Mathematical Model Of Process Research Articles

Characterization of rotary valve control vibration system for vibration stress relief applications

To enhance the vibration system characteristic distortion and pressure loss, we propose a novel rotary valve control vibration system. The paper presents the designed structural composition and generation mechanism of the rotary valve control vibration system. It also derives the mathematical model for the rotary valve distribution process and the overall system. The flow field inside the rotary valve is dynamically simulated using the multiple reference frame model, allowing for the determination of the change rule of the rotary valve’s output characteristics. An AMESim model was developed to analyze the vibration characteristics of the rotary valve control system. The effects of parameters such as inlet pressure, motor speed, and oil supply pump displacement were investigated. A rotary valve control vibration system experimental bench was constructed to experimentally verify the output characteristics of the rotary valve and the vibration characteristics of the system. The results indicate that the characteristic curve of the designed vibration system closely resembles a sinusoidal wave. Additionally, the rotary valve exhibits low pressure loss, making it more suitable for vibration stress relief applications. By appropriately increasing the inlet pressure and decreasing the motor speed, the vibration characteristics of the system can be improved.

A Novel Model to Predict Shape Variation of Steel Strip During Feeding in Slab Continuous Casting

To comprehensively comprehend variation of strip shape (strip feeding depth and maximum steel sheath cross‐sectional area) under different process parameters (strip feeding speed, strip oscillation frequency, strip amplitude, molten steel superheat, strip width, and strip thickness), a mathematical model of feeding strip process has been developed herein. Flow near steel strip is analyzed. Meanwhile, the qualitative relationship between strip shape and process parameters is derived based on energy conservation within the system of molten steel and steel strip. The results show that strip feeding depth is positively correlated with strip feeding speed, strip width, and strip thickness, while it's negatively correlated with strip oscillation frequency, strip amplitude, and molten steel superheat; maximum steel sheath cross‐sectional area is positively correlated with strip width and strip thickness, while it's negatively correlated with strip feeding speed, strip oscillation frequency, strip amplitude, and molten steel superheat. Based on the calculated results, the quantitative relationships are proposed to predict the strip feeding depth and maximum steel sheath cross‐sectional area with aforementioned process parameters, which are suitable for the situations that the strip tip is located between the outlet of submerged entry nozzle and the end of the liquid core.

Modeling single cell trajectory using forward-backward stochastic differential equations.

Recent advances in single-cell sequencing technology have provided opportunities for mathematical modeling of dynamic developmental processes at the single-cell level, such as inferring developmental trajectories. Optimal transport has emerged as a promising theoretical framework for this task by computing pairings between cells from different time points. However, optimal transport methods have limitations in capturing nonlinear trajectories, as they are static and can only infer linear paths between endpoints. In contrast, stochastic differential equations (SDEs) offer a dynamic and flexible approach that can model non-linear trajectories, including the shape of the path. Nevertheless, existing SDE methods often rely on numerical approximations that can lead to inaccurate inferences, deviating from true trajectories. To address this challenge, we propose a novel approach combining forward-backward stochastic differential equations (FBSDE) with a refined approximation procedure. Our FBSDE model integrates the forward and backward movements of two SDEs in time, aiming to capture the underlying dynamics of single-cell developmental trajectories. Through comprehensive benchmarking on multiple scRNA-seq datasets, we demonstrate the superior performance of FBSDE compared to other methods, highlighting its efficacy in accurately inferring developmental trajectories.

SCIENTIFICALLY BASED RECOMMENDATIONS FOR INCREASING THE EFFICIENCY OF REAL ESTATE USE AT THE REGIONAL LEVEL

It is proved that real estate is an essential element affecting the functioning of regions, as its use forms the material basis of regional development. In recent years, there has been a decrease in the efficiency of real estate use at the regional level. In this context, we should note the negative impact of external and internal factors and the consequences of Russian aggression. Therefore, theoretical provisions regarding the definition of real estate need further improvement, considering international experience. In addition, the approach to applying the method and models for forming a quantitative basis for real estate use to develop relevant scientifically based recommendations needs reconsideration. The research has achieved the goal of developing scientifically based recommendations for increasing the efficiency of real estate use at the regional level. We have solved the following tasks in the article: substantiating theoretical provisions regarding the definition of regional real estate, forming directions for improving the efficiency of real estate use at the regional level, and proposing a mechanism for using real estate. Real estate is defined as a set of land plots and other objects located on it, forming spatial support from above and below, the use of which has a long-term nature and the movement of which leads to a violation of their functional characteristics. Spatial, functional, investment, and environmental factors influence the formation and use of real estate. Their interaction and definition allow building a multi-level system of assessment indicators to form a quantitative basis for making informed decisions. To increase the level of real estate use in the regions, we have further developed methodological approaches, as recommendations, to the assessment of real estate use based on methods and models that characterise the directions and features of the use of spatial, functional, investment, and environmental support, which provide the opportunity to form a mathematical basis and identify the appropriate toolkit for developing a method for assessing the level of real estate use in regions. Of particular importance are the results of mathematical modelling of real estate use processes at the regional level based on the establishment of relationships between systemic spatial, functional, investment, and environmental factors and an integral indicator by applying the method of correlation-regression analysis, model adequacy criteria, which allows determining directions for increasing the efficiency of use of the real estate. A mechanism for the use of real estate at the regional level is proposed based on the results of the assessment, mathematical modelling, and forecasting of the factors of real estate use, which, unlike the existing ones, made it possible to determine the directions of implementation of scientifically based recommendations and build geospatial monitoring maps. As a result of the study, we have developed a mechanism for real estate use at the regional level as a comprehensive tool for ensuring the efficiency of real estate use in the regions. Keywords: real estate, regional level, efficiency of use, recommendations, mechanism, geospatial monitoring maps, methods, models.

NEURAL NETWORK MODELING OF PLASMA-CHEMICAL PROCESSES OF OBTAINING NANOSYSTEMS

Plasma-chemical technology is a new area of industrial chemical technology. Chemical processes in low-temperature plasma, the regularities of reactions, and the basis of plasma-chemical technology will require computer simulation. Building adequate simulation models of plasma-chemical processes for developing nanosystems and computer simulations with them allows the development of applied research studies in this subject area. Computer intelligence technologies provide an opportunity to use non-classical approaches to building mathematical models of chemical processes. Neural network technologies make it possible to create mathematical simulation models of various processes.

Mathematical modeling of the creation process and aging of polymer composite materials

Based on the analysis of the literature on the possibility of using neural networks to create new materials with high functional properties, the article considers a solution to the problem of determining the operational stability of polymeric composite materials by creating physical and chemically sound mathematical prediction models. Epoxy resins of the UP-637 and EA brands with an isophorone diamine hardener were chosen as the matrix of the model composite material, and oligobutadiene rubber of the SKN-10 KTR brand was chosen as the modifier. It justifies directions of work necessary for development of new materials creation methodology with optimal characteristics, building a model for changing the properties of materials at variation of composition and implementation of full-scale mathematical modeling of physical and chemical processes of polymer composite materials aging at changing level and time of climatic factors influence. Verification of the obtained dependence of service characteristics on the composition of the material and the level of influencing climatic factors was carried out on the basis of data from full-scale tests in a temperate climate. The proposed methodology for modelling the properties of polymer composite materials will reduce the development time of new materials and allow creation of polymer composites based on epoxy resin containing fillers of various natures (carbon, mineral and polymer) with high performance parameters.

Finite Difference Method for Solving Parabolic-Type Integro-Differential Equations in Multidimensional Domain with Nonhomogeneous First-Order Boundary Conditions

Introduction. We investigate a multidimensional (in terms of spatial variables) parabolic-type integro-differential equation with nonhomogeneous first-order boundary conditions. The locally one-dimensional finite difference scheme developed herein can be applied to solve various applied problems leading to multidimensional parabolic-type integro-differential equations. Examples include mathematical modelling of cloud processes, addressing the issue of active intervention in convective clouds to prevent hail and artificially enhance precipitation, as well as describing the droplet mass distribution function due to microphysical processes such as condensation, coagulation, fragmentation, and freezing of droplets in convective clouds.Materials and Methods. In this study, an approximate solution to the initial-boundary value problem is constructed using the locally one-dimensional scheme of A.A. Samarsky with a specified order of approximation О(h2 +τ). The primary research method employed is the method of energy inequalities.Results. A priori estimates have been obtained in the discrete interpretation, from which uniqueness, stability, and convergence of the solution of the locally one-dimensional difference scheme to the solution of the original differential problem follow, with a convergence rate equal to the order of approximation of the difference scheme.Discussion and Conclusions. The research findings can be utilized for further development of boundary value problem theory for parabolic equations with variable coefficients. Additionally, they may find applications in the fields of difference scheme theory, computational mathematics, and numerical modelling.

Исследования математических моделей процессов деформаций зданий и сооружений

Purpose. The article is aimed at analyzing changes in the dynamic characteristics of a building and establishing the dependence of shear deformation accelerations on the building's storey to predict the effect of seismic vibrations on the technical condition of the building, taking into account the engineering and geological properties of the foundation. Methodology. A number of instrumental observations using geodetic devices, automated monitoring systems and engineering seismic stations were made to study the issues of assessing changes in the dynamic characteristics of high-rise buildings and structures. To create mathematical models of deformation processes of buildings and structures, the study of interaction of structural elements of the building with the engineering-geological structure of the ground in the upper and lower parts of the megapolis was proposed. Findings. The results on ground shaking intensity acceleration, effective duration, spectral coefficients and periods of spectrum maximum are obtained. The results of measurements of vibrations on different floors of a high-rise building based on instrumental records of seismic station of local and distant earthquake have been obtained. Dependences of accelerations of shear deformations on the floor of the building with regard to engineering-geological properties of the base have been established. Predictive models of deformation processes of the building taking into account dynamic characteristics of ground vibrations and energy class of earth crust movements have been proposed. Originality. The analytical technique of correlation analysis of random variables is proposed, by means of which normally distributed linear and nonlinear processes are studied to create a mathematical model of deformation processes of buildings of different storeys. Practical value. The obtained results of the study of deformation processes of buildings and their structural elements allow to predict the dynamic model of the process of displacements of points of the structure taking into account the dynamic characteristics of ground vibrations and energy class movements of the Earth's crust

Mathematical modeling of early processes of morphogenesis of epithelial tissues

Studying morphogenetic processes through traditional methods, such as observa-tion and experimentation, can be highly complex and laborious. Utilizing mathematical modeling methods makes it possible to analyze big data and uncover patterns that may be unnoticed when employing traditional approaches. In this study, a vertex mathemati-cal model of squamous epithelial tissue morphogenesis is proposed. The elementary unit of the system is the cell, which can dynamically change its shape and size. We in-troduce a new potential that accounts not only for the elasticity of cell perimeters and areas but also for the elasticity of their internal angles. Additionally, we introduce an inte-gral equation of chemical signaling, which allows for the consideration of chemo-mechanical cell-cell interactions. In addition to the above, the model incorporates im-portant processes of real epithelia, such as cell proliferation and intercalation. Based on the simulation results, a diagram of the system's principal states was constructed as a function of control parameters. A parameter range is identified within which the cellular system adopts the most energetically favorable and stable configurations. Furthermore, two processes occur in the early stages of morphogenesis, namely morula formation and blastula formation. This paper provides a detailed physical and mathematical description of these processes. The obtained results can be utilized in developing methods for influ-encing morphogenetic processes in medical applications.

APPLICATION OF THE SAMUELSON EQUATION TO THE EVANS MODEL

Mathematical modeling of economic processes is an actual direction of research, because the well-being of citizens and the country as a whole depends on it. In the case of the market, the prices of most goods and services are not planned centrally, are not directly regulated by the state, but are freely set and changed by the market itself. The main factors that control the movement of prices in the market are the demand and supply of goods. In the economy, the most important are dynamic models, the parameters of which change over time. The Evans model (Walras-Evans-Samuelson model) is currently one of the basic concepts explaining the dynamic establishment of the equilibrium price in the market of one product under the influence of supply and demand. This is due to the fact that knowing the dynamics of the economic parameter we are interested in, we can try to build a forecast of its further evolution. The article examines the market of one product. For convenience, we will assume that the functions of the dependence of demand and supply on the price are given by linear relationships. The construction of the Evans model is that the change in price is directly proportional to the excess of demand over supply and the duration of this excess. The Samuelson differential equation with an initial condition, that is, the Cauchy problem, is obtained. Samuelson's equation has a stationary (equilibrium) point, which is a positive price at which supply and demand will be equal. The analysis of the obtained solution of the problem shows that over a long enough time (relatively speaking, at ) the price asymptotically approaches the equilibrium value. If we are not interested in the temporal dependence, but only in the equilibrium price, then it can be found from the differential equation immediately by setting the condition , this is the so-called limit stationary mode. The solution of the Cauchy problem is found by the method of variation of the constant. The parameterization of the model using the fractional differentiation operator in the sense of Gerasimov-Caputo is considered. The resulting solution was analyzed depending on the parameter . For this, the asymptotic representation of the function was used for large values of the argument. Conclusions are made regarding price dynamics in time relative to the equilibrium price when demand and supply are equal.

Mathematical Model of Oxygen Regime Analysis in a Bioreactor

Purpose. Today, aeration tanks are widely used to treat industrial and municipal wastewater. Assessing the efficiency of water treatment in aeration tanks under different operating conditions is an important task. To solve this problem, it is necessary to have mathematical models that allow to quickly obtain data on the effect of treatment in aeration tanks. The main objective of this work is to develop a numerical box model to determine the efficiency of wastewater treatment in an aeration tank. Methodology. For mathematical modeling of the biological wastewater treatment process in a bioreactor, zero-dimensional material balance equations are used, which are written in relation to the concentration of substrate, activated sludge, and dissolved oxygen in wastewater. The Monod model is used to calculate the substrate oxidation process. The Euler method is used to integrate the modeling equations. A simplified model of biological water treatment in a bioreactor is considered, which makes it possible to obtain an analytical solution to the problem. The obtained analytical expression makes it possible to quickly determine the change in the concentration of dissolved oxygen in wastewater depending on the change in the concentration of activated sludge in the bioreactor. The constructed numerical model makes it possible to determine the dynamics of changes in the concentration of contaminants, activated sludge and oxygen in wastewater during their stay in the bioreactor. Findings. A tool for theoretical evaluation of the efficiency of biological wastewater treatment in an aeration tank is proposed. A numerical model has been built that allows determining the concentration of dissolved oxygen, substrate and activated sludge at the outlet of the aeration tank. Originality. An effective numerical model has been developed that allows to quickly calculate the dynamics of wastewater treatment in a bioreactor and, based on this information, to evaluate the efficiency of the reactor. Practical value. The constructed mathematical model can be useful in the reconstruction of biological wastewater treatment facilities, as well as at the design stage of bioreactors to take into account their operation under different operating conditions. A computer program has been developed that implements the constructed numerical model. The results of a computer experiment are presented.

Comparative analysis of two-dimensional and three-dimensional modeling of heat transfer during operation of a gas infrared heater indoor

Relevance. It is proposed to heat local work areas with systems based on gas infrared heaters, capable of directing radiative heat flow to reduce heating costs in large premises. However, the widespread use of gas infrared heaters is hampered by the existing difficulties with the preliminary assessment of convective-radiative heat flows movement, on which the number and location of heating devices depends. The preliminary assessment is complicated by the need in some cases for 3D modeling of complex physical processes. It is necessary to evaluate the possibility of replacing labor-intensive 3D modeling with a method for calculating a heating system using gas infrared emitters based on a 2D approach to reduce the time spent on calculations. Aim. To prove that the use of a two-dimensional model of the processes under consideration makes it possible to obtain the main characteristics of the thermal regime of the premises, making it possible to replace spatial modeling. Objects. Heating system with a light-type gas infrared heater and an air exchange system. Methods. Two-dimensional and three-dimensional mathematical modeling of conjugate heat transfer processes using the finite element method. Mathematical modeling was carried out in the COMSOL Multiphysics software environment using the modules: “Heat Transfer Interface in Liquids”, “Radiation between Surfaces” and “Turbulent Flow, k-ε Interface”. Results. The article presents the results of mathematical modeling performed in three-dimensional and two-dimensional formulations. The distribution of temperatures in the air and enclosing structures, as well as the flow lines of heated air and air, which was heating, in the volume of the premise are presented. The results of two-dimensional and three-dimensional modeling were compared. Satisfactory similarity of the calculated average air temperatures in the local working area was established based on the results. The difference was less than 2℃ for different spatial modeling approaches.

Математическая модель процесса СВЧ и конвективной выпечки хлеба из сбивного теста

Whipped yeast-free bakery products require effective energy supply to dough in order to optimize energy consumption, baking time, and quality. This article introduces a verified mathematical model of microwave and convective baking for whipped bread based on heat and mass exchange equations.
 A full-scale experiment to verify the calculations involved dough samples with a humidity of 56 ± 1%. The samples underwent microwave and convective processing until the temperature in the crumb center reached 98 ± 1°C.
 The mathematical model was formalized as energy and mass conservation equations, which made it possible to consider baking as a non-stationary process of heat and mass transfer of moisture in an isotropic incompressible continuous medium in the diffusion approximation. The equation took into account the unstable phase transition boundary. The practical verification showed the mean error for microwave baking as 14.5% in temperature and 18.2% in moisture content. For convective baking, the results included 12.6% in temperature and 9.7% in moisture content. The mathematical model proved adequate to the real processes of heat and mass transfer. The error in calculating the temperature and moisture content fields was sufficient tooptimize the process.
 The physical and mathematical model of the baking process made it possible to evaluate the effect of technological variables on the temperature and moisture concentration fields in the dough samples. The mathematical model and the computational experiment can be used to identify static and dynamic characteristics of baking as an object of automatic control, i.e., to identify optimal control channels and actions, as well as to adjust the automatic control system to specific quality indicators.

FORMATION OF TWO-PHASE ZONES DURING INTERNAL OXIDATION OF BINARY ALLOYS

In the paper the formation patterns of two-phase regions during the internal oxidation process in low-alloyed binary alloys is studied. The goal of the research is the creation of a mathematical model for the internal oxidation process, which is to describe the kinetics of formation and evolution of internal oxidation zones, the study of the patterns governing the two-phase zone formation during internal oxidation, the study of the space-time dynamics of the structural parameters of the two-phase area, namely the number of the oxide particles, their average radius and the phase volume, at different stages of the internal oxidation zone evolution. The two-phase process of diffusion saturation with light components applied to binary alloys is analyzed theoretically. The conditions for formation of disperse oxide particles are formulated. A mathematical model for the formation of two-phase areas as well as the numerical solution for the system of equations describing the kinet- ics of formation and evolution of the two-phase area for different values of the process parameters is proposed. The modeling and experiments demonstrate that the distribution of structural parameters of the two-phase area has complex, non-monotonous nature. The influence of the main parameters of the process on the kinetics of the formation of the two-phase area in a lightly-alloyed binary nickel-based alloy plate is also determined. All stages of the plate’s oxidation process are studied – from the inception of the particles to the coalescence of second-stage particles. The results of the work could be used for developing new technologies in thermal and chemical-thermal treatments for disperse strengthening of materials using internal oxidation, as a physical basis for seeking ways of providing certain distributions of the internal oxidation zone structural parameters, which are required to give the al- loy a necessary set of physical and mechanical properties. The comparison of the modeling and experimental results shows a good correlation, which allows them to be recommended for developing new technologies in disperse strengthening, new heat-resistant steels, disperse-strengthened magnetic materials and electrotechnical alloys.

SIMULATION OF DYNAMIC PROCESSES IN A p - i - n DIODE BY THE METHODS OF PERTURBATION THEORY

In the paper a mathematical model of the dynamic process of the electron-hole plasma formation in the active region ( i - region) of a semiconductor p - i - n - diode in the direct bias mode with a harmonic signal fed on the diode is developed. The basis of the model is a nonlinear nonstationary sin- gularly perturbed boundary value problem for a system of continuity equations of electron-hole currents and Poisson's equation. The algorithm for searching the charge carrier concentration distributions and the potential distribution is based on the asymptotic method of boundary functions and the Fourier method. In the course of the research, a technique for decomposing a nonlinear problem based on the development of perturbation theory me- thods was proposed. The initial nonlinear problem is reduced to a recurrent sequence of linear stationary boundary value problems, solved by classical and partially original analytical-numerical methods. The identification of the boundary functions in the solution of the problem provides, in particular, in contrast to the classical approximation of ambipolar diffusion, an adequate description of the electric field strength behavior in the active region of p - i - n - diodes. The obtained research results shed light on the peculiarities of the formation of the impedance characteristics of p - i - n - structures. The results of the work reveal more deeply the nature of the physical processes in the studied technical system and are aimed at improving the methodology for modeling and designing control semiconductor devices.

Research on Prediction Model of Particulate Matter in Dalian Street Canyon

In urban areas where populations commonly reside, particle mass concentrations in street canyons can pose significant risks to human health. This study aimed to investigate the diffusion mechanism of particle mass concentrations in urban street canyons by developing and applying a prediction model based on the mathematical modeling of physical processes. The prediction model considered factors such as the influence of traffic wind, natural wind, traffic flow, and other relevant variables influencing particle mass concentrations in street canyons. Field measurements were conducted in Dalian, China, to verify the feasibility of the model. Particle mass concentrations, traffic flow, temperature, relative humidity, and wind speed were measured on Shichang Street (a two-lane one-way road), Tangshan Street (a four-lane two-way road), and Shengli Road (a six-lane two-way road). The results indicated that the majority of traffic peaks occurred around 19:00 on all road types. The PM1.0 mass concentration was well diluted on the four-lane two-way road, with the least dilution observed on the two-lane one-way road. A strong correlation between the particle mass concentrations and traffic flow was discovered. Furthermore, a prediction model was established, accurately predicting the particle mass concentrations when the prediction step was from 5 to 15 s. The coefficient of determination (R2) between the predicted and measured values on the two-lane one-way road, four-lane two-way road, and six-lane two-way road was 0.9319, 0.6582, and 0.9238, respectively. Additionally, the prediction model allowed for a detailed analysis of traffic flow limitations, corresponding to the recommended World Health Organization (WHO) PM2.5 values. Overall, the findings of this study offer valuable insights for forecasting particle exposure levels in street canyons.

Mathematical modelling of the emission characteristics of a field electron cathode in a scanning electron microscope under biosampling conditions

Currently, the use of electron microscopes in medicine is developing intensively, including scanning electron microscopes (SEM), which are designed to solve a huge number of problems in various fields with a wide range of electron accelerating voltages and electron beam energies. The development of an SEM with certain emission characteristics, with a range of lower beam energies for the study of biological samples, is an urgent task because modifying the SEM to solve problems in medicine, for example, would make it possible to obtain higher-quality images of biospecimens for diagnostics and monitoring the effectiveness of therapy. To develop new SEMs with certain characteristics, it is proposed to conduct less expensive research using numerical methods based on mathematical models of processes in electron-optical SEM systems. In this regard, this work sets the task of determining the size and shape of the beam, the main emission characteristics of the field electron cathode (FEC) of the SEM, which is under the influence of the electric field that excites electron emission and the external longitudinal magnetic field by studying the movement of the outermost electron of the beam, taking into account the influence of space charge beam electrons, external magnetic field. In the model, the FEC is approximated by a paraboloid of rotation, and the concept of a boundary “outermost” electron is introduced, the trajectory of which determines the shape and size of the beam. The problem of calculating the emission characteristics along the trajectory of the outermost electron of a FEC is solved using a mathematical model that includes the following equations: motion of the “outermost” electron, Maxwell outside and inside the beam, continuity of the current density, Fowler-Nordheim equation. As a result, a system of 18 first-order ordinary differential equations was obtained, the numerical calculation of which using the 4th order Runge-Kutta method allows us to obtain the emission characteristics of the FEC. As a result, it is suggested that it would be feasible to modify SEMs for more effective use in the medical field, taking into account their increasing use in disease diagnosis and the possible improvement of image quality through the development of FEC SEMs with more suitable characteristics.

Post-COVID breathlessness: a mathematical model of respiratory processing in the brain.

Breathlessness is among the most common post-COVID symptoms. In a considerable number of patients, severe breathlessness cannot be explained by peripheral organ impairment. Recent concepts have described how such persistent breathlessness could arise from dysfunctional processing of respiratory information in the brain. In this paper, we present a first quantitative and testable mathematical model of how processing of respiratory-related signals could lead to breathlessness perception. The model is based on recent theories that the brain holds an adaptive and dynamic internal representation of a respiratory state that is based on previous experiences and comprises gas exchange between environment, lung and tissue cells. Perceived breathlessness reflects the brain's estimate of this respiratory state signaling a potentially hazardous disequilibrium in gas exchange. The internal respiratory state evolves from the respiratory state of the last breath, is updated by a sensory measurement of CO2 concentration, and is dependent on the current activity context. To evaluate our model and thus test the assumed mechanism, we used data from an ongoing rebreathing experiment investigating breathlessness in patients with post-COVID without peripheral organ dysfunction (N = 5) and healthy control participants without complaints after COVID-19 (N = 5). Although the observed breathlessness patterns varied extensively between individual participants in the rebreathing experiment, our model shows good performance in replicating these individual, heterogeneous time courses. The model assumes the same underlying processes in the central nervous system in all individuals, i.e., also between patients and healthy control participants, and we hypothesize that differences in breathlessness are explained by different weighting and thus influence of these processes on the final percept. Our model could thus be applied in future studies to provide insight into where in the processing cascade of respiratory signals a deficit is located that leads to (post-COVID) breathlessness. A potential clinical application could be, e.g., the monitoring of effects of pulmonary rehabilitation on respiratory processing in the brain to improve the therapeutic strategies.

Mathematical modelling of transient processes in a HVAC transmission line considering the effect lightning protection cables in the state of two-phase short-circuiting

Mathematical modelling of transient processes in a HVAC transmission line considering the effect lightning protection cables in the state of two-phase short-circuiting

Extremal Problems for Hyperbolic Systems with Boundary Conditions Involving Integral Time Lags

Extremal problems for integral time lag hyperbolic systems are presented. The optimal boundary control problems for hyperbolic systems in which integral time lags appear in the Neumann boundary conditions are solved. Such systems constitute, in a linear approximation, a universal mathematical model for many processes in which transmission signals at a certain distance with electric, hydraulic and other long lines take place. The time horizon is fixed. Making use of Dubovicki-Milyutin scheme, necessary and sufficient conditions of optimality for the Neumann problem with the quadratic performance functionals and constrained control are derived.