Search results for: mathematical equations

Authors: Nieves M. C. Talavera-Prieto, Abel G. M. Ferreira, António T. G. Portugal, Rui J. Moreira, Jaime B. Santos

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The knowledge of biodiesel density over large ranges of temperature and pressure is important for predicting the behavior of fuel injection and combustion systems in diesel engines, and for the optimization of such systems. In this study, cottonseed oil was transesterified into biodiesel and its density was measured at temperatures between 288 K and 358 K and pressures between 0.1 MPa and 30 MPa, with expanded uncertainty estimated as ±1.6 kg.m^-3. Experimental pressure-volume-temperature (pVT) cottonseed data was used along with literature data relative to other 18 biodiesels, in order to build a database used to test the correlation of density with temperarure and pressure using the Goharshadi–Morsali–Abbaspour equation of state (GMA EoS). To our knowledge, this is the first that density measurements are presented for cottonseed biodiesel under such high pressures, and the GMA EoS used to model biodiesel density. The new tested EoS allowed correlations within 0.2 kg•m-3 corresponding to average relative deviations within 0.02%. The built database was used to develop and test a new full predictive model derived from the observed linear relation between density and degree of unsaturation (DU), which depended from biodiesel FAMEs profile. The average density deviation of this method was only about 3 kg.m-3 within the temperature and pressure limits of application. These results represent appreciable improvements in the context of density prediction at high pressure when compared with other equations of state.

Keywords: biodiesel density, correlation, equation of state, prediction

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Authors: Can Liu, Graham Markowitz, John Balay, Ben Pratt

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Baseline or natural hydrology is commonly employed for hydrologic modeling and quantification of hydrologic alteration due to manmade activities. It can inform planning and policy related efforts for various state and federal water resource agencies to restore natural streamflow flow regimes. A common challenge faced by hydrologists is how to replicate unaltered streamflow conditions, particularly in large watershed settings prone to development and regulation. Three different methods were employed to estimate baseline streamflow conditions for 6 major subbasins the Susquehanna River Basin; those being: 1) incorporation of consumptive water use and reservoir operations back into regulated gaged records; 2) using a map correlation method and flow duration (exceedance probability) regression equations; 3) extending the pre-regulation streamflow records based on the relationship between concurrent streamflows at unregulated and regulated gage locations. Parallel analyses were perform among the three methods and limitations associated with each are presented. Results from these analyses indicate that generating baseline streamflow records at large-scale watersheds remain challenging, even with long-term continuous stream gage records available.

Keywords: baseline hydrology, streamflow gage, subbasin, regression

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Authors: Mishu Gupta, Rama Gupta

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It has been elucidated here that non- autonomous discrete non-linear Schrödinger equation is associated with saturable non-linearity through photo-refractive media. We have investigated the localized solution of non-autonomous saturable discrete non-linear Schrödinger equations. The similarity transformation has been involved in converting non-autonomous saturable discrete non-linear Schrödinger equation to constant-coefficient saturable discrete non-linear Schrödinger equation (SDNLSE), whose exact solution is already known. By back substitution, the solution of the non-autonomous version has been obtained. We have analysed our solution for the hyperbolic and periodic form of gain/loss term, and interesting results have been obtained. The most important characteristic role is that it helps us to analyse the propagation of electromagnetic waves in glass fibres and other optical wave mediums. Also, the usage of SDNLSE has been seen in tight binding for Bose-Einstein condensates in optical mediums. Even the solutions are interrelated, and its properties are prominently used in various physical aspects like optical waveguides, Bose-Einstein (B-E) condensates in optical mediums, Non-linear optics in photonic crystals, and non-linear kerr–type non-linearity effect and photo refracting medium.

Keywords: B-E-Bose-Einstein, DNLSE-Discrete non linear schrodinger equation, NLSE-non linear schrodinger equation, SDNLSE - saturable discrete non linear Schrodinger equation

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Authors: Ashish Ashish

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In the last few decades, the discrete chaos of difference equations has gained a massive attention of academicians and scholars due to its tremendous applications in each and every branch of science, such as cryptography, traffic control models, secure communications, weather forecasting, and engineering. In this article, a generalized logistic discrete map is established and discrete chaos is reported through period doubling bifurcation, period three orbit and Lyapunov exponent. It is interesting to see that the generalized logistic map exhibits superior chaos due to the presence of an extra degree of freedom of an ordered parameter. The period doubling bifurcation and Lyapunov exponent are demonstrated for some particular values of parameter and the discrete chaos is determined in the sense of Devaney's definition of chaos theoretically as well as numerically. Moreover, the study discusses an extended chaos based image encryption and decryption scheme in cryptography using this novel system. Surprisingly, a larger key space for coding and more sensitive dependence on initial conditions are examined for encryption and decryption of text messages, images and videos which secure the system strongly from external cyber attacks, coding attacks, statistic attacks and differential attacks.

Keywords: chaos, period-doubling, logistic map, Lyapunov exponent, image encryption

Procedia PDF Downloads 152

Authors: Hamid Ahmadi, Neda Azari Dodaran

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This paper aims to study the structural behavior of tubular KT-joints subjected to axial loading at fire induced elevated temperatures. At first, a finite element (FE) model was developed and validated against the data available from experimental tests. Then, a set of 810 FE analyses were performed to study the influence of temperature and dimensionless geometrical parameters (β, γ, θ, and τ) on the ultimate strength and initial stiffness. The joints were analyzed under two types of axial loading and five different temperatures (20 ºC, 200 ºC, 400 ºC, 550 ºC, and 700 ºC). Results show that the ultimate strength and initial stiffness of KT-joints decrease considerably by increasing the temperature. In the joints having bigger values of the β, the temperature elevation leads to less reduction in ultimate strength; while in the joints with bigger values of the γ, the temperature elevation results in more reduction in ultimate strength. The influence of the θ on the ultimate strength is independent from the temperature. To our knowledge, there is no design formula available for determining the ultimate strength of KT-joints at elevated temperatures. Hence, after parametric study, two equations were developed through nonlinear regression, for calculating the ultimate strength of KT-joints at elevated temperatures.

Keywords: axial loads, fire condition, parametric formula, static strength, tubular KT-joint

Procedia PDF Downloads 154

Authors: Hussein Togun, Tuqa Abdulrazzaq, S. N. Kazi, A. Badarudin, M. K. A. Ariffin, M. N. M. Zubir

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Heat transfer and laminar fluid flow over backward facing step with and without obstacle numerically studied in this paper. The finite volume method adopted to solve continuity, momentum and energy equations in two dimensions. Backward facing step without obstacle and with different dimension of obstacle were presented. The step height and expansion ratio of channel were 4.8mm and 2 respectively, the range of Reynolds number varied from 75 to 225, constant heat flux subjected on downstream of wall was 2000W/m2, and length of obstacle was 1.5, 3, and 4.5mm with width 1.5mm. The separation length noticed increase with increase Reynolds number and height of obstacle. The result shows increase of heat transfer coefficient for backward facing step with obstacle in compared to those without obstacle. The maximum enhancement of heat transfer observed at 4.5mm of height obstacle due to increase recirculation flow after the obstacle in addition that at backward. Streamline of velocity showing the increase of recirculation region with used obstacle in compared without obstacle and highest recirculation region observed at obstacle height 4.5mm. The amount of enhancement heat transfer was varied between 3-5% compared to backward without obstacle.

Keywords: separation flow, backward facing step, heat transfer, laminar flow

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Authors: Djalal Boualili

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This article considers the problem of sizing prime movers for combined heating and power (CHP) systems operating at full load to satisfy a fraction of a facility's electric load, i.e. a base load. Prime mover sizing is examined using three criteria: operational cost, carbon dioxide emissions (CDE), and primary energy consumption (PEC). The sizing process leads to consider ratios of conversion factors applied to imported electricity to conversion factors applied to fuel consumed. These ratios are labelled RCost, R CDE, R PEC depending on whether the conversion factors are associated with operational cost, CDE, or PEC, respectively. Analytical results show that in order to achieve savings in operational cost, CDE, or PEC, the ratios must be larger than a unique constant R Min that only depends on the CHP components efficiencies. Savings in operational cost, CDE, or PEC due to CHP operation are explicitly formulated using simple equations. This facilitates the process of comparing the tradeoffs of optimizing the savings of one criterion over the other two – a task that has traditionally been accomplished through computer simulations. A hospital building, located in Chlef, Algeria, was used as an example to apply the methodology presented in this article.

Keywords: sizing, heating and power, ratios, energy consumption, carbon dioxide emissions

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Authors: Zaouche Mohammed, Amini Mohammed, Foughali Khaled, Hamissi Aicha, Aktouf Mohand Arezki, Boureghda Ilyes

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In this paper, we present a piloting law based on the adaptive differentiators via high order sliding mode controller, by using an aircraft in virtual simulated environment. To deal with the design of an autopilot controller, we propose a framework based on Software in the Loop (SIL) methodology and we use Microsoft^TM Flight Simulator (FS-2004) as the environment for plane simulation. The aircraft dynamic model is nonlinear, Multi-Input Multi-Output (MIMO) and tightly coupled. The nonlinearity resides in the dynamic equations and also in the aerodynamic coefficients' variability. In our case, two (02) aircrafts are used in the flight tests, the Zlin-142 and MQ-1 Predator. For both aircrafts and in a very low altitude flight, we send the piloting control inputs to the aircraft which has stalled due to a command disconnection. Then, we present the aircraft’s dynamic behavior analysis while reestablishing the command transmission. Finally, a comparative study between the two aircraft’s dynamic behaviors is presented.

Keywords: adaptive differentiators, second order sliding modes, dynamic adaptation of the gains, microsoft flight simulator, Zlin-142, MQ-1 predator

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Authors: G. Punithavathy

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The research proposes a statistical model for the distributed acoustic sensor interrogation units that broadcast a laser pulse into the fiber optics, where interactions within the fiber determine the localized acoustic energy that causes light reflections known as backscatter. The backscattered signal's amplitude and phase can be calculated using explicit equations. The created model makes amplitude signal spectrum and autocorrelation predictions that are confirmed by experimental findings. Phase signal characteristics that are useful for researching optical time domain reflectometry (OTDR) system sensing applications are provided and examined, showing good agreement with the experiment. The experiment was successfully done with the use of Python coding. In this research, we can analyze the entire distributed acoustic sensing (DAS) component parts separately. This model assumes that the fiber is in a static condition, meaning that there is no external force or vibration applied to the cable, that means no external acoustic disturbances present. The backscattered signal consists of a random noise component, which is caused by the intrinsic imperfections of the fiber, and a coherent component, which is due to the laser pulse interacting with the fiber.

Keywords: distributed acoustic sensing, optical fiber devices, optical time domain reflectometry, Rayleigh scattering

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Authors: Hassen M. Ouakad

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In this paper, the influence of van der Waals, as well as electrostatic forces on the structural behavior of MEMS and NEMS actuators, has been investigated using of a Euler-Bernoulli beam continuous model. In the proposed nonlinear model, the electrostatic fringing-fields and the mid-plane stretching (geometric nonlinearity) effects have been considered. The nonlinear integro-differential equation governing the static structural behavior of the actuator has been derived. An original Galerkin-based reduced-order model has been developed to avoid problems arising from the nonlinearities in the differential equation. The obtained reduced-order model equations have been solved numerically using the Newton-Raphson method. The basic design parameters such as the pull-in parameters (voltage and deflection at pull-in), as well as the detachment length due to the van der Waals force of some investigated micro- and nano-actuators have been calculated. The obtained numerical results have been compared with some other existing methods (finite-elements method and finite-difference method) and the comparison showed good agreement among all assumed numerical techniques.

Keywords: MEMS, NEMS, fringing-fields, mid-plane stretching, Galerkin

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Authors: S. Matour, M. Mahdavinejad, R. Fayaz

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Daylight utilization is a key factor in achieving visual and thermal comfort, and energy savings in integrated building design. However, lack of measured data related to this topic has become a major challenge with the increasing need for integrating lighting concepts and simulations in the early stages of design procedures. The current paper deals with the values of daylight illuminance on horizontal and south facing vertical surfaces; the data are estimated using IESNA model and measured values of the horizontal and vertical illuminance, and a regression model with an acceptable linear correlation is obtained. The resultant illuminance frequency curves are useful for estimating daylight availability on south facing surfaces in Tehran. In addition, the relationship between indirect vertical illuminance and the corresponding global horizontal illuminance is analyzed. A simple parametric equation is proposed in order to predict the vertical illumination on a shaded south facing surface. The equation correlates the ratio between the vertical and horizontal illuminance to the solar altitude and is used with another relationship for prediction of the vertical illuminance. Both equations show good agreement, which allows for calculation of indirect vertical illuminance on a south facing surface at any time throughout the year.

Keywords: Tehran daylight availability, horizontal illuminance, vertical illuminance, diffuse illuminance

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Authors: Riddhi Jangid, Gajendra Pratap Singh

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Petri nets, a mathematical tool, is used for modeling in different areas of computer sciences, biological networks, chemical systems and many other disciplines. A Petri net model of a given system is created by the graphical representation that describes the properties and behavior of the system. While looking for the behavior of any system, 1-safe Petri nets are of particular interest to many in the application part. Boolean Petri nets correspond to those class in 1- safe Petri nets that generate all the binary n-vectors in their reachability analysis. We study the class by changing different parameters like the token counts in the places and how the structure of the tree changes in the reachability analysis. We discuss here an extended class of Boolean Petri nets that generates n-ary trees in their reachability-based analysis.

Keywords: marking vector, n-vector, petri nets, reachability

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Authors: Klathea Sevilla, Marjorie Remolador, Bryan Baltazar, Imee Saladaga, Loureal Camille Inocencio, Ma. Rosario Concepcion Ang

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The underutilization of biomass resources in the Philippines, combined with its growing population and the rise in fossil fuel prices confirms demand for alternative energy sources. The goal of this paper is to provide a comparison of MODIS-based and Landsat-based agricultural land cover maps when used in the estimation of rice hull’s available energy potential. Biomass resource assessment was done using mathematical models and remote sensing techniques employed in a GIS platform.

Keywords: biomass, geographic information system (GIS), remote sensing, renewable energy

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Authors: Panagiotis Kyratsis, Konstantinos Kakoulis

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Nowadays, the rapid development of CAD systems’ programming environments results in the creation of multiple downstream applications, which are developed and becoming increasingly available. CAD based manufacturing simulations is gradually following the same trend. Drilling is the most popular hole-making process used in a variety of industries. A specially built piece of software that deals with the drilling kinematics is presented. The cutting forces are calculated based on the tool geometry, the cutting conditions and the tool/work piece materials. The results are verified by experimental work. Finally, the response surface methodology (RSM) is applied and mathematical models of the total thrust force and the thrust force developed because of the main cutting edges are proposed.

Keywords: CAD, application programming interface, response surface methodology, drilling, RSM

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Authors: Martins Onyekwelu Onuorah, Jnr Dahiru Usman

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Introduction: In the realm of public health, the threat posed by Monkeypox continues to elicit concern, prompting rigorous studies to understand its dynamics and devise effective containment strategies. Particularly significant is its recurrence in variable populations, such as the observed outbreak in Nigeria in 2022. In light of this, our study undertakes a meticulous analysis, employing a data-driven approach to explore, validate, and propose optimized intervention strategies tailored to the distinct dynamics of Monkeypox within varying demographic structures. Utilizing a deterministic mathematical model, we delved into the intricate dynamics of Monkeypox, with a particular focus on a variable population context. Our qualitative analysis provided insights into the disease-free equilibrium, revealing its stability when R0 is less than one and discounting the possibility of backward bifurcation, as substantiated by the presence of a single stable endemic equilibrium. The model was rigorously validated using real-time data from the Nigerian 2022 recorded cases for Epi weeks 1 – 52. Transitioning from qualitative to quantitative, we augmented our deterministic model with optimal control, introducing three time-dependent interventions to scrutinize their efficacy and influence on the epidemic's trajectory. Numerical simulations unveiled a pronounced impact of the interventions, offering a data-supported blueprint for informed decision-making in containing the disease. A comprehensive cost-effectiveness analysis employing the Infection Averted Ratio (IAR), Average Cost-Effectiveness Ratio (ACER), and Incremental Cost-Effectiveness Ratio (ICER) facilitated a balanced evaluation of the interventions’ economic and health impacts. In essence, our study epitomizes a holistic approach to understanding and mitigating Monkeypox, intertwining rigorous mathematical modeling, empirical validation, and economic evaluation. The insights derived not only bolster our comprehension of Monkeypox's intricate dynamics but also unveil optimized, cost-effective interventions. This integration of methodologies and findings underscores a pivotal stride towards aligning public health imperatives with economic sustainability, marking a significant contribution to global efforts in combating infectious diseases.

Keywords: monkeypox, equilibrium states, stability, bifurcation, optimal control, cost-effectiveness

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Authors: Hamid Rostami, Ali Fallah Yeznabad, Mohammad H. Baziar

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The energy-based method for evaluating seismic soil liquefaction has two main sections. First is the demand energy, which is dissipated energy of earthquake at a site, and second is the capacity energy as a representation of soil resistance against liquefaction hazard. In this study, using a statistical analysis of recorded data by 14 down-hole array sites in California, an empirical equation was developed to estimate the demand energy at sites. Because determination of capacity energy at a site needs to calculate several site calibration factors, which are obtained by experimental tests, in this study the standard penetration test (SPT) N-value was assumed as an alternative to the capacity energy at a site. Based on this assumption, the empirical equation was employed to calculate the demand energy for 193 liquefied and no-liquefied sites and then these amounts were plotted versus the corresponding SPT numbers for all sites. Subsequently, a discrimination analysis was employed to determine the equations of several boundary curves for various liquefaction likelihoods. Finally, a comparison was made between the probabilistic model and the commonly used stress method. As a conclusion, the results clearly showed that energy-based method can be more reliable than conventional stress-based method in evaluation of liquefaction occurrence.

Keywords: energy demand, liquefaction, probabilistic analysis, SPT number

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Authors: Bamikole J. Adeyemi, Prashant Jadhawar, Lateef Akanji

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Theoretically, there exist two mathematical interfaces (fluid-solid and fluid-fluid) when a liquid film is present on solid surfaces. These interfaces overlap if the mineral surface is oil-wet or mixed wet, and therefore, the effects of disjoining pressure are significant on both boundaries. Hence, dewetting is a necessary process that could detach oil from the mineral surface. However, if the thickness of the thin water film directly in contact with the surface is large enough, disjoining pressure can be thought to be zero at the liquid-liquid interface. Recent studies show that the integration of fluid-fluid interactions with fluid-rock interactions is an important step towards a holistic approach to understanding smart water effects. Experiments have shown that the brine solution can alter the micro forces at oil-water interfaces, and these ion-specific interactions lead to oil emulsion formation. The natural emulsifiers present in crude oil behave as polyelectrolytes when the oil interfaces with low salinity water. Wettability alteration caused by low salinity waterflooding during Enhanced Oil Recovery (EOR) process results from the activities of divalent ions. However, polyelectrolytes are said to lose their viscoelastic property with increasing cation concentrations. In this work, the influence of cation concentrations on the dynamics of viscoelastic liquid-liquid interfaces is numerically investigated. The resultant ion concentrations at the crude oil/brine interfaces were estimated using a surface complexation model. Subsequently, the ion concentration parameter is integrated into a mathematical model to describe its effects on the dynamics of a viscoelastic interfacial thin film. The film growth, stability, and rupture were measured after different time steps for three types of fluids (Newtonian, purely elastic and viscoelastic fluids). The interfacial films respond to exposure time in a similar manner with an increasing growth rate, which resulted in the formation of more droplets with time. Increased surfactant accumulation at the interface results in a higher film growth rate which leads to instability and subsequent formation of more satellite droplets. Purely elastic and viscoelastic properties limit film growth rate and consequent film stability compared to the Newtonian fluid. Therefore, low salinity and reduced concentration of the potential determining ions in injection water will lead to improved interfacial viscoelasticity.

Keywords: liquid-liquid interfaces, surfactant concentrations, potential determining ions, residual oil mobilization

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Authors: Seyed Esmail Seyedi Bariran, Laysheng Ewe, Amy Ling

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Since supplier selection appears as a vital decision, selecting supplier based on the best and most accurate ways has a lot of importance for enterprises. In this study, a new Artificial Intelligence approach is exerted to remove weaknesses of supplier selection. The paper has three parts. First part is choosing the appropriate criteria for assessing the suppliers’ performance. Next one is collecting the data set based on experts. Afterwards, the data set is divided into two parts, the training data set and the testing data set. By the training data set the best structure of GEP and ANN are selected and to evaluate the power of the mentioned methods the testing data set is used. The result obtained shows that the accuracy of GEP is more than ANN. Moreover, unlike ANN, a mathematical equation is presented by GEP for the supplier selection.

Keywords: supplier selection, automotive supply chains, ANN, GEP

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Authors: A. J. Regan, F. J. Lidgey, M. Betteridge, P. Georgiou, C. Toumazou, K. Hayatleh, J. R. Dibble

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Our goal is development of an algorithm capable of predicting the directional trend of the Standard and Poor’s 500 index (S&P 500). Extensive research has been published attempting to predict different financial markets using historical data testing on an in-sample and trend basis, with many authors employing excessively complex mathematical techniques. In reviewing and evaluating these in-sample methodologies, it became evident that this approach was unable to achieve sufficiently reliable prediction performance for commercial exploitation. For these reasons, we moved to an out-of-sample strategy based on linear regression analysis of an extensive set of financial data correlated with historical closing prices of the S&P 500. We are pleased to report a directional trend accuracy of greater than 55% for tomorrow (t+1) in predicting the S&P 500.

Keywords: financial algorithm, GPU, S&P 500, stock market prediction

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Authors: Maitree Thamma, Witchupong Wiboonjaroen, Thanat Suknuan, Karan Homchat

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First order plus dead time (FOPDT) is a high dynamic system. Therefore, the controller must be intelligent. This paper presents the development and implementation of self-tuning Fuzzy-PID controller for controlling the FOPDT system. The water level process used represented FOPDT system and the mathematical model of the system was approximated by using System Identification toolbox in Matlab. The control programming and Fuzzy-PID algorithm used Matlab/Simulink and run on Microcontroller STM32.

Keywords: real-time control, self-tuning fuzzy-PID, FOPDT system, the water lever process

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Authors: Melissa Ramirez, Mohammad Awal

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The Inflow Performance Relationship (IPR) of a well is a relation between the oil production rate and flowing bottom-hole pressure. This relationship is an important tool for petroleum engineers to understand and predict the well performance. In the petroleum industry, IPR correlations are used to design and evaluate well completion, optimizing well production, and designing artificial lift. The most commonly used IPR correlations models are Vogel and Wiggins, these models are applicable to homogeneous and isotropic reservoir data. In this work, a new IPR model is developed to determine inflow performance relationship of oil wells in a naturally fracture reservoir. A 3D black-oil reservoir simulator is used to develop the oil mobility function for the studied reservoir. Based on simulation runs, four flow rates are run to record the oil saturation and calculate the relative permeability for a naturally fractured reservoir. The new method uses the result of a well test analysis along with permeability and pressure-volume-temperature data in the fluid flow equations to obtain the oil mobility function. Comparisons between the new method and two popular correlations for non-fractured reservoirs indicate the necessity for developing and using an IPR correlation specifically developed for a fractured reservoir.

Keywords: inflow performance relationship, mobility function, naturally fractured reservoir, well test analysis

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Authors: Ahmet Y. Gurkan, Cagatay S. Koksal, Cagri Aydin, U. Oral Unal

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The present paper covers the viscous flow computations for the asymmetric diffuser section of a large, high-speed cavitation tunnel which will be constructed in Istanbul Technical University. The analyses were carried out by using the incompressible Reynold-Averaged-Navier-Stokes equations. While determining the diffuser geometry, a high quality, separation-free flow field with minimum energy loses was particularly aimed. The expansion angle has a critical role on the diffuser hydrodynamic performance. In order obtain a relatively short diffuser length, due to the constructive limitations, and hydrodynamic energy effectiveness, three diffuser sections with varying expansion angles for side and bottom walls were considered. A systematic study was performed to determine the most effective diffuser configuration. The results revealed that the inlet condition of the diffuser greatly affects its flow field. The inclusion of the contraction section in the computations substantially modified the flow topology in the diffuser. The effect of the diffuser flow on the test section flow characteristics was clearly observed. The influence of the introduction of small chamfers at the corners of the diffuser geometry is also presented.

Keywords: asymmetric diffuser, diffuser design, cavitation tunnel, viscous flow, computational fluid dynamics (CFD), rans

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Authors: Neda Lovričević, Đilda Pečarić, Josip Pečarić

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The Jensen functional in its discrete form is brought in relation to the Csiszar divergence functional, this time via its monotonicity property. This approach presents a generalization of the previously obtained results that made use of interpolating Jensen-type inequalities. Thus the monotonicity property is integrated with the Zipf-Mandelbrot law and applied to f-divergences for probability distributions that originate from the Csiszar divergence functional: Kullback-Leibler divergence, Hellinger distance, Bhattacharyya distance, chi-square divergence, total variation distance. The Zipf-Mandelbrot and the Zipf law are widely used in various scientific fields and interdisciplinary and here the focus is on the aspect of the mathematical inequalities.

Keywords: Jensen functional, monotonicity, Csiszar divergence functional, f-divergences, Zipf-Mandelbrot law

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Authors: masmoudi Jabri Khaoula, Zitouni Hana, Bousselmi Latifa, Akrout Hanen

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Mathematical modeling has become an essential tool for sustainable wastewater management, particularly for the simulation and the optimization of complex processes involved in activated sludge systems. In this context, the activated sludge model (ASM3h) was used for the simulation of a Biological Membrane Reactor (MBR) as it includes the integration of biological wastewater treatment and physical separation by membrane filtration. In this study, the MBR with a useful volume of 12.5 L was fed continuously with poultry slaughterhouse wastewater (PSWW) for 50 days at a feed rate of 2 L/h and for a hydraulic retention time (HRT) of 6.25h. Throughout its operation, High removal efficiency was observed for the removal of organic pollutants in terms of COD with 84% of efficiency. Moreover, the MBR has generated a treated effluent which fits with the limits of discharge into the public sewer according to the Tunisian standards which were set in March 2018. In fact, for the nitrogenous compounds, average concentrations of nitrate and nitrite in the permeat reached 0.26±0.3 mg. L-1 and 2.2±2.53 mg. L-1, respectively. The simulation of the MBR process was performed using SIMBA software v 5.0. The state variables employed in the steady state calibration of the ASM3h were determined using physical and respirometric methods. The model calibration was performed using experimental data obtained during the first 20 days of the MBR operation. Afterwards, kinetic parameters of the model were adjusted and the simulated values of COD, N-NH4+and N- NOx were compared with those reported from the experiment. A good prediction was observed for the COD, N-NH4+and N- NOx concentrations with 467 g COD/m³, 110.2 g N/m³, 3.2 g N/m³ compared to the experimental data which were 436.4 g COD/m³, 114.7 g N/m³ and 3 g N/m³, respectively. For the validation of the model under dynamic simulation, the results of the experiments obtained during the second treatment phase of 30 days were used. It was demonstrated that the model simulated the conditions accurately by yielding a similar pattern on the variation of the COD concentration. On the other hand, an underestimation of the N-NH4+ concentration was observed during the simulation compared to the experimental results and the measured N-NO3 concentrations were lower than the predicted ones, this difference could be explained by the fact that the ASM models were mainly designed for the simulation of biological processes in the activated sludge systems. In addition, more treatment time could be required by the autotrophic bacteria to achieve a complete and stable nitrification. Overall, this study demonstrated the effectiveness of mathematical modeling in the prediction of the performance of the MBR systems with respect to organic pollution, the model can be further improved for the simulation of nutrients removal for a longer treatment period.

Keywords: activated sludge model (ASM3h), membrane bioreactor (MBR), poultry slaughter wastewater (PSWW), reuse

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Authors: Adewoyin O. Olusegun, Akinwumi I. Isaac

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In some part of the world where legislations related to site investigations before constructions are not strictly enforced, the expenses and time required for carrying out a comprehensive geotechnical investigation to characterize a site can discourage prospective private residential building developers. Another factor that can discourage a developer is the fact that most of the geotechnical tests procedures utilized during site investigations, to a certain extent, alter the existing environment of the site. This study suggests a quick, non-destructive and non-intrusive method of obtaining key subsoil geotechnical properties necessary for foundation design for proposed engineering facilities. Seismic wave velocities generated from near surface refraction method was used to determine the bulk density of soil, Young’s modulus, bulk modulus, shear modulus and allowable bearing capacity of a competent layer that can bear structural load at the particular study site. Also, regression equations were developed in order to directly obtain the bulk density of soil, Young’s modulus, bulk modulus, shear modulus and allowable bearing capacity from the compressional wave velocities. The results obtained correlated with the results of standard geotechnical investigations carried out.

Keywords: characterize, environment, geophysical, geotechnical, regression

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Authors: Hadi Aghazadeh, Seyed Ebrahim Afjei, Alireza Siadatan

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In this paper, a proper approach is taken to assess a set of the most effective rotor design parameters for an external-rotor permanent magnet assisted synchronous reluctance motor (PMaSynRM) and therefore to tackle the design complexity of the rotor structure. There are different advantages for introducing permanent magnets into the rotor flux barriers, some of which are to saturate the rotor iron ribs, to increase the motor torque density and to improve the power factor. Moreover, the d-axis and q-axis inductances are of great importance to simultaneously achieve maximum developed torque and low torque ripple. Therefore, sensitivity analysis of the rotor geometry of an 8-pole external-rotor permanent magnet assisted synchronous reluctance motor is performed. Several magnetically accurate finite element analyses (FEA) are conducted to characterize the electromagnetic performance of the motor. The analyses validate torque and power factor equations for the proposed external-rotor motor. Based upon the obtained results and due to an additional term, permanent magnet torque, added to the reluctance torque, the electromagnetic torque of the PMaSynRM increases.

Keywords: permanent magnet assisted synchronous reluctance motor, flux barrier, flux carrier, electromagnetic torque, and power factor

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Authors: Kamal, J. P. Narayan

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In the present wok the effects of basin-shape-ratio on the frequency content and spectral amplitudes of the basin-generated surface waves and the associated spatial variation of ground motion amplification and differential ground motion in a 3D semi-spherical basin has been studied. A recently developed 3D fourth-order spatial accurate time-domain finite-difference (FD) algorithm based on the parsimonious staggered-grid approximation of the 3D viscoelastic wave equations was used to estimate seismic responses. The simulated results demonstrated the increase of both the frequency content and the spectral amplitudes of the basin-generated surface waves and the duration of ground motion in the basin with the increase of shape-ratio of semi-spherical basin. An increase of the average spectral amplification (ASA), differential ground motion (DGM) and the average aggravation factor (AAF) towards the centre of the semi-spherical basin was obtained.

Keywords: 3D viscoelastic simulation, basin-generated surface waves, basin-shape-ratio effects, average spectral amplification, aggravation factors and differential ground motion

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Authors: Fahim Kahlouche, Alaoua Bouaicha, Sihem Chaîbeddra, Sid-Ali Rafa, Abdelhamid Benouali

Abstract:

A designing of a structure requires its realization on rough or sloping ground. Besides the problem of the stability of the landslide, the behavior of the foundations that are bearing the structure is influenced by the destabilizing effect of the ground’s slope. This article focuses on the analysis of the slope stability exposed to loading by introducing the different factors influencing the slope’s behavior on the one hand, and on the influence of this slope on the foundation’s behavior on the other hand. This study is about the elastoplastic modelization using FLAC 2D. This software is based on the finite difference method, which is one of the older methods of numeric resolution of differential equations system with initial and boundary conditions. It was developed for the geotechnical simulation calculation. The aim of this simulation is to demonstrate the notable effect of shear modulus « G », cohesion « C », inclination angle (edge) « β », and distance between the foundation and the head of the slope on the stability of the slope as well as the stability of the foundation. In our simulation, the slope is constituted by homogenous ground. The foundation is considered as rigid/hard; therefore, the loading is made by the application of the vertical strengths on the nodes which represent the contact between the foundation and the ground. 

Keywords: slope, shallow foundation, numeric method, FLAC 2D

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Authors: Anthony P. Anies, Jose C. Muñoz

Abstract:

A new shortcut method for the design of reactive-dividing wall columns (RDWC) is proposed in this work. The RDWC is decomposed into its thermodynamically equivalent configuration naming the Petlyuk column, which consists of a reactive prefractionator and an unreactive main fractionator. The modified FUGK(Fenske-Underwood-Gilliland-Kirkbride) shortcut distillation method, which incorporates the effect of reaction on the Underwood equations and the Gilliland correlation, is used to design the reactive prefractionator. On the other hand, the conventional FUGK shortcut method is used to design the unreactive main fractionator. The shortcut method is applied to the synthesis of dimethyl ether (DME) through the liquid phase dehydration of methanol, and the results were used as the starting design inputs for rigorous simulation in Aspen Plus V8.8. A mole purity of 99 DME in the distillate stream, 99% methanol in the side draw stream, and 99% water in the bottoms stream were obtained in the simulation, thereby making the proposed shortcut method applicable for the preliminary design of RDWC.

Keywords: aspen plus, dimethyl ether, petlyuk column, reactive-dividing wall column, shortcut method, FUGK

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Authors: Ekaterina M. Myasnikova, Andrey A. Makashov, Alexander V. Spirov

Abstract:

First manifestation of a segmentation pattern in the early Drosophila development is the formation of expression domains (along with the main embryo axis) of genes belonging to the trunk gene class. Highly variable expression of genes from gap family in early Drosophila embryo is strongly reduced by the start of gastrulation due to the gene cross-regulation. The dynamics of gene expression is described by a gene circuit model for a system of four gap genes. It is shown that for the formation of a steep and stationary border by the model it is necessary that there existed a nucleus (modeling point) in which the gene expression level is constant in time and hence is described by a stationary equation. All the rest genes expressed in this nucleus are in a dynamic equilibrium. The mechanism of border formation associated with the existence of a stationary nucleus is also confirmed by the experiment. An important advantage of this approach is that properties of the system in a stationary nucleus are described by algebraic equations and can be easily handled analytically. Thus we explicitly characterize the cross-regulation properties necessary for the robustness and formulate the conditions providing this effect through the properties of the initial input data. It is shown that our formally derived conditions are satisfied for the previously published model solutions.

Keywords: drosophila, gap genes, reaction-diffusion model, robustness

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