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The mathematical models of the mechanical systems "pipeline – pressure sensor" are considered. These systems are designed to measure the pressure in gas-liquid media, for example, to control the pressure of the working medium in the combustion chambers of engines. Based on the proposed models described by systems of differential equations, the joint dynamics of the sensitive element of the pressure sensor and the working medium in the pipeline is investigated. To describe the dynamics, both linear and nonlinear models of the mechanics of a solid deformable body and the mechanics of fluid and gas are used under various assumptions about the physical model of the working medium: incompressible ideal, compressible ideal. Analytical and numerical methods for solving the indicated initial-boundary value problems are developed. [ABSTRACT FROM AUTHOR]

The paper considers the possibility of improving the characteristics of power electronic converters by using model-based optimization. To show the validity of the approach, a specific example of a single-transistor resonant converter with direct mode detection is considered. This type of converter is characterized by the absence of a transient process and in order to improve the energy performance it is chosen to optimize the operating mode in order to obtain the maximum value of the first harmonic of the current through the resonant inductance. The obtained results are also useful in expanding the use of the power circuit as a DC-DC converter in this case a transformer is used and it is of particular importance to reduce the losses in it. Thus, with the used optimization, on the one hand, greater efficiency is achieved, and on the other hand, the production of products with reduced weight and size indicators and improved characteristics. [ABSTRACT FROM AUTHOR]

On the basis of thermodynamic analysis, new mathematical models of the combustion process (thermal theory) and vibrational combustion are constructed. A global inhomogeneity of the system can be described as an inhomogeneous distribu- tion of the enthalpy over a two-component mixture. In this case, for the combustion process in the phase space of the variables (Q, P, T, n, S, E), an increase in the enthalpy is not a total differential. An increase in the enthalpy is a total differential on the local equilibrium manifold (a laminar combustion process). These two assertions, which allow one to single out in the phase space the corresponding adiabatic of the combustion process (the Hugoniot adiabatic) and the equation for the entropy, close the classical mathematical model of the combustion process. The above numerical experiments show that two regimes of the combustion process (deflagration and detonation) depend on the structure of the standard chemical potential Moreover, a control of the passive com- ponent velocity at the inlet results in (depending on the structure of the standard chemical potential) high-frequency oscillations, which are responsible for a blow-up. [ABSTRACT FROM AUTHOR]

Since the end of 2019, with the outbreak of the new virus COVID-19, the world changed entirely in many aspects, with the pandemia affecting the economies, healthcare systems and the global socium. As a result from this pandemic, scientists from many countries across the globe united in their efforts to study the virsus's behavior and are attempting to predict mathematically its infection model in order to limit its impact and developing new methods and models to achieve this goal. In this paper we explore a time-depended SEIR model, in which the dynamics of the infection in four groups from a selected target group (population), divided according to the infection, are modeled by a system of nonlinear ordinary differential equations. Several basic parameters are involved in the model: coefficients of infection rate, incubation rate, recovery rate. The coefficients are adaptable to each specific infection, for each individual country, and depend on the measures to limit the spread of the infection and the effectiveness of the methods of treatment of the infected people in the respective country. If such coefficients are known, solving the nonlinear system is possible to be able to make some hypotheses for the development of the epidemic. This is the reason for using Bulgarian COVID-19 data to first of all, solve the so-called "inverse problem" and to find the parameters of the current situation. Reverse logic is initially used to determine the parameters of the model as a function of time, followed by computer solution of the problem. Namely, this means predicting the future behavior of these parameters, and finding (and as a consequence applying mass-scale measures, e.g., distancing, disinfection, limitation of public events), a suitable scenario for the change in the proportion of the numbers of the four studied groups in the future. In fact, based on these results we model the COVID-19 transmission dynamics in Bulgaria and make a two-week forecast for the numbers of new cases per day, active cases and recovered individuals. Such model, as we show, has been successful for prediction analysis in the Bulgarian situation. We also provide multiple examples of numerical experiments with visualization of the results. [ABSTRACT FROM AUTHOR]

The problem of the layered plates throwing in the conditions of incomplete dispersal of detonation products (DP) is devoted to quite a lot of work, but this problem is usually solved either by various numerical methods, which in practice are not applicable due to the significant difficulties for calculations, or in one-dimensional form, that does not allows for the correct determination of pressure in DP and turn angles after the impact of the plates. This paper provides a mathematical model of multi-layered throwing calculation using fairly simple analytical equations to determine the above parameters when solving various applications for explosive processing of materials by a sliding detonation wave. [ABSTRACT FROM AUTHOR]

The aim of this work is to analyze the application of fractional derivatives in time for the mathematical modeling of complex processes. As an example, a bioprocess is considered and the related distribution of nutrients, bacteria and bioproduct in multiphase fluid systems. The mathematical model under investigation includes convection, diffusion, bioreaction and boundary conditions at the interfaces: interface mass-transfer and adsorption. Different approaches of time-fractional modeling of a biopro- cess are discussed. To evaluate the ability of a fractional order model to correctly reproduce the behavior that the underlying process must exhibit, numerical procedures are developed and computer simulations are performed. [ABSTRACT FROM AUTHOR]