Многомоментные потоковые модели производственной линии (Multi-Movements Flow Model Production Line)

Dynamic equations of a holonomic system in generalized coordinates with distributed link masses are obtained with the connected graph method. It is shown that these equations are identical to the equations obtained from the dynamic equations of this system in the Lagrange form. The structure of these equations is analogous to the structure of the equations of dynamics of a holonomic system with localized masses. They can be used as a mathematical base for algorithms for producing equations of multilink mechanism dynamics.

The model of the technological process for enterprises with the production method of production is investigated. The dynamics of macroparameters of the production process is considered: inter-operational stocks and the rate of processing of subjects of labour on technological operations along the technological route. Balance equations are presented for macroparameters of the technological process, which express differential dependencies between macroparameters. The linearization of the system of balance equations is performed and the equations of the perturbed state for macroparameters of the closed system of balance equations are written down. Criteria of stability for macroparameters of the production system relative to the normative unperturbed state are determined. Conditions of the stability of the production system functioning are presented. The interrelation between the magnitude of the tempo and the magnitude of the inter-operational reserve of basic products is shown, which ensures the stable functioning of the production process. A system of equations for the perturbed state of a production system for a special case of stability theory is considered (the case of one zero root of the characteristic equation of the system).

The Boltzmann transport equation (BTE) can be transformed in an equivalent balance equation system for an infinite number of moments. If this system is trunctated, an approximate balance equation system is obtained. The equations consist of moments, space and time derivatives of the moments, and coefficients being functions of the moments. We show that the coefficients for a three moment (hydrodynamic) model can easily be extracted from exact solutions of the BTE for homogeneous material. No approximations have to be made concerning the energy-momentum-relation or the shape of the distribution function. In principle, the method can be extended to higher order equations.

The object of this study is the process of liquid combustion in spillage, and the subject is the temperature distribution along the wall of a vertical steel tank when it is heated under the thermal influence of fire and cooled by water. A system of equations describing the water cooling of the wall of a vertical steel tank under the conditions of the thermal effect of a fire spilling a flammable liquid has been constructed. The system consists of a heat balance equation for the tank wall, a heat balance equation for the water film flowing over the wall, and a mass balance equation for the water film. The equations take into account the radiative heat exchange with the flame, the environment, the internal space of the tank, as well as the convective heat exchange with the surrounding air, the vapor-air mixture, and the liquid inside the tank, as well as between the water film and the wall. The joint solution to the system of equations makes it possible to determine the temperature distribution along the tank wall and the water film at an arbitrary time point, as well as to determine the thickness and flow rate of the water film at a certain point. The finite difference method was used to solve the system of heat and mass balance equations. It is shown that the insufficient intensity of water supply for cooling leads to boiling of water from the film, as a result of which the wall temperature in such areas can reach 300 °C. A delay in the supply of water, even with sufficient intensity, could lead to the establishment of a film-like mode of boiling. In such a situation, the water film is thrown away from the wall, as a result of which the part of the wall below the film boiling zone remains without cooling. The practical significance of the built model is the possibility of determining the necessary intensity of water supply for cooling the tank and the limit time for the start of cooling

ABSTRACTModeling of the production of nitrogen oxide molecules in DC discharges in laminar longitudinal flows of atmospheric‐pressure air is performed. Two‐dimensional nonequilibrium discharge model includes the system of gas dynamic equations and balance equations for various plasma components. Simulations are performed for the discharge currents 50–600 mA and gas flow velocities 1–10 m/s. In considered conditions, the gas temperature in the discharge core varies in the range of 3000–6000 K. Spatial profiles of the densities and fluxes of produced species are obtained, both inside the discharge and in the afterglow region. The energy cost for the production of nitrogen oxides is calculated, depending on the discharge current, gap length, and gas flow velocity. The results of the simulation are compared with available experimental data.

Dynamic modeling and control for dual-flexible servo system considering two-dimensional deformation based on neural network compensation

Background: The membrane protein-pigment complexes of photosynthetic isolated reaction centers (RC) Rhodobacter Sphaeroides are macromolecular systems for studying the physical mechanisms of electron and proton transport in biological structures, the role of molecular dynamics. The experimental kinetics of cyclic electron transfer in molecular complexes has a multiexponential character with negative values of decrements. For their description, a system of balance equations is used. Objective of the work is to determine the features of the kinetics of cyclic electron transfer in the RC using two models of electron transfer and the connection of such features with space-time motions in the RC. Materials and methods: Measurement of the absorption kinetics was performed at 865 nm using a two-channel diode spectrometer. The experimental kinetics of RC absorption (the main reaction of the system) was represented by the fitting method in the form of a sum of three exponential functions. In the first model with time-variable rate constants of the balance equations, the wavelet transform method of the logarithmic derivative of the electron transfer kinetics was used. In the second model, the equation of state and three differential equations with constant coefficients were used as the algebraic sum of the rate constants. To determine the values of the rate constants in the balance equation, an optimization problem was solved. The solution of the system of balance equations by the matrix method made it possible to determine the features of the kinetics of the population of substates of the RC. Results of calculations showed that the features of the wavelet spectrum of the logarithmic derivative of the electron transfer kinetics in the first model coincided with the features of the population kinetics of substates of the RC of the second RC model. These features were in the bands 1 s, 3 s, 60 s from the moment of switching on (off) the light and depend on the photoexcitation parameters. Conclusions: The features of the kinetics of the populations of substates in the RC both at the stage of illumination and at the relaxation stage are determined by changes in the structure of the RC in the form of effects of hidden parameters of the structural self-regulation of the RC (feedback through the RC structure).

A simplified approach to solving the equations of population dynamics (Lotka–Volterra equations), which is a nonlinear multidimensional system of ordinary differential equations of the first order, describing the competitive interaction of universities included in some world university ranking, is proposed. The phase variables in these equations are the values of the integral indicator of the university ranking, which is called Overall or Total Score. The simplification consists in reducing this system to a system of independent Verhulst equations with analytic solutions in exponents of time and passing from them to stationary solutions when time tends to infinity. It is shown that with this approach and a given growth rate Overall (Total) Score, it is possible to find symmetric coefficients of interuniversity competition for no more than three competing universities. When finding such coefficients for the first three universities in the THE ranking, numerical solutions of the original system of population dynamics equations were obtained using the Runge–Kutta method in MatLab. It is shown that the development of this approach, based on the equations of population dynamics, can consist in turning to the concept of competitive – cooperative university interactions. The system of differential equations describes the process of changing the integral indicator during the period between two ratings. Using the found values of the coefficients of interuniversity competition, the system is solved sequentially for all stages of the ranking, and the decisions at the previous stage are used as the initial conditions for the next one.

It is well known that the traditional modeling theories adopt the Cartesian coordinates to establish the dynamic equation of solar array system. The order of this equation is often very high, which is inconvenient for controller design. The Cartesian coordinates are difficult to be measured in practice. In this paper, the joint coordinates are used as generalized variables to establish the dynamic equation of the solar array system. The single direction recursive construction method and the Jourdain’s velocity variation principle are used in modeling the system. The order of the established equation is lower, and the joint coordinates are easily measured in practice. Besides the dynamics modeling, joint friction and control design are extensively studied in this paper too. A three-dimensional revolute joint model is introduced, and the contribution of joint friction to the dynamic equation of the system is deduced. A fuzzy PD controller is designed to eliminate the drift of spacecraft caused by the deployment of solar array. In the end of this paper, numerical simulations are carried out to analyze the deployment dynamics and control effect of the solar array system with friction.

This paper considers one-dimensional equations of acoustics equations of inhomogeneous media and the system of gas dynamics equations with constant entropy. Using the Riemann approach, the gas dynamics equations are reduced to a second-order linear hyperbolic equation with variable coefficients. Solutions to this equation are constructed using Euler–Darboux transformations. This allows us to find new exact solutions of the equations of acoustics and gas dynamics, depending on two arbitrary functions.

The paper gives the data on mathematical modeling of simultaneous absorption of chlorine and hydrogen chloride by alkaline solutions. The mathematical model of the process includes the system of differential equations of component-wise material balance and the system of kinetic equations. The system of material balance equations describes the change in concentrations of components along the column height. For its solving it is necessary to know the numerical values of chemisorption acceleration coefficients. They are determined from the system of equations describing the inetics of chemisorption. The gradients of components oncentrations create various conditions of mass transfer processes along the height of the column. This leads to the fact that in one unit there can be various zones of hemisorption process along the height of the packed layer. Each zone is characterized by its reaction order for absorbing component and its kinetic constants. Various zones of the course of binary absorption with chemical reaction were considered. Taking into account the zones, the mathematical model of chemisorption was designed for the countercurrent packed absorber. The peculiarity of the developed mathematical model is the lack of iterative algorithm for calculation. The use of band mathematical model of chemisorption of two gases allows calculation of similar columns at the stages of design and research of industrial processes. The results can be used for calculation and optimization of existing columns of gas emission neutralization in organochlorine production.

This paper presents a semi-analytical method for solving a system of equations of gas dynamics in Eulerian coordinates. Since only spatial derivatives are replaced by finite differences, the system of gas dynamic equations is reduced to a system of ordinary differential equations on a spatial grid. An approximate analytical solution of this system of differential equations for a small time-interval is used to describe the dynamics of a gas in the entire required time interval. Verification was carried out on one-dimensional test problems on the decay of an arbitrary discontinuity and the propagation of stationary shock waves of various intensities. To compare one-dimensional problems, the solution of test problems is given by the simple-to-implement basic particle-in-cell method. It is shown that the semianalytical method has high accuracy of calculations, and is also the most universal method for calculating applied problems.

As an improvement of the four-component scattering power decomposition with rotation of coherency matrix (Y4R) and extension of volume model (S4R), the general four-component decomposition with unitary transformation (G4U) was devised to make the full use of the polarimetric information in coherency matrix. This article enables an extension to G4U by deriving the scattering balance equation system in G4U to investigate the role of unitary transformation first. Despite self-contained, the scattering balance equation system in Y4R and S4R is independent of the ${T}_{13}$ entry of coherency matrix. To include ${T}_{13}$ in decomposition, the unitary transformation in G4U adds a ${T}_{13}$ -related but redundant balance equation into the original system. As a result, ${T}_{13}$ is accounted for by G4U, and we attain no exact solution to the equation system but some approximate ones. By deducing the general expression of the approximate solutions, a generalized G4U (GG4U) is then created and denoted as ${G}({\psi })$ . The decomposition constant $\psi $ determines a GG4U by producing a $\psi $ -rotated double-bounce scattering matrix. We treat this as the scattering preference of $\mathcal {G}({\psi })$ to characterize the physical mechanism. By assigning appropriate values to $\psi $ , we attain GG4U of different preferences, while ${G}({0})$ and ${G}({+} {\pi }/{8})$ just correspond to S4R and G4U. A dual G4U ${G}(-{\pi }/{8})$ is also achieved. The duality ${G}({\pm }{\pi }/{8})$ provides us an adaptive improvement to both G4U and S4R by strengthening the double-bounce scattering over urban and building area while enhancing the surface scattering over water and land area. Both theoretical derivation and experiments on ten polarimetric synthetic aperture radar data sets validate the outperformance. Nonetheless, for whatever unitary transformation employed, there is, forever, a ${T}_{13}$ -related residual component in GG4U. Thus, the incorporation of unitary transformation into Y4R and S4R for the full modeling of polarimetric information is impossible in theory only when the canonical scattering model with nonzero $(\mathrm {1, 3})$ entry of coherency matrix is used to add the balance equation system an independent ${T}_{13}$ -related equation rather than a redundant one.

Dynamic response of shear-deformable axisymmetric orthotropic circular plate structures solved by the DQEM and EDQ based time integration schemes

Paper presents two models for gravity instability simulations using compressible gas formulations, and especially, using regularised gas dynamic equations, or, in other words, the quasi-gas dynamic (QGD) equation system. The first part of the paper describes the layer flow for a single-component gas and the second one is one-fluid approximation for a gas mixture. Here a density equation for a mixture is split in two equations for each gas species. Momentum and energy equations are presented for a mixture with unified velocity and temperature and aggregated density and pressure. Examples of numerical calculations of Rayleigh-Taylor instability for different Atwood numbers are shown. The obtained results correspond to the well-known behaviour features of the Rayleigh-Taylor instability.