# mathematical model

## Simulation of Change in Density and Viscosity of Crude Oil When Mixing

The deviation of density and viscosity values of oil mixtures from those calculated according to the additivity rule has been examined. Mathematical models have been developed for determining the properties of mixtures with different compositions taking into account the group composition of the source components. Mixtures containing components with a high content of alkanes and a low content of arenes have been found to be characterized by extreme deviations of density towards the maximum and kinematic viscosity towards the minimum.

## Mathematical Model of Movement of Bulk Material in a Vibratory Separator

Aim. The aim is to construct the mathematical model of the movement of loose material in a vibrating separator. Method. The calculation scheme of the vibration separator with two eccentric vibrators with an independent drive was built. Based on the scheme, it is assumed that the vibration separator performs only vertical oscillations in the plane of rotation of the eccentric vibrators.

## 3D model and numerical algorithm for gas filtration in porous media

The article presents a three-dimensional mathematical model of the gas filtration process in porous media and a numerical algorithm for solving the initial-boundary value problem.  The developed model is described using the nonlinear differential equation in partial derivatives with the appropriate initial and boundary conditions.  The proposed mathematical apparatus makes it possible to carry out hydrodynamic calculations taking into account changes in the main factors affecting the process under consideration: permeability, porosity, and thickness of layers, gas recovery coefficient, visc

## Influence of vehicle acceleration intensity on dual-mass flywheel elements and transmission load

Modern high-torque low-speed internal combustion engines (ICEs) generate torsional vibrations close in disturbance frequency to gearboxes natural oscillation frequencies. Effective absorption of such oscillations requires a new torsional vibration damper between the internal combustion engine and gearbox design, which is implemented in the form of a dual-mass flywheel (DMF). One of the main reasons for DMF failure is its spring components destruction.

## Dynamics of Adsorption of Copper Ions in Fixed-Bed Column and Mathematical Interpretation of the First Stage of the Process

The dynamics of the adsorption process in the fixed-bed column was experimentally studied on the example of the system natural zeolite - water solution of copper salt with low concentrations, which are characteristic for wastewater treatment processes from toxic contaminants. The initial curves of the adsorption process for the height of the sorbent layer of 5 and 7 cm were constructed. The equilibrium of such processes can be described by Henry's linear equation. The adsorption process in the layer consists of two stages, which are examined in the study.

## Physical and Mathematical Models of Target Component Extraction from Rectlinear Capillaries

The extraction of the solid component from the rectilinear capillary has been investigated. The presence of two extraction zones (convective and molecular diffusion) was confirmed. The effect of the system vacuumizing on the extraction rate has been studied. The convection zone during vacuumizing was found to be increased due to the appearance of the vapor phase bubbles. The mass transfer coefficients for the convective zone have been determined.

## MULTIPARAMETRIC MODEL OF FREQUENCY TRACTION DEVICE AND INTERFACE OF THE PRORAM FOR ITS ANALYSIS

The article is devoted to the problem of designing frequency tracking devices in a complex signal and noise situation. The article presents a mathematical model of the device, which takes into account possible structural and parametric changes of the device, changes in the frequency of the input signal, its angular modulation and time-varying noise level in the input mixture. Developed and described software application for the analysis of this model allows you to quickly change the values of parameters and monitor the response of the device to changes in the input signal.

## Solving the Forward Kinematics Problem for a Welding Manipulator With Six Degrees of Freedom

The article proposes a solution of the forward kinematics problem for a welding manipulator with six degrees of freedom. Solving this problem is the first necessary step in creating a control system for this manipulator. This will make it possible to determine the displacement, accelerations and moments in each of the manipulator parts and will ensure accurate positioning of the welding tool.

## Multiplicity of Overvoltages during Arc Single Phase Earth Faults in 35 kV Electrical Grids

The arc overvoltages during the single phase to earth faults in electrical distribution grids of 6-35 kV are the object of the research in this paper. The development of 35 kV distribution electrical grids is accompanied by the construction of new overhead and cable power lines. It causes a change of the capacitive earth fault current in the grids and also affects the multiplicity of overvoltages in electrical distribution grids during the single phase to earth faults.

## Mathematical modeling of convection drying process of wood taking into account the boundary of phase transitions

The article deals with constructing and implementing mathematical models of non-isothermal moisture transfer during drying of anisotropic capillary-porous materials, in particular wood, taking into account the movement of the evaporation zone for non-steady drying schedules, as well as to the development of effective analytical and numerical methods for their implementation.  An analytical-numerical method for the determination of non-isothermal moisture transfer under non-steady schedules of the drying process has been developed, taking into account the dynamics of the phase transition bou