Simplified System Of Equations Research Articles

Adaptive time-step unscented kalman filtering (ATS-UKF) based observer design for urea selective catalytic reduction (SCR) performance of diesel engines

To reduce the number of sensors in the SCR catalyst, state feedback and fault diagnosis information are provided. Firstly, a model based on the coupling of flow, heat transfer, and gas-solid phase catalytic reaction in the SCR system is investigated in this paper. The parabolic partial differential equations are simplified by the variable substitution method and the method of lines approach (MOL). The simplified system of equations is solved by backward differentiation formulas (BDF) with adaptive adjustment time step strategy. Meanwhile, the chemical reaction parameters are accurately calibrated per second using the Levenberg-Marquardt method. Secondly, the ATS-UKF is designed in this paper, and to ensure the synchronisation between the ATS-UKF and the SCR model calculations, the time step of solving the BDF by the SCR model is taken as the time step of propagating the sigma points. Two observation scenarios are assumed: (1) no downstream NH3 concentration sensor, ammonia coverage and downstream NH3 concentration are observed by ATS-UKF; (2) no downstream NOx sensor, ammonia coverage and downstream NOx concentration are observed by ATS-UKF. Finally, the paper carries out bench tests. In the first case, the ammonia coverage obtained by the ATS-UKF reached 0.99 with respect to the model-calculated value R². The mean absolute error (MAE) between the observed and experimental values of the ATS-UKF for the downstream NH3 concentration was 2.76 ppm. In the second case, the ammonia coverage obtained by the ATS-UKF reached 0.99 with respect to the model-calculated value R², and the MAE between the observed and experimental values of the ATS-UKF for the downstream NOx concentration was 1.53 ppm. Environmental ImplicationThe Adaptive Time-Step Unscented Kalman Filtering (ATS-UKF) enhances urea Selective Catalytic Reduction (SCR) in diesel engines, improving environmental outcomes. This method minimizes sensor dependence, enabling more precise SCR system management and effective emission reduction. By advancing emission control technologies, ATS-UKF contributes to global air pollution mitigation efforts, supporting cleaner air and environmental sustainability. Its innovative approach in monitoring and predicting SCR performance marks a significant step towards eco-friendly diesel engine operation.

Dynamic damping of vibrations of a solid body mounted on viscoelastic supports

The study of the problem of damping vibrations of a solid body mounted on viscoelastic supports is an urgent task. The paper considers the problem of reducing the level of vibrations on the paws of electric machines using dynamic vibration dampers. For this purpose, the paw of electric machines is represented in the form of a subamortized solid body with six degrees of freedom mounted on viscoelastic supports. The aim of the work is to develop calculation methods and algorithms for studying the oscillations of the resonant amplitudes of a solid body mounted on viscoelastic supports. Dynamic oscillation (vibration) damping method consists in attaching a system to the protected object, the reactions of which reduce the scope of vibration of the object at the points of attachment of this system. Applying the D’Alembert principle, the equations of small vibrations of a solid with dampers are derived. For practical calculations, a simplified system of equations was obtained that takes into account only three degrees of freedom. Numerical calculations were carried out on a computer to determine the amplitude-frequency characteristics of the main body. Numerical experiments were carried out using the Matlab mathematical package. Considering that a solid body is characterized by vibration, as a rule, in a continuous and wide frequency range, therefore, dynamic vibration dampers are used to protect a solid body mounted on viscoelastic supports. It was found that when the damper is set at a frequency of 50 Hz, the vibration level at the left end of the frequency interval of rotary motion of the rotor-converter, decreases to 37.5 dB, and at the right end — to 42.5 dB. At a frequency of 50 Hz, the paws do not oscillate. When setting the dampers to a frequency of 51.5 Hz, the maximum vibration level does not exceed 40 dB. The optimal setting of the dampers is within the frequency of 50.60...50.70 Hz, and a two-mass extinguisher is 10–15% more efficient than a single-mass one. Thus, the paper sets the tasks of dynamic damping of vibrations of a solid body mounted on viscoelastic supports, develops solution methods and an algorithm for determining the dynamic state of a solid body with passive vibration of the object in question.

Prediction of the rupture pressure of a corroded pipeline by ANN

This work highlights the use of artificial intelligence (AI) in fracture mechanics, in particular to solve complex problems such as the fracture of a corroded pipeline subjected to both internal pressure and axial compressive stress. The paper describes the use of artificial neural networks (ANN), a popular technique in AI, to replace the empirical expression of the DNV method with a system of simple equations based on weights and biases. The use of ANN avoids problems associated with theory, such as assumptions, boundary conditions and exact modeling. The choice of neural network structure was made on the basis of the required accuracy, measured by indicators such as the coefficient of determination R2 and the root mean square error MSE during the validation phase. The results obtained with this neural network model were satisfactory, showing good linear correlation with the target values and low divergence during the validation phase. The implementation of this model in computer applications facilitates the prediction of failure pressure without requiring in-depth expertise in finite element analysis.

On three-dimensional rotating viscoelastic jets in the Giesekus model

We investigate three-dimensional nonlinear rotating viscoelastic curved jets in the presence of gravity force. Applying the Giesekus model for the viscoelastic stress parts of the jet flow system and using perturbation methods with a consistent scaling, a relatively simple system of equations with realistic three-dimensional centerlines is developed. We determine numerically the relevant solution quantities of the model in terms of the radius, speed, tensile force, stretching rate, strain rate and the jet centerline versus arc length and for different parameter values associated with gravity, viscosity, rotation, surface tension and viscoelasticity. Considering the jet flow system in full 3-dimensions and in the presence of gravity can be significant, impacting the jet speed, strain rate, tensile force, stretching rate and the centerline curvature are notably increased in magnitude and the jet radius size is reduced and this becomes more dominant with larger values of the arc length, gravity, rotation and viscoelasticity. In particular, for a typical value of the gravity and for an order one value of the arc length, we found that gravity makes jet speed higher by at least a factor of 2 and makes jet radius lower by a factor of 0.6 or smaller as we compare to the corresponding values when gravity is not considered.

Non-holonomic equations for the normal extremals in geometric control theory

Applying the point of view of non-holonomic mechanics, we arrive at a new and simple system of equations for the normal sub-Riemannian geodesics. These use a partial connection that is canonically available, given a choice of complement to the distribution. We also describe conditions which, if satisfied, mean that even this choice of complement is determined canonically, and that this determines a distinguished connection on the tangent bundle.The geodesic equations obtained split into mutually driving horizontal and complementary parts. The method facilitates efficient choices of adapted coframes and reveals structures that are reminiscent of tractor calculi. We illustrate the features on examples, including some with non-constant symbols.

Analysing the Stock Market as an Economic Lever, Using a Qualitative and a Quantitative Model

The article aims to provide a perspective on economic growth by relying on the influence and use of the stock market as an economic lever. Two methods will be used: a quantitative one, determined by a multiple linear regression model, and a qualitative one that encumbers a sustainable vector model for generating economic growth. The data panel covers 36 states, for a period of 21 years. The paper manages to identify the main control functions that the stock exchange has over the macroeconomic context, through the quantitative and qualitative method, and to highlight the most important positive and negative attributes of using qualitative methods, in contrast to quantitative ones. The results show a predominant probabilistic characteristic of quantitative methods, in contrast to the flexibility and complexity of the qualitative method, which has been used. Additionally, the quantitative method offers a strictly cartesian perspective for determining future scenarios, while the sustainable vector model, based on a fractalized vision of reality, manages to capture a plurality of perspectives, as well as the interrelationships between the determining parameters, thus being a complex system of simple equations, as opposed to the quantitative method which is defined as a simple system of complex equations.

Investigation of ammonia oxidation reactor in the mode of maximum nitrogen productivity

The production of nitric acid is quite complex and complicated by different stages of production, the main stages are the preparation of ammonia-air mixture to ensure and carry out the oxidation process at the stage of obtaining nitric oxide with subsequent use at the stage of absorption to obtain the final product of nitric acid. In the production of nitric acid, special attention is paid to the oxidation stage, at this stage the main product is formed, which provides nitric acid during the reaction of nitrogen with water at the stage of adsorption. The oxidation stage is the main cost part in the formation of the price function of the cost of the product, so the task of improving the productivity of equipment at this stage, one of the important tasks in building a control system and operation of the ammonia oxidation reactor.The article considers the use of a simplified mathematical [1] model of reactor space dynamics. Based on this model, studies were conducted and the acceleration curve of the APS oxidation reactor was constructed. One of the important features of the oxidation reactor is its complex multi-section structure [2]. The oxidation takes place on three series-mounted layers in the reactor. This design allows you to increase the flow rate of the load and increase the yield of nitrogen from the reactor. Therefore, the mathematical model provides a simplified system of equations with a sequential calculation of each layer in the dynamics of the reactor and the technological parameters of the process at a given time.The oxidation reactor is considered in the article as an object of automatic control and is described by a mathematical model of dynamics in the form of differential equations. The reaction volume dynamics model reflects the dependence of the temperature in the contact layer on the load flow, as well as the dependence of the concentration of nitric oxide on the flow rate and temperature of the reaction mixture at the time of contact with the catalyst.This mathematical model, adequate to the actual course of the oxidation process, will investigate the dependence of the yield of nitric oxide on the specified input values of the flow rate in each section of the reactor. Increasing the yield of nitric oxide will increase the productivity of the reactor, by meeting the quality requirements of the starting product [3] and reducing the economic costs of nitric acid production.The proposed mathematical model allows us to consider a reactor with three layers of contact in the mode of maximum load, which allows to obtain the maximum degree of conversion of ammonia-air mixture. The obtained results of the research allow to form the requirements for the automatic control system and to reflect the reaction of the object to the change of the controlled parameters.

Исследование в области анализа мягкой лекарственной формы «Метротербиназоль», используемой в медицинской практике

Aim. Development of a method of analysis of metronidazole and terbinafine in ointment «Metroterbinazol» using spectrophotometry. Materials and methods. A soft dosage form containing 0.1 g of metronidazole, terbinafine and 9.8 g of Tizol gel was used as the object of research. Pharmacopoeia reagents and the method of spectrophotometry were used for experimental work. Measurements were carried out on the SF-2000 spectrophotometer in the near ultraviolet region (λ = 210-340 nm). Results. To achieve this goal, we studied the electronic absorption spectra and optical characteristics of metronidazole and terbinafine in the substance, ethanol solution and in the presence of Tizol gel. The curve of ε (terb) – ε (met) to the wavelength observed a maximum at a wavelength of 223 nm, which corresponds to the maximum of absorption of terbinafine and is close to a less pronounced first absorption maximum of metronidazole (226 nm), also pronounced minimum at a wavelength of 312 nm, which is similar to the second maximum of absorption of metronidazole. The results obtained suggest that the optimal wavelengths are 223 nm and 312 nm. On an artificial mixture with a similar concentration of ingredients according to the prescription, testing was conducted for the analysis of drugs in the joint presence. As a result of experiments, it was found that the mass of metronidazole, found by the Firordt method and the simplified system of equations, is in the limit of 0.0959-0.1053 g, terbinafine – 0.1072-0.1110 g, which corresponds to the permissible deviations. Based on the research, a method for the spectrophotometric analysis of terbinafine and metronidazole in «Metroterbinazole» ointment has been developed that allows quantifying them within the permissible deviations provided for in the regulatory documentation. Conclusion. A method of spectrophotometric quantitative determination of terbinafine and metronidazole is proposed, which allows analyzing medicinal products with a relative error of ± 1.49-1.50% and establishing the quality of manufacturing of «Metroterbinazole» ointment within acceptable standards of deviations.

Asymptotic Estimate of Stability of a Supersonic Boundary Layer in a Vibrationally Excited Gas on a Plate

An asymptotic theory of the neutral stability curve of a supersonic boundary layer in a vibrationally excited molecular gas on a flat plate is constructed. The equations of the two-temperature viscous heat-conducting gas dynamics are considered as the initial mathematical model of the flow. On the basis of their linearization about the self-similar boundary layer solution for a perfect gas, a spectral problem is derived for the eighth-order system of linear ordinary differential equations. An algebraic secular equation with a typical decoupling into inviscid and viscous parts is derived from the linear combination of the boundary values of its solutions decreasing outside the boundary layer which solved numerically. It is shown that the neutral stability curves calculated in this way confirm the effect of increasing flow stability against the background of the relaxation process and within 12–15% agree with the previously obtained results of the direct numerical solution of the full spectral problem. The solution of the simplified system of equations for calculating the critical Reynolds number gives a similar result.

A compact and simpler formulation of the component method for steel connections

A simpler and a more general formulation of the component method (CM) proposed by the European Standard of Steel Structures is presented in this work. There are two main differences from the methodology proposed in Eurocode 3-Part 1–8: first) the moment-rotation curve is obtained from the moment and axial equilibrium equations using only the translational stiffness (springs) of the components (i.e. avoiding the concept of rotational stiffness), and two) the shear response of the column panel zone is distributed over the joint and located at the level where other components exist, instead of concentrating it at the level of the compression zone, as Eurocode 3-Part 8 does. By using basic kinematic conditions and solving a simple system of equations, all the information regarding the behavior of the joint is obtained. Two examples are presented.

Exponential integrators with parallel-in-time rational approximations for the shallow-water equations on the rotating sphere

Abstract High-performance computing trends towards many-core systems are expected to continue over the next decade. As a result, parallel-in-time methods, mathematical formulations which exploit additional degrees of parallelism in the time dimension, have gained increasing interest in recent years. In this work we study a massively parallel rational approximation of exponential integrators (REXI). This method replaces a time integration of stiff linear oscillatory and diffusive systems by the sum of the solutions of many decoupled systems, which can be solved in parallel. Previous numerical studies showed that this reformulation allows taking arbitrarily long time steps for the linear oscillatory parts. The present work studies the non-linear shallow-water equations on the rotating sphere, a simplified system of equations used to study properties of space and time discretization methods in the context of atmospheric simulations. After introducing time integrators, we first compare the time step sizes to the errors in the simulation, discussing pros and cons of different formulations of REXI. Here, REXI already shows superior properties compared to explicit and implicit time stepping methods. Additionally, we present wallclock-time-to-error results revealing the sweet spots of REXI obtaining either an over 6 × higher accuracy within the same time frame or an about 3 × reduced time-to-solution for a similar error threshold. Our results motivate further explorations of REXI for operational weather/climate systems.

On the dynamics of the general Bianchi IX spacetime near the singularity

We show that the complex dynamics of the general Bianchi IX universe in the vicinity of the spacelike singularity can be approximated by a simplified system of equations. Our analysis is mainly based on numerical simulations. The properties of the solution space can be studied by using this simplified dynamics. Our results will be useful for the quantization of the general Bianchi IX model.

Methodology for the navigation optimization of a terrain-adaptive unmanned ground vehicle

The goal of this article is to design a navigation algorithm to improve the capabilities of an all-terrain unmanned ground vehicle by optimizing its configuration (the angles between its legs and its body) for a given track profile function. The track profile function can be defined either by numerical equations or by points. The angles between the body and the legs can be varied in order to improve the adaptation to the ground profiles. A new dynamic model of an all-terrain vehicle for unstructured environments has been presented. The model is based on a half-vehicle and a quasi-static approach and relates the dynamic variables of interest for navigation with the topology of the mechanism. The algorithm has been created using a simple equation system. This is an advantage over other algorithms with more complex equations which need more time to be calculated. Additionally, it is possible to optimize to any ground-track-profile of any terrain. In order to prove the soundness of the algorithm developed, some results of different applications have been presented.

Partition of metallic cations between aqueous solutions and mixed crystals of hydrated cobalt and nickel nitrates: Modelling of the influence of temperature and composition

Abstract A systematic study of the solid-liquid equilibria of the H2O-Co(NO3)2-Ni(NO3)2 ternary system enabled to define the liquidus and the solidus curves of the isotherms at 287.15 K and 313.5 K. Two widespread solid solutions, Co(1-σ)Niσ(NO3)2.6H2O and Ni(1-ω)Coω(NO3)2.6H2O, were observed. They were formed by the substitution of Co2+ cations by Ni2+ cations in the monoclinic structure of the cobalt nitrate hexahydrate and the substitution of Ni2+ by Co2+ in the triclinic structure of the nickel nitrate hexahydrate. Two series of tie-lines for each crystallographic structure of these hexahydrates were obtained. The analyses of these tie-lines and those of the previous studies at 258.15 K and 303.15 K enabled a thermodynamic modelling of the solid-liquid equilibria within a temperature range from 258.15 K to 313.15 K. The simple equation system obtained allows to calculate the accurate composition of the mother solution, at a defined temperature, to reach the appropriate cationic ratio in the crystallised solid solution.

Multi-shell transport model for L-H transition

A coupled model of transport, turbulence, and mesoscale flows is proposed, including turbulence spreading. The model consists of transport equations for plasma density and pressure coupled to a shell model of drift wave turbulence, which incorporates coupling to mesoscale flows via disparate scale interactions. The model can describe the turbulent cascade and its dynamical interplay with zonal and mean shear flows as well as the profile evolution (including the profiles of turbulence intensity itself) due to these self-consistent turbulent fluxes. This simple system of equations is shown to capture the low to high confinement (L-H) transition. It is also observed that as the heating is increased, the system goes through an intermediate phase that displays oscillations between zonal flows and turbulence. The transition towards the H mode, which is characterized by the presence of a strong mean shear flow at the edge, is triggered by the mesoscale dynamics due to the action of zonal flows, with turbulence spreading playing an important role in the H to L back transition.

Profits and Fractal Properties: Notes on Marx, Countertendencies and Simulation Models

ABSTRACTThere are new reasons for revisiting Marx’s elaboration on the rate of profit because contemporary debates provide findings from the MEGA Project, long-term data on the rate of profit, and tools for dealing with complexity and non-equilibrium systems. This article proposes that the interplay between the tendency and the countertendencies of the rate of profit to fall can be translated into a simple system of equations, one based on each chapter of Section Three of Capital—as if Marx sought to mathematically formalise his insights. This article reviews previous debates, presents data and runs a simulation model, showing that the rate of profit behaves as fractals.

Chaotic Motion of a Reentry Capsule During Descent into the Atmosphere

Conical-shaped reentry capsules with a spherical bottom and a displaced center of mass from the axis of symmetry are widely used in astronautics for payload delivery. In the case of control-system breakage, modern reentry capsules allow a successful landing to be carried out in an uncontrolled mode. At the same time, the aerodynamic features of this particular shape create preconditions for chaotic motion. This can lead to an overturn of the capsule, thus creating the risk of an accident. This article explores uncontrolled descent of the reentry capsule, with slight asymmetry, into the atmosphere. The system of differential equations describing uncontrollable descent of an asymmetric capsule in the atmosphere was recorded. Fast and slow variables were introduced. A simplified system of equations was obtained, describing the change of the spatial angle of attack. It was shown that chaotic motion can occur during the uncontrolled descent in the atmosphere. The algorithm of damping coefficient selection was developed on the basis of Melnikov’s method. Its application allows for the elimination of chaos in the whole descent trajectory, thus increasing the system reliability.

The importance of the unsteady Kutta condition when modelling gust–aerofoil interaction

The Kutta condition is applied to aerofoils with sharp trailing edges to allow for viscous effects to be considered within a simplified system of equations that are inviscid. This paper discusses in detail the inclusion of an unsteady Kutta condition at a sharp trailing edge during gust–aerofoil interaction and illustrates how the analytic solution for the far-field noise generated by this interaction changes if the unsteady Kutta condition is neglected, or more precisely, if the unsteady pressure is permitted to be singular at the trailing edge. The analytic solution, both with and without the unsteady Kutta condition, is compared with numerical results that have no imposed unsteady Kutta condition. Importantly the results agree well only when the unsteady Kutta condition is neglected in the analytic solution. This paper highlights where the far-field acoustics are most affected by neglecting the unsteady Kutta condition for a variety of singularities that can occur in the unsteady pressure at the trailing edge and shows that results permitting different behaviour in the unsteady surface pressure at the trailing edge could give significantly different far-field noise predictions, even though the surface pressure elsewhere along the aerofoil surface agrees with benchmark solutions.

VEKTOR AUTO-REGRESI:CATATAN HISTORIS DAN PENGEMBANGAN

The purpose of this paper is to describe the development of econometric time-series modeling from early development to contemporary issues. Economic structural model begins with the Keynesian macro model with a simple equation system to a system with hundreds of equations. One interesting issue in the econometric modeling of time series stationarity issue is the emergence of the new standards in advanced econometric analysis. The model system with a new approach known as VAR with emphasis in the data: let the data speak (let's Data talk). This model has become the new standard with variations VECM and several derivative models. This paper concludes with a brief discussion of new approaches to discuss the adjustments that are non-linear.

Solving Systems of Volterra Integral Equations with Cardinal Splines

This work is a continuation of the earlier article [1]. We establish new numerical methods for solving systems of Volterra integral equations with cardinal splines. The unknown functions are expressed as a linear combination of horizontal translations of certain cardinal spline functions with small compact supports. Then a simple system of equations on the coefficients is acquired for the system of integral equations. It is relatively straight forward to solve the system of unknowns and an approximation of the original solution with high accuracy is achieved. Several cardinal splines are applied in the paper to enhance the accuracy. The sufficient condition for the existence of the inverse matrix is examined and the convergence rate is investigated. We demonstrated the value of the methods using several examples.