mathematical model

In this article, we propose a PEARM mathematical model to depict the dynamic of a population that reacts in the spread of the gaming disorder with media coverage.  The basic reproduction number and existence of free equilibrium point and endimec equilibrium point are obtained with same fundamental properties of the model including existence and positivity as well as boundedness of equilibria are investigated.  By using Routh–Hurwitz criteria, the local stability of free equilibrium point and endimec equilibrium point are obtained.  Also, we propose an optimal strategy to implement the optim

Single-phase commutator motors (SPCM) with sequential excitation have a simple design and low cost, and therefore promising for use in the drive of household appliances and electric hand tools. This necessitates the creation of mathematical models of SPCM, which would allow both the development of new and modernization of existing models of such motors. The aim of the article is to create an engineering mathematical model of the magnetic state of SPCM using circular methods.

The results of mathematical modelling of the turbine unit with the K-325-23.5 steam turbine are presented. The mathematical model of the turbine is a system of equations for the components of the heat-balance diagram and the main dependencies of its operating characteristics obtained through the thermal full-scale tests. The developed mathematical model allows adjusting the results of the full-scale tests, creating normative characteristics and conducting research of the intermediate modes of the turbine operation.

In this work, research the essence of the wood drying process in a periodic wood drying chamber. This paper provides a mathematical model of a wood drying chamber, which describes the general essence of physical drying processes using the equipment available in the wood drying chamber. This approach allows to take into account the physical parameters of the necessary equipment, such as heaters, fans, humidifying nozzles or other. This approach also allows to ignore some design characteristics that may differ depending on the type of wood drying chamber.

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.

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.

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

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.

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.

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.