the kinetic equation.

Mathematical modeling of impurity diffusion process under given statistics of a point mass sources system. II

Modeling of the impurity diffusion process in a layer under the action of a system of random point sources is carried out.  Mass sources of different power are uniformly distributed in a certain internal interval, that may also coincide with the entire region of the layer.  The statistics of random sources is given.  The solution of the initial-boundary value problem is found as the sum of the homogeneous problem solution and the convolution of the Green's function with the system of the random point sources.  Averaging of the solution is performed on the internal subinterval and in the ent

A generalized diffusive IS-LM business cycle model with delays in gross product and capital stock

In this paper, we suggest a diffusive and delayed IS-LM business cycle model with interest rate, general investment and money supply under homogeneous Neumann boundary conditions.  The time delays are respectively incorporated into capital stock and gross product.  We first demonstrate the model's sound mathematical and economic posing.  By examining the corresponding characteristic equation, the local stability of the economic equilibrium and the existence of Hopf bifurcation are proved.

Global stability of fractional partial differential equations applied to the biological system modeling a viral infection with Hattaf time-fractional derivative

In this article, we study the global stability of fractional partial differential equations applied to the biological system modeling a viral infection.  The reaction in the proposed biological system is described by the new generalized Hattaf fractional (GHF) derivative.  However, the diffusion is modeled by the Laplacian operator.

Mathematical modeling of impurity diffusion process under given statistics of a point mass sources system. I

The model of the impurity diffusion process in the layer where a system of random point mass sources acts, is proposed.  Mass sources of various power are uniformly distributed in a certain internal interval of the body.  Statistics of random sources are given.  The solution of the initial-boundary value problem is constructed as a sum of the homogeneous problem solution and the convolution of the Green's function and the system of the random point mass sources.  The solution is averaged over both certain internal subinterval and the entire body region.  Simulation unit

Mathematical analysis of a spatiotemporal dynamics of a delayed IS-LM model in economics

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.

USE OF MODIFIED ADSORBENTS TO REMOVE PESTICIDES FROM WASTEWATER

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.

Mathematical modeling and analysis of Phytoplankton–Zooplankton–Nanoparticle dynamics

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.

STUDY OF KINETIC PROCESSES DURING CANDIED FRUITS INDUSTRIAL SATURATION

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.

Circular Model of Interaction of Enterprise Innovation Capacity and Exports

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.