The Mathematical Models of the Operation Process for Critical Production Facilities Using Advanced Technologies

The paper presents data on the problems of monitoring and diagnosing the technical conditions of critical production facilities, such as torpedo ladle cars, steel ladles. The accidents with critical production facilities, such as torpedo ladle cars, lead to losses and different types of damages in the metallurgical industry. The paper substantiates the need for a mathematical study of the operation process of the noted critical production facilities. A Markovian graph has been built that describes the states of torpedo ladle cars during their operation. A mathematical model is presented that allows determining the optimal frequency of diagnostics of torpedo ladle cars, which, in contrast to the existing approaches, take into account the procedures for preventive diagnostics of torpedo ladle cars, without taking them out of service. Dependence of the utilization coefficient on the period of diagnostics of PM350t torpedo ladle cars was developed. The results (of determining the optimal period of diagnostics for PM350t torpedo ladle cars) are demonstrated. The system for automated monitoring and diagnosing the technical conditions of torpedo ladle cars, without taking them out of service, has been developed and described.

Mathematical analysis of two-phase blood flow through a stenosed curved artery with hematocrit and temperature dependent viscosity

A two-phase blood flow model is considered to analyze the fluid flow and heat transfer in a curved tube with time-variant stenosis. In both core and plasma regions, the variable viscosity model ( Hematocrit and non linear temperature-dependent, respectively) is considered. A toroidal coordinate system is considered to describe the governing equations. The perturbation technique in terms of perturbation parameter ε is used to obtain the temperature profile of blood flow. In order to find the velocity, wall shear stress and impedance profiles, a second-order finite difference method is employed with the accuracy of 10−6 in the each iteration. Under the conditions of fully-developed flow and mild stenosis, the significance of various physical parameters on the blood velocity, temperature, wall shear stress (WSS) and impedance are investigated with the help of graphs. A validation of our results has been presented and comparison has been made with the previously published work and present study, and it revels the good agreement with published work. The present mathematical study suggested that arterial curvature increase the fear of deposition of plaque (atherosclerosis), while, the use of thermal radiation in heat therapies lowers this risk. The positive add in the value of λ1 causes to increase in plasma viscosity; as a result, blood flow velocity in the stenosed artery decreases due to the assumption of temperature-dependent viscosity of the plasma region. Clinical researchers and biologists can adopt the present mathematical study to lower the risk of lipid deposition, predict cardiovascular disease risk and current state of disease by understanding the symptomatic spectrum, and then diagnose patients based on the risk.

SOME ASPECTS ABOUT MATHEMATICAL MODELING FOR EPIDEMIC MANAGEMENT

The mathematical study of epidemics and their management has been performed for many years, however, in the last few years, new models have been published. Public health is considered very important and has to be monitored, as it is permanently under risk due to the appearance of even more types of microorganisms. Compartmental models, such as exponential models, SI, SIS, SIR, SEIRS, SEIAR, MESIR models, other generalized SIR models were and still are remarkable for studying the spread of an epidemic and for their simulations in software such as MATLAB, Maple, GLEAMviz, etc. The paper has two main objectives: a. to present new simulations in Maple and GLEAMviz for the spread of COVID-19; b. to suggest a generalization of the SIR model for analyzing the spread of COVID-19 and a simulation of it in GLEAMviz. The conclusions are that, generally, mathematical models show a value of a reproduction threshold, which can be used to forecast whether the pandemic is the increasing or decreasing phase, and that mathematical models and simulations in various programs facilitate the improvement of methods of analysis of an epidemic situation and the management of the public health system.

Mathematical Study of Nonlinear Mixed Convection Unsteady Flow in a Parallel Plate Inclined Channel in the Proximity of Time Periodic Boundary Conditions: Flow Reversal

This report is executed to examine the task of assimilating parameters on bipartite convection stream structure in a sloped pipeline while certain plate is disorderly warmed. The dictating motivation and energy identifications are ascertained and consequent expressions for thermal reading, liquid movement, fanning friction and stress flatten are acquired. The purpose of non-linear Boussinesq simulation is to escalate liquid movement, inverse stream generation at the channel plates, stress flatten, and fanning factor. In particular, the liquid motion escalates at the channel left portion and depletes at the channel right portion with the progress of time. A particular case of our development shows an excellent compromise with the previous consequences in the literature.

Mathematical modeling of the demographic dividend (DD) capture applied in economy.

The purpose of this work is to develop tools and techniques for modeling the capture of the Demographic Dividend. We presented the ordinary differential equation (ODE) system modeling the variation of economically dependent and economically non dependent populations. The system uses natality, natural mortality, infant mortality, migration (incoming and outgoing), and transfers. The mathematical study of this ODE system shows the existence of an equilibrium point whose stability depends on a certain number of system parameters. Numerical simulations of the resulting model were performed using scenarios approach.

Mathematical Study of a Two-Stage Anaerobic Model When the Hydrolysis Is the Limiting Step

A two-step model of the anaerobic digestion process is mathematically and numerically studied. The focus of the paper is put on the hydrolysis and methanogenesis phases when applied to the digestion of waste with a high content of solid matter: existence and stability properties of the equilibrium points are investigated. The hydrolysis step is considered a limiting step in this process using the Contois growth function for the bacteria responsible for the first degradation step. The methanogenesis step being inhibited by the product of the first reaction (which is also the substrate for the second one), and the Haldane growth rate is used for the second reaction step. The operating diagrams with respect to the dilution rate and the input substrate concentrations are established and discussed.