ON STABILITY OF STATIONARY STATES OF REVERSIBLE REACTIONS OF THE FIRST ORDER

The article discusses reversible first-order reactions. A system of differential equations is written. First integral and stationary state found. Using Lyapunov's direct method, stationary stability was investigated

Geometrization of the theory of electromagnetic and spinor fields on the background of the Schwarzschild spacetime

The geometrical Kosambi–Cartan–Chern approach has been applied to study the systems of differential equations which arise in quantum-mechanical problems of a particle on the background of non-Euclidean geometry. We calculate the geometrical invariants for the radial system of differential equations arising for electromagnetic and spinor fields on the background of the Schwarzschild spacetime. Because the second invariant is associated with the Jacobi field for geodesics deviation, we analyze its behavior in the vicinity of physically meaningful singular points r = M, ∞. We demonstrate that near the Schwarzschild horizon r = M the Jacobi instability exists and geodesics diverge for both considered problems.

Cell lysis analysis for respiratory viruses through simulation modeling

An ordinary system of differential equations leading to a simulation model is propose as methodological approach to analysis the incidence of infectious-contagious diseases, in this case using SARS-CoV-2 virus as pathogenic model. The dynamics of the model are drive by the interaction between susceptible cells contemplating respiratory epithelial cells and viral infection mediated by two types of lysis response. To perform the simulations, values of some variables and parameters were selected from referenced sources, considering that previous reports suggested that the viral load in the lower respiratory tract might reach its peak in the second week after the beginning of disease symptoms. The scenarios described in the simulations evidence the performance of the cell lysis response from susceptible cells that have been infected. The recommend model shows that an excess response from both the original virus and the mutated virus leads to an increase in the approximate time to control viral infection within the organism.

The Parametric Optimization of Voltage Multiplier

The evolutionary model of voltage multiplier parametric optimization which includes 5 diodes and 5 capacitors is reviewed. It executes the transformation of alternating into constant voltage using a five times larger amplitude. The valve work is modelled according to the scheme of an ideal key. The original mathematical model of voltage multiplier which includes additional logical variables is deducted. It aссepts binary meanings 0 and 1, where 0 corresponds to closed valve status and 1 corresponds to open. In order to receive such a model, it is necessary to indicate the amount of open and closed valve combinations. Then for each of them, it is necessary to write the system of differential equations. Comparing them with each other the single differential equation system with additional logical variables is written as a generalization. The evolutional model is used in order to select the capacitor volume meaning. The goal function forecasts two conditions: maximum meaning of output voltage 1 kV and its minimal fluctuations in the stable regime.

SIR model for propagation of COVID-19 in the Paraíba's State (Brazil)

This work aims to apply the SIR-type compartmental model (Susceptible - Infected - Removed) in the evolution of Covid-19 in Paraíba's State and Campina Grande City. For that, the parameters of the model were considered to be variable during time evolution, within an appropriate range. The system of differential equations was solved numerically using the Euler method. The parameters were obtained by adjusting the model to the infected data provided by the Paraíba Health Department. According to the results obtained, the model describes the infected population well. There was a reduction in the effective reproduction number in Paraíba and the town of Campina Grande. It is noteworthy that understanding the dynamics of infection transmission and evaluating the effectiveness of control measures is crucial to assess the potential for sustained transmission to occur in new areas. The model can also be applied to describe epidemic dynamics in other regions and countries.

The Influence of the Friction-Sliding Coefficient of Support Structures and Parameters of Seismic Actions on Reactions and Reliability of Structures with Seismic Protection

The study is focused on a structure represented by a multimass elastic cantilever rod with dry friction seismic isolation elements in the support part under a horizontal random impact of a seismic type. The paper aims at investigating the seismic reaction and selecting optimal parameters of the seismic isolation system involving random impact characteristics, limit parameters of the structure, and the seismic isolation system. The researches are based on dynamic computations; the impacts and fluctuations of the system are random processes. The dynamic model of the structure with the considered seismic isolation is presented in the form of a cantilever rod with concentrated masses; a system of differential equations describing the displacement of the structure with the seismic-isolating sliding elements at the level of the top of the foundations is compiled; and a seismic impact is modeled in the form of a nonstationary random process. An algorithm is developed to integrate the system of differential equations of motion and to determine the statistical characteristics of the seismic reaction and reliability indicators of the structures with the seismic isolation. A method aimed at evaluating effectiveness of the seismic isolation system and selecting its rational parameters is suggested. We developed the computational dynamic model of the structure with the seismic-isolating sliding elements installed at the top level of the foundations, and elastic and rigid limiters for the movement of the sliding supports. This model is made in the form of a multimass cantilever rod that takes into account the relative movements of the masses and the stops of the system on the movement limiters. The structure’s movement under a seismic impact is described by a system of differential equations that takes into account the conditions of transitions of the structure from the state of sticking to the state of sliding and vice versa. The statistical characteristics of the seismic reaction and the reliability indicators of the structure in the process of vibrations are determined for different values of the maximum acceleration of the ground vibration, the prevailing period of impact, the number of masses in the calculated model and the coefficient of friction-sliding of the support elements. The influence of the impact parameters and the system on the efficiency of the seismic isolation of the structures with sliding elements is estimated. The proposed approach to selecting the optimal parameters of the seismic isolation system can be used as a research method aimed at improving efficiency of systems with different design options for seismic isolation of structures.

Aggregated space combat modeling

The use of aggregated combat modeling in the cislunar environment has been demonstrated to inform acquisition decisions for the United States Space Force (USSF). First, the cislunar space is hypothesized as a future strategic conflict environment. As such, Lanchester, Lotka–Volterra, and Brackney models could be appropriate to describe such conflict. All models encompass a system of differential equations which parametrically capture the dynamics between friendly and hostile forces. While the Brackney model was constructed to explain two-dimensional land battle, this article adapts it for the respective three-dimensional space domain and applies it to strategic procurement. The analysis demonstrates the pre-eminence of Space Domain Awareness (SDA) in certain contexts while recognizing conditions in which spacecraft survivability holds greater importance.

Study of stiff differential equations of mathematical description of izomerization of pentane-hexane cut process

This paper provides a brief overview of the existing definitions of a stiff system of differential equations. Further, on the example of the accepted scheme of chemical transformations of the catalytic isomerization process of the pentane-hexane fraction, the stiffness of the system of differential equations was studied. In the course of the work, a method for studying the direct kinetic problem for stiffness is presented. In the Matlab software, the results of solving a system of differential equations by five methods (solvers) were compared. The given method can be tried for solving other problems of chemical kinetics.

Construction of mathematical modelling of a population of microalgae

This article devoted to the development of the mathematic model of the technological process of the chlorella cultivation process, its features and solving of this mathematic model. The Exponential growth of microalgae population under conditions of unlimited nutrient resources and population space proceeds at a rate proportional to the number of species of predominant cells and is described by the differential equation. In the presence of several inhibitors, specific velocity equations with the number of inhibitors can be used, but, as a rule, there are practically no elements acting as inhibitors in the cultivation of Chlorella microalgae. The modeling of this particular class of objects did not take into account the effect of inhibitors on the growth of microalgae. The consumption of nutrients to support the life of microalgae is described by the differential equation. In the course of this work, the processes of cultivation of microalgae were brought together into a system of equations. As a result, a system of differential equations of the technological process of Chlorella cultivation was obtained. Thus, the obtained system of equations describes the process of cultivation of microalgae and its technological process, implemented in a periodic mode.