Themathematical Model Research Articles

Reconstruction of the rotor output signal of a direct current motor using numerical approximation

In many areas of technology and research, who study behavior process have increasingly relied on mathematical models. Most of the time the mathematical model is used, representing the important aspect of a dynamic system. Sometimes the mathematical model does not have an appropriate structure and it can be loss the relevant information, nevertheless output signal characterization based on an input signal using laboratory measurements in real time can keep the relevant information, which it is not contemplated in the mathematical model because they involve losses or disturbances. In this work the speed of the rotor magnetic field with respect to the stator magnetic field for a dc motor in real time is showing, the data will be processed and a polynomial approximation is depicting and can effectively trigger with the mathematical model. Finally, a stability analysis is present, it shows the regions or system stability points (pre-fault, fault and post-fault), and the direction from which stability is reached through time.

Design and Implementation of Adaptive and Artificial Intelligence Controller for Brushless Motor Drive Electric Vehicle

<div>Brushless direct current (BLDC) motor aims to obtain high efficiency when compared to conventional DC motors due to several reasons. But when it comes to the control then its control is much more complicated due to the requirement of a phase supply switching circuit. Usually, the conventional and classical proportional integral derivative (PID) controller is used but it is quite cumbersome to tune its fixed gains. APID controller is used where PID fails to fulfill the objectives in varying situations. So, the adaptive proportional integral derivative (APID) controller is utilized to enhance the results. An artificial neural network (ANN) controller is one of the recent control methods, which gives accurate and precise results and utilizes ANN to give more accurate results. But it lacks fuzzy logic, that is, human tendency, and finally, the artificial neuro-fuzzy inference system (ANFIS) controller is concluded as the best controller to limit the speed of the BLDC motor. ANFIS includes all the advantages of controllers and provides the most accurate results. The mathematical model of all the controllers is discussed and its performance is simulated in MATLAB/Simulink. ANFIS includes all the advantages of controllers and provides the most accurate results.</div>

Diagnostics of supercapacitors using cyclic voltammetry: Modeling and experimental applications

In this article, we analyzed a method of cyclic voltammetry (CV) with respect to diagnostics of supercapacitors. The main goal deals with the study of the voltage sweep rate limits allowing to reach equilibrium conditions during recording of CV curves. A mathematical model of cycling based on the De Levie model has been developed. Using this model, the CV curves of a supercapacitor with two symmetric porous electrodes and a separator have been calculated numerically for different sweep rates. These curves are in a good agreement with experimental CV curves. For the first time, an exact analytical solution is obtained for linear voltage sweep for a symmetric supercapacitor during the charge process. The concept of equilibrium CV curves is proposed and the criterium for the equilibrium conditions depending on voltage sweep rate and other parameters of the system is established. When the potential sweep rate exceeds the equilibrium conditions, the CV curves deviate from a rectangular shape and take the form of a “modified ellipses with sharp edges”. A review of publications related with experimental measurements of CV curves has been provided using the developed concept of equilibrium conditions. Application of themathematical model to experimental CV curves makes it possible to reveal the presence of Faraday reactions.

Deleuze’s philosophy of language

This paper analyzes the possibility of outlining a certain kind of philosophy of language, whose frameworks and contours can be recognized within a broader specter of Deleuze?s oeuvre. Even though the French thinker is not someone whose name we often associate with any kind of notion concerning a discipline such as philosophy of language, the paper aims at presenting that the philosophy of language is implicitly present within Deleuze?s writings, nevertheless. As a backbone to this thesis, we cite the analyses that are based on a number of different texts by Deleuze, written in different periods of his life. The recurring motif of these texts is the subject of literature, and these papers were later published under the name of Essays Critical and Clinical. To make our investigations more thorough, it was rather necessary to incorporate other key publications by Deleuze (written by himself or in co-authorship with F?lix Guattari), as well. On top of that, the paper specially parses the pertinence of narration for constituting a highly idiosyncratic approach in treating language, as well as the structure of reality which is primarily understood as bound to language and story-telling. The said approach is named the ?narrative method?. This method is constructed as a certain kind of heuristic device with the ability to untangle various problems stemming from the usual ways we treat language (language understood as an expression of thought, or as information, e.g.), as well as the poststructuralist approach (language understood as an instance that goes beyond subjectivity). The text is divided into two parts: the first part deals with the importance of characterizing language as self-expressive, coupled with insisting on its fundamentally story-telling nature. The second part of the text explores the possibility of potentially correlating the way language operates with the mathematical model known as the Markov chain. The end result of the research can be doubly summarized: on the one hand, the paper puts in the foreground a prospect of understanding Deleuze?s philosophy of language, and on the other hand, the paper insists on supplementing thus instituted philosophy of language with the insight of radical narrativity of every linguistic event.

Numerical Examination on Impact of Hall Current on Peristaltic Flow of Eyring-Powell Fluid under Ohmic-Thermal Effect with Slip Conditions

Aims:: This article is intended to investigate and determine the combined impact of Slip and Hall current on Peristaltic transmission of Magneto-hydrodynamic (MHD) Eyring- Powell fluid. Background: The hall term arises, taking strong force-field under consideration. Velocity, thermal, and concentration slip conditions are applied. The energy equation is modeled by considering the Joule-thermal effect. To observe the non-Newtonian behavior of the fluid, the constitutive equations of Eyring-Powell fluid are encountered. Objective: Flow is studied in a wave frame of reference traveling with the wave's velocity. The mathematical modeling is done by utilizing adequate assumptions of long wavelength and low Reynolds number. Method: The closed-form solution for momentum, temperature, and concentration distribution is computed analytically using the regular perturbation technique for the small fluid ter(A). Results: Graphical results are presented and discussed in detail to analyze the behavior of sundry parameters on flow quantities (i.e., velocity, temperature, and concentration profile). It is noticed that Powell-Eyring fluid parameters (A,B) have a significant role in the outcomes. Conclusion: The fluid parameter A magnifies the velocity profile, whereas the other fluid parameter B shows the opposite behavior.

Thermal flow of micropolar gold-blood nanofluid flowing through a permeable channel with impact of gyarotactic microorganisms

Presently, the scientists across the world are carrying out the theoretical as well as the experimental examinations for describing the importance of nanofluid in the heat transfer phenomena. Such fluids can be obtained by suspending nanoparticles in base fluid. Experimentally, it has proved that the thermal characteristics of nanofluid are much better and appealing as compared to traditional fluid. The current work investigates the heat transfer for flow of blood that comprises of micropolar gold nanoparticles. A microorganism creation also affects the concentration of nanoparticles inside the channel. Suitable transformation has used to change the mathematical model to dimensionless form and then have solved by employing the homotopy analysis method. In this investigation it has revealed that, fluid?s motion decays with growth in Reynolds, Darcy numbers and volumetric fraction. Thermal characteristics support by augmentation in volumetric fraction, while oppose by Prandtl number. Density of microorganism weakens by growth in Peclet and bioconvection Lewis numbers.

A new general fractional derivative relaxation phenomenon

This article addresses a novel anomalous relaxation model with the new general fractional derivative of the Sonine kernel. This operator is considered in the sense of general fractional derivative proposed in the work [Yang et al., General fractional derivatives with applications in viscoelasticity, Academic Press, New York, USA, 2020]. The solution of the mathematical model is obtained with the aid of Laplace transform. The comparison among the classical and anomalous relaxation models is discussed in detail. This result is proposed as a mathematical tool to model the anomalous relaxation behavior of the complex materials.

A Review on Lumped-Kinetic Modelling Methodologies for an industrial FCCU - riser reactor for catalytic cracking

A comprehensive review of scientific literature on various lumped kinetic models used in modelling FluidisedCatalytic Cracking Units (FCCU) used in the petrochemical industry has been done, along with a brief introductionto the working of FCCU. The most popular four lumped kinetic model has been discussed in detail along with themathematical model and then solved using MATLAB. The modified form of the model that considers axialdispersion has also been discussed. The results of the simulation have been plotted and analysed. A brief overviewof three, five, six, seven, nine, and twelve lumped kinetic models has also been discussed.

Control Design for the NPC Three-Level Grid-Connected Converter with Non-Ideal Grid System

Background: The large-scale distributed new energy integrations bring about various non-ideal grid situations, which could deteriorate the control performance of grid-connected converters. Objective: This study aims to improve the control performance of the grid-connected converters when the grid is non-ideal. Methods: Firstly, a neutral point clamped (NPC) three-level grid-connected converter was studied, and the characteristics of the non-ideal grid were analyzed in detail. Then, a real-time signal extraction method called generalized sliding discrete Fourier transform (GSDFT) has been proposed to extract the non-ideal signals, e.g., harmonic components and negative sequence components, based on which a double closed-loop control strategy was designed to improve the control performance of the grid-connected converters when the grid is non-ideal. Results: The experimental results show that the converter double closed-loop control strategy in the non-ideal grid environment is suitable for a variety of non-ideal grid environments, and the gridconnected effect is good. Conclusion: Firstly, this paper analyzes the characteristics of non-ideal grid and establishes the mathematical model of NPC three-level grid-connected converter in non-ideal grid environment. Secondly, aiming at the problem of characteristic harmonics and negative sequence components in non-ideal power grid, a real-time and fast extraction method of non-ideal signals based on generalized sliding discrete Fourier transform is proposed. Finally, taking the three-phase grid current of grid-connected converter as the control target, the closed-loop control strategy of non-ideal signal extraction based on GSDFT is designed, and a good control effect is achieved.

DYNAMICS OF AN ELECTRON BEAM FORMED BY MAGNETRON GUN WITH THE SECONDARY EMISSION CATHODE IN THE DECLINING MAGNETIC FIELD OF SOLENOID: EXPERIMENT AND SIMULATION

The article presents the results of research and calculations on the formation of a radial electron beam by a magnetron gun with a secondary emission cathode in the electron energy range 35...65 keV and measuring its parameters during transportation in the total decreasing magnetic field of thesolenoid and the stray field of permanent magnets. The beam was transported in a system consisting of copper rings with an inner diameter of 66 mm,located at a distance of 85 mm from the exit of the magnetron gun. The dependence of the beam current on the amplitude and gradient of the fielddecay has been studied. The studies carried out have shown the possibility of stable formation of a radial electron beam with an energy of tens of keVin the decreasing magnetic field of the solenoid. By optimizing the distribution of the magnetic field (created by the solenoid and ring magnets) and itsdecay gradient, it is possible to achieve an increase in the incident of electrons on one ring (up to ~72% of the beam current). On the basis of themathematical model of the movement of the electron flow, a software tool has been synthesized that makes it possible to obtain and interpret thecharacteristics of the resulting flows. The obtained numerical dependences are in satisfactory agreement with the experimental results for a magneticfield with a large decay gradient. Various configurations of the magnetic field are considered. Solutions to the direct problem of modeling electrontrajectories for given initial conditions and parameters are obtained. Various configurations of the magnetic field are considered. It is shown that forthe selected initial conditions for the electron beam and the distributions of the longitudinal magnetic field along the axis of the gun and the transportchannel, the electron flux falls on a vertical section, the length of which is on the order of a millimeter. Thus, by changing the amplitude anddistribution of the magnetic field, it is possible to control the current in the radial direction along the length of the pipe, and, therefore, the place of theelectron irradiation.

Impact of different thin layer drying temperatures on the drying time and quality of butterfly pea flowers

With attractive flower colours ranging from dark green to purple, Butterfly pea (Clitoria ternatea L.) is grown year-round in Vietnam. The purpose of this study is to determine the effect of air temperature on drying time and antioxidant compounds of Butterfly pea flowers, fitting the drying curves and testing the goodness of fit. In this study, air drying characteristics of the Butterfly pea flowers were determined using drying air temperature from 55oC to 70oC at a constant air velocity of 1 m/s. The data of experimental moisture loss were fitted to selected seven thin-layer drying models. The effect of drying conditions on the anthocyanin and total phenolic compound changes of Butterfly pea flower were compared. The effect of temperature on the diffusivity was described using the Arrhenius equation with an activation energy of 71.63 kJ.mol- ¹. At increasing temperature, the effective moisture diffusivity values ranged from 2.39×10-12 and 7.76×10-12 m²s - ¹. The mathematical models were compared according to the three statistical parameters such as the coefficient of determination (R2 ), reduced chi-square (χ 2 ) and root mean square error (RMSE) between the observed and predicted moisture ratios. The highest value of R2 (99.8%) and the lowest values of χ 2 (0.0004) and RMSE (0.0178) were observed for drying air temperature of 70oC. Among the seven mathematical models tested with experimental data, the Page model could sufficiently be described the drying characteristics of the Butterfly pea flower.

PEMODELAN RANTAI PASOK FLEKSIBEL PADA PEMURNIAN MINYAK SAWIT: STUDI KASUS DI PT X

The development of the CPO-producing industry provides great benefits for the CPO refining industry.CPO is used as the main raw material for refined derivative products such as oleopangan products (cooking oil,margarine, shortening) and oleochemicals (fatty acids, fatty alcohol, glycerine). A related problem is theinefficiency in the distribution network caused by the complexity of the existing system and related to the manytypes or product variants that must be integrated in shipping. The aim of this research was to design a flexiblesupply chain network for domestic palm oil refined products using a soft computing approach with a geneticalgorithm. The simulation results using GA showed that the optimal solution completion time of themathematical model only takes 57 seconds. The optimization of the model that has been formulated was tested incases where the results were measured by the variables of the number of products distributed, distribution flowin the supply chain network, minimum cost (Z), and network facilities. The design was also tested by verificationof the optimization model by correcting errors in the model until the model produces a feasible solution andvalidating the optimization model to experts through the Association of Indonesian Palm Oil Entrepreneurs(GAPKI) North Sumatra, the Medan Palm Oil Research Center (PPKS) and Public Appraisal ServiceConsultants that often handles problems in the oil palm sector. According to experts, the designed modelrepresented the real situation so that it can be said that the model has been validated. The design is flexiblebecause it is able to meet the existing demand with utilities above 100% for 9 periods at a cost of Rp630,892,386.Keywords: multi-product, CPO refinery supply chain, genetic algorithm, optimization, flexible supply chainnetwork design

Slip Effects on a Ree-Eyring Liquid Peristaltic Flow Towards an Inclined Channel and Variable Liquid Properties

The current paper aims to model the flow of blood in narrow arteries by taking non-Newtonian Ree-Eyring fluid. The impact of wall properties, slip, mass, and heat transport are considered. In earlier studies, the viscosity of blood was considered a constant parameter. However, many researchers have claimed that the blood’s viscosity in the peripheral region is less than that of the core region. Thus, the present model incorporates the variation in thermal conductivity and viscosity, which takes a vital character in scrutinizing blood flow in narrow arteries. The mathematical model is developed on low Reynold’s number approximation and long wavelength, leading to the governing non-linear equations representing the flow phenomena. The governing non-linear partial differential equations are resolved by utilizing the series solution method (perturbation technique). MATLAB programming has been used to plot the pictorial representation of all the parameters through the flow quantities. The investigation shows that the variable velocity slip parameter and viscosity develops the velocity profiles. Further, the liquid parameter can be used to control the dimension of the trapped bolus. Moreover, the obtained outcomes aid in recognizing the flow of blood in micro arteries.

Impact of System Parameters of Optical Fiber Link on Four Wave Mixing

Background: The invention of WDM technology in optical communication system has completely revolutionized the telecomm industry through its high data carrying capacity and efficiency of transmission. Advanced optical modulation formats with high spectral efficiency, advanced components like Reconfigurable Optical Add Drop Multiplexers (ROADMS), OXC, and large bandwidth requirements contributed significantly in existence of dynamic, flexible translucent and transparent networks. In these networks, it is common practice to increase the power levels as much as possible to overcome the power penalty effects and better transmission, but this introduces several non-linear impairments in the link and hence degrades the quality of signal flowing. These impairments arise when several high strength optical fields of different wavelengths interact with molecular vibrations and acoustic waves. The different non-linear impacts include Self Phase Modulation (SPM), Cross Phase Modulation (XPM), Four Wave Mixing (FWM) and scattering effects like Stimulated Raman Scattering (SRS), Stimulated Brillouin Scattering (SBS). The main cause of these impairments is variation in refractive index of fiber (also called Kerr effect) due to intensity of signal flowing through fiber. Due to the degradation impact posed by these impairments, it is crucial to analyze their cause, their influence on system performance and mitigation techniques so as to improve the overall quality of transmission. The monitoring of impairments is quite a challenging task due to their dependency on time, present state of network, signals flowing in adjoining channels and fibers. Objective: The present work aims to identify and describe the role of FWM in optical networks. The mathematical model of FWM is studied to know the parameters influencing the overall impact on system performance. The power of optical source, channel spacing, distance of transmission and presence of dispersion are considered as key factors influencing FWM power being developed. Their impact on FWM power and hence, FWM efficiency is calculated. In addition, the influence of FWM on Quality of transmission is quantified in terms of BER and Q-factor. Methods: The analysis is done through a two-channel transmitter system with varied power, channel spacing, distance of transmission and presence of other degradation factors (dispersion) is taken into account. The corresponding optical spectrums are analysed. Results: In this paper, the non-linear impairment FWM posing degradation effect on the signal quality has been discussed. The basics involved are presented along with the mathematical model. It has been found that FWM results in power transfer from one channel to generation of new waves which may lead to power depletion and interference. The new waves generated depend on the number of wavelengths travelling in the fiber and channel spacing. The influence of FWM on system performance is presented in terms of BER and Q-value. Conclusion: It has been concluded that the increased power of transmission and decreased channel spacing are the crucial factors increasing the magnitude of FWM and need to be closely monitored. On the other hand, increased distance of propagation and presence of certain level of dispersion leads to decrease in FWM power. Therefore, if selected carefully, they may act as source of FWM mitigation without requiring any external compensating device.

Supercritical CO2 extraction of oils from red grape varieties: Yields and extraction parameters

In this work, the extraction by supercritical carbon dioxide of grapeseed oil from five red grape varieties was investigated. Apart from an indigenous variety Prokupac, as the domestic, and Merlot and Cabernet Sauvignon, as international grape varieties the most represented in the Republic of Serbia, Pinot Noir and Gamay were studied as well. Extraction conditions were: temperature of 50?C, 250 bar pressure, and 0.3 kg/h flow rate of CO2. It was shown that the extraction kinetics of international grape varieties, mutually similar differ significantly from the domestic one. The obtained oil yields were in the range of 8.3% w/w (Gamay) to 10.4% w/w (Pinot Noir) for the international varieties and 5.0% w/w for the domestic variety. The mathematical model ?Sovova? was applied to define transport parameters regulating the oil mass transfer inside the seed particles and determine the agreement between experimental and model curves. The interpretation of results took into account the differences of grade seed morphologies (outer surfaces and inner layers) which was investigated by SEM analysis.

Optimal Parallel Control of $$n$$ FIFO-Queues in Shared Memory

The aim of this research is to construct and analyze the mathematical model of $$n$$ parallel circular FIFO-queues, located in a shared memory. The mathematical model is built in the form of random walks on an integer lattice in $$n$$ -dimensional space. Operations (with given probabilities) occur at each step of the discrete time.

Fuzzy Logic Based Time Series Prediction Algorithm Using Nearest Neighborhood Clustering

This paper presents a fuzzy logic based prediction algorithm using nearest neigh-borhood clustering for the prediction of time series. The proposed algorithm hasbeen developed by using nearest neighborhood clustering scheme and optimalfuzzy system. The presented algorithm is tested by the prediction of Mackey-Glass time series, time series obtained from Logistic Map equation and an oilrefinery data series. To the best of our knowledge very few studies have at-tempted to predict Logistic Map. The results of the experimentation show thatthe presented prediction algorithm is able to predict linear, nonlinear and evenchaotic time series to a reasonable accuracy. It performes well even when themathematical model of time series does not exist.

Modeling of Plastic Deformation Based on the Theory of an Orthotropic Cosserat Continuum

In the paper, the plastic deformation of heterogeneous materials is analyzed by direct numerical simulation based on the theory of an elastic-plastic orthotropic Cosserat continuum, with the plasticity condition taking into account both the shear and rotational mode of irreversible deformation. With the assumption of a block structure of a material with elastic blocks interacting through compliant plastic interlayers, this condition imposes constraints on the shear components of the asymmetric stress tensor, which characterize shear, and on the couple stresses, which irreversibly change the curvature characteristics of the deformed state of the continuum upon reaching critical values. The equations of translational and rotational motion together with the governing equations of the model are formulated as a variational inequality, which correctly describes both the state of elastic-plastic deformation under applied load and the state of elastic unloading. The numerical implementation of the mathematical model is performed using a parallel computing algorithm and an original software for cluster multiprocessor systems. The developed approach is applied to solve the problem of compressing a rectangular brick-patterned blocky rock mass by a rough nondeformable plate rotating with constant acceleration. The effect of the yield stress of the compliant interlayers on the stress-strain state of the rock mass in shear and bending is studied. The field of plastic energy dissipation in the rock mass is analyzed along with the fields of displacements, stresses, couple stresses, and rotation angle of structural elements. The obtained results can help to validate the hypothesis about the predominant effect of curvature on plastic strain localization at the mesolevel in microstructural materials.

The impact of microwave radiation in the processes of carbon dioxide absorption by chlorophyll-producing microalgae

The influence of microwave radiation on the rate of СО2 uptake by chlorophyll-producing microalgae of the Chlorella Vulgaris has been established. Experimental dependencies of greenhouse gases absorption by microalgae depending on the impact of microwave electromagnetic (MEM) field have been obtained. The mathematical model of the dynamics of biomass growth of Chlorella Vulgaris microalgae depending on the time of electromagnetic radiation has been constructed. Based on the mathematical model solution and the experimental data obtained, a chart of the dependence of CO2 absorption by microalgae of the Chlorella Vulgaris provided that microwave radiation is present, has been constructed. The optimal value of microwave electromagnetic radiation for the design of technological schemes for the industrial purification of gas emissions from carbon dioxide by biological method has been established.

Influence of single and dual mass flywheel usage in IC engines on the resonance behavior of the power transmission system

In internal combustion engines, due to the transmission of torsional vibrations caused by the irregularity of the combustion process to the gearbox, resonance occurs especially at low engine speeds. Resonance causes noise in the power transmission system. Therefore, driving comfort reduces and additional loads on the gearbox arise. Nowadays, with the concern of fuel consumption, the manufacturers turn to engine designs that keep the engine's working range as wide as possible. In this study, the mathematical models of power transmission systems using single-mass and dual-mass flywheel were analyzed and both systems were compared in terms of engine speed at which resonance occurs. In addition, the effects of the design parameters such as the mass moment of inertia and spring stiffness on the resonance behavior of the power transmission system using dual mass flywheel were examined. It has been observed that the dual mass flywheel drops the speed which resonance occurs in the power transmission system far below engine idle speed so that the resonance speed is kept away from the engine's working range.