Search results for: mathematical model.
7610 Estimating the Runoff Using the Simple Tank Model and Comparing it with the SCS-CN Model - A Case Study of the Dez River Basin
Authors: H. Alaleh, N. Hedayat, A. Alaleh, H. Ayazi, A. Ruhani
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Run-offs are considered as important hydrological factors in feasibility studies of river engineering and irrigation-related projects under arid and semi-arid condition. Flood control is one of the crucial factor, the management of which while mitigates its destructive consequences, abstracts considerable volume of renewable water resources. The methodology applied here was based on Mizumura, which applied a mathematical model for simple tank to simulate the rainfall-run-off process in a particular water basin using the data from the observational hydrograph. The model was applied in the Dez River water basin adjacent to Greater Dezful region, Iran in order to simulate and estimate the floods. Results indicated that the calculated hydrographs using the simple tank method, SCS-CN model and the observation hydrographs had a close proximity. It was also found that on average the flood time and discharge peaks in the simple tank were closer to the observational data than the CN method. On the other hand, the calculated flood volume in the CN model was significantly closer to the observational data than the simple tank model.
Keywords: Simple tank, Dez River, run-off, lag time, excess rainfall.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 25847609 Transmission Expansion Planning with Economic Dispatch and N-1Constraints
Authors: A. Charlangsut, M. Boonthienthong, N. Rugthaicharoencheep
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This paper proposes a mathematical model for transmission expansion employing optimization method with scenario analysis approach. Economic transmission planning, on the other hand, seeks investment opportunities so that network expansions can generate more economic benefits than the costs. This approach can be used as a decision model for building new transmission lines added to the existing transmission system minimizing costs of the entire system subject to various system’s constraints and consider of loss value of transmission system and N-1 checking. The results show that the proposed model is efficient to be applied for the larger scale of power system topology.
Keywords: Transmission Expansion Planning, Economic Dispatch, Scenario Analysis, Contingency.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 20907608 A Qualitative Description of the Dynamics in the Interactions between Three Populations: Pollinators, Plants, and Herbivores
Authors: Miriam Sosa-Díaz, Faustino Sánchez-Garduño
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In population dynamics the study of both, the abundance and the spatial distribution of the populations in a given habitat, is a fundamental issue a From ecological point of view, the determination of the factors influencing such changes involves important problems. In this paper a mathematical model to describe the temporal dynamic and the spatiotemporal dynamic of the interaction of three populations (pollinators, plants and herbivores) is presented. The study we present is carried out by stages: 1. The temporal dynamics and 2. The spatio-temporal dynamics. In turn, each of these stages is developed by considering three cases which correspond to the dynamics of each type of interaction. For instance, for stage 1, we consider three ODE nonlinear systems describing the pollinator-plant, plant-herbivore and plant-pollinator-herbivore, interactions, respectively. In each of these systems different types of dynamical behaviors are reported. Namely, transcritical and pitchfork bifurcations, existence of a limit cycle, existence of a heteroclinic orbit, etc. For the spatiotemporal dynamics of the two mathematical models a novel factor are introduced. This consists in considering that both, the pollinators and the herbivores, move towards those places of the habitat where the plant population density is high. In mathematical terms, this means that the diffusive part of the pollinators and herbivores equations depend on the plant population density. The analysis of this part is presented by considering pairs of populations, i. e., the pollinator-plant and plant-herbivore interactions and at the end the two mathematical model is presented, these models consist of two coupled nonlinear partial differential equations of reaction-diffusion type. These are defined on a rectangular domain with the homogeneous Neumann boundary conditions. We focused in the role played by the density dependent diffusion term into the coexistence of the populations. For both, the temporal and spatio-temporal dynamics, a several of numerical simulations are included.Keywords: Bifurcation, heteroclinic orbits, steady state, traveling wave.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 14887607 Thermohydraulic Performance of Double Flow Solar Air Heater with Corrugated Absorber
Authors: S. P. Sharma, Som Nath Saha
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This paper deals with the analytical investigation of thermal and thermohydraulic performance of double flow solar air heaters with corrugated and flat plate absorber. A mathematical model of double flow solar air heater has been presented, and a computer program in C++ language is developed to estimate the outlet temperature of air for the evaluation of thermal and thermohydraulic efficiency by solving the governing equations numerically using relevant correlations for heat transfer coefficients. The results obtained from the mathematical model is compared with the available experimental results and it is found to be reasonably good. The results show that the double flow solar air heaters have higher efficiency than conventional solar air heater, although the double flow corrugated absorber is superior to that of flat plate double flow solar air heater. It is also observed that the thermal efficiency increases with increase in mass flow rate; however, thermohydraulic efficiency increases with increase in mass flow rate up to a certain limit, attains the maximum value, then thereafter decreases sharply.
Keywords: Corrugated absorber, double flow, solar air heater, thermohydraulic efficiency.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 14917606 Mathematical Model of Smoking Time Temperature Effect on Ribbed Smoked Sheets Quality
Authors: Rifah Ediati, Jajang
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The quality of Ribbed Smoked Sheets (RSS) primarily based on color, dryness, and the presence or absence of fungus and bubbles. This quality is strongly influenced by the drying and fumigation process namely smoking process. Smoking that is held in high temperature long time will result scorched dark brown sheets, whereas if the temperature is too low or slow drying rate would resulted in less mature sheets and growth of fungus. Therefore need to find the time and temperature for optimum quality of sheets. Enhance, unmonitored heat and mass transfer during smoking process lead to high losses of energy balance. This research aims to generate simple empirical mathematical model describing the effect of smoking time and temperature to RSS quality of color, water content, fungus and bubbles. The second goal of study was to analyze energy balance during smoking process. Experimental study was conducted by measuring temperature, residence time and quality parameters of 16 sheets sample in smoking rooms. Data for energy consumption balance such as mass of fuel wood, mass of sheets being smoked, construction temperature, ambient temperature and relative humidity were taken directly along the smoking process. It was found that mathematical model correlating smoking temperature and time with color is Color = -169 - 0.184 T4 - 0.193 T3 - 0.160 0.405 T1 + T2 + 0.388 t1 +3.11 t2 + 3.92t3 + 0.215 t4 with R square 50.8% and with moisture is Moisture = -1.40-0.00123 T4 + 0.00032 T3 + 0.00260 T2 - 0.00292 T1 - 0.0105 t1 + 0.0290 t2 + 0.0452 t3 + 0.00061 t4 with R square of 49.9%. Smoking room energy analysis found useful energy was 27.8%. The energy stored in the material construction 7.3%. Lost of energy in conversion of wood combustion, ventilation and others were 16.6%. The energy flowed out through the contact of material construction with the ambient air was found to be the highest contribution to energy losses, it reached 48.3%.Keywords: RSS quality, temperature, time, smoking room, energy
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 27417605 Combined Sewer Overflow forecasting with Feed-forward Back-propagation Artificial Neural Network
Authors: Achela K. Fernando, Xiujuan Zhang, Peter F. Kinley
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A feed-forward, back-propagation Artificial Neural Network (ANN) model has been used to forecast the occurrences of wastewater overflows in a combined sewerage reticulation system. This approach was tested to evaluate its applicability as a method alternative to the common practice of developing a complete conceptual, mathematical hydrological-hydraulic model for the sewerage system to enable such forecasts. The ANN approach obviates the need for a-priori understanding and representation of the underlying hydrological hydraulic phenomena in mathematical terms but enables learning the characteristics of a sewer overflow from the historical data. The performance of the standard feed-forward, back-propagation of error algorithm was enhanced by a modified data normalizing technique that enabled the ANN model to extrapolate into the territory that was unseen by the training data. The algorithm and the data normalizing method are presented along with the ANN model output results that indicate a good accuracy in the forecasted sewer overflow rates. However, it was revealed that the accurate forecasting of the overflow rates are heavily dependent on the availability of a real-time flow monitoring at the overflow structure to provide antecedent flow rate data. The ability of the ANN to forecast the overflow rates without the antecedent flow rates (as is the case with traditional conceptual reticulation models) was found to be quite poor.Keywords: Artificial Neural Networks, Back-propagationlearning, Combined sewer overflows, Forecasting.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 15127604 Improvements in Edge Detection Based on Mathematical Morphology and Wavelet Transform using Fuzzy Rules
Authors: Masrour Dowlatabadi, Jalil Shirazi
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In this paper, an improved edge detection algorithm based on fuzzy combination of mathematical morphology and wavelet transform is proposed. The combined method is proposed to overcome the limitation of wavelet based edge detection and mathematical morphology based edge detection in noisy images. Experimental results show superiority of the proposed method, as compared to the traditional Prewitt, wavelet based and morphology based edge detection methods. The proposed method is an effective edge detection method for noisy image and keeps clear and continuous edges.Keywords: Edge detection, Wavelet transform, Mathematical morphology, Fuzzy logic.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 23947603 Mathematical Modeling to Predict Surface Roughness in CNC Milling
Authors: Ab. Rashid M.F.F., Gan S.Y., Muhammad N.Y.
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Surface roughness (Ra) is one of the most important requirements in machining process. In order to obtain better surface roughness, the proper setting of cutting parameters is crucial before the process take place. This research presents the development of mathematical model for surface roughness prediction before milling process in order to evaluate the fitness of machining parameters; spindle speed, feed rate and depth of cut. 84 samples were run in this study by using FANUC CNC Milling α-Τ14ιE. Those samples were randomly divided into two data sets- the training sets (m=60) and testing sets(m=24). ANOVA analysis showed that at least one of the population regression coefficients was not zero. Multiple Regression Method was used to determine the correlation between a criterion variable and a combination of predictor variables. It was established that the surface roughness is most influenced by the feed rate. By using Multiple Regression Method equation, the average percentage deviation of the testing set was 9.8% and 9.7% for training data set. This showed that the statistical model could predict the surface roughness with about 90.2% accuracy of the testing data set and 90.3% accuracy of the training data set.
Keywords: Surface roughness, regression analysis.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 21177602 Numerical Simulation and Experimental Validation of the Tire-Road Separation in Quarter-Car Model
Authors: Quy Dang Nguyen, Reza Nakhaie Jazar
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The paper investigates vibration dynamics of tire-road separation for a quarter-car model; this separation model is developed to be close to the real situation considering the tire is able to separate from the ground plane. A set of piecewise linear mathematical models is developed and matches the in-contact and no-contact states to be considered as mother models for further investigations. The bound dynamics are numerically simulated in the time response and phase portraits. The separation analysis may determine which values of suspension parameters can delay and avoid the no-contact phenomenon, which results in improving ride comfort and eliminating the potentially dangerous oscillation. Finally, model verification is carried out in the MSC-ADAMS environment.
Keywords: Quarter-car vibrations, tire-road separation, separation analysis, separation dynamics, ride comfort, ADAMS validation.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1777601 A Physical Theory of Information vs. a Mathematical Theory of Communication
Authors: Manouchehr Amiri
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This article presents a general notion of physical bit information that is compatible with the basics of quantum mechanics and incorporates the Shannon entropy as a special case. This notion of physical information leads to the Binary Data Matrix model (BDM), which predicts the basic results of quantum mechanics, general relativity, and black hole thermodynamics. The compatibility of the model with holographic, information conservation, and Landauer’s principle is investigated. After deriving the “Bit Information principle” as a consequence of BDM, the fundamental equations of Planck, De Broglie, Bekenstein, and mass-energy equivalence are derived.
Keywords: Physical theory of information, binary data matrix model, Shannon information theory, bit information principle.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1167600 Using the Simple Fixed Rate Approach to Solve Economic Lot Scheduling Problem under the Basic Period Approach
Authors: Yu-Jen Chang, Yun Chen, Hei-Lam Wong
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The Economic Lot Scheduling Problem (ELSP) is a valuable mathematical model that can support decision-makers to make scheduling decisions. The basic period approach is effective for solving the ELSP. The assumption for applying the basic period approach is that a product must use its maximum production rate to be produced. However, a product can lower its production rate to reduce the average total cost when a facility has extra idle time. The past researches discussed how a product adjusts its production rate under the common cycle approach. To the best of our knowledge, no studies have addressed how a product lowers its production rate under the basic period approach. This research is the first paper to discuss this topic. The research develops a simple fixed rate approach that adjusts the production rate of a product under the basic period approach to solve the ELSP. Our numerical example shows our approach can find a better solution than the traditional basic period approach. Our mathematical model that applies the fixed rate approach under the basic period approach can serve as a reference for other related researches.Keywords: Economic Lot, Basic Period, Genetic Algorithm, Fixed Rate.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 19297599 Prediction of Solidification Behavior of Al Alloy in a Cube Mold Cavity
Authors: N. P. Yadav, Deepti Verma
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This paper focuses on the mathematical modeling for solidification of Al alloy in a cube mold cavity to study the solidification behavior of casting process. The parametric investigation of solidification process inside the cavity was performed by using computational solidification/melting model coupled with Volume of fluid (VOF) model. The implicit filling algorithm is used in this study to understand the overall process from the filling stage to solidification in a model metal casting process. The model is validated with past studied at same conditions. The solidification process is analyzed by including the effect of pouring velocity as well as natural convection from the wall and geometry of the cavity. These studies show the possibility of various defects during solidification process.Keywords: Buoyancy driven flow, natural convection driven flow, residual flow, secondary flow, volume of fluid.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 23057598 A Simulation Model and Parametric Study of Triple-Effect Desalination Plant
Authors: Maha BenHamad, Ali Snoussi, Ammar Ben Brahim
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A steady-state analysis of triple-effect thermal vapor compressor desalination unit was performed. A mathematical model based on mass, salinity and energy balances is developed. The purpose of this paper is to develop a connection between process simulator and process optimizer in order to study the influence of several operating variables on the performance and the produced water cost of the unit. A MATLAB program is used to solve the model equations, and Aspen HYSYS is used to model the plant. The model validity is examined against a commercial plant and showed a good agreement between industrial data and simulations results. Results show that the pressures of the last effect and the compressed vapor have an important influence on the produced cost, and the increase of the difference temperature in the condenser decreases the specific heat area about 22%.
Keywords: Steady-state, triple effect, thermal vapor compressor, MATLAB, Aspen HYSYS.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 10567597 Kinematic Modelling and Maneuvering of A 5-Axes Articulated Robot Arm
Authors: T.C. Manjunath
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This paper features the kinematic modelling of a 5-axis stationary articulated robot arm which is used for doing successful robotic manipulation task in its workspace. To start with, a 5-axes articulated robot was designed entirely from scratch and from indigenous components and a brief kinematic modelling was performed and using this kinematic model, the pick and place task was performed successfully in the work space of the robot. A user friendly GUI was developed in C++ language which was used to perform the successful robotic manipulation task using the developed mathematical kinematic model. This developed kinematic model also incorporates the obstacle avoiding algorithms also during the pick and place operation.
Keywords: Robot, Sensors, Kinematics, Computer, Control, PNP, LCD, Software.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 44537596 ISTER (Immune System - Tumor Efficiency Rate): An Important Key for Planning in Radiotherapic Facilities
Authors: O. Sotolongo-Grau, D. Rodriguez-Perez, J. A. Santos-Miranda, M. M. Desco, O. Sotolongo-Costa, J. C. Antoranz
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The use of the oncologic index ISTER allows for a more effective planning of the radiotherapic facilities in the hospitals. Any change in the radiotherapy treatment, due to unexpected stops, may be adapted by recalculating the doses to the new treatment duration while keeping the optimal prognosis. The results obtained in a simulation model on millions of patients allow the definition of optimal success probability algorithms.
Keywords: Mathematical model, radiation oncology, dynamical systems applications.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 15297595 Mathematical Modeling of the Working Principle of Gravity Gradient Instrument
Authors: Danni Cong, Meiping Wu, Hua Mu, Xiaofeng He, Junxiang Lian, Juliang Cao, Shaokun Cai, Hao Qin
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Gravity field is of great significance in geoscience, national economy and national security, and gravitational gradient measurement has been extensively studied due to its higher accuracy than gravity measurement. Gravity gradient sensor, being one of core devices of the gravity gradient instrument, plays a key role in measuring accuracy. Therefore, this paper starts from analyzing the working principle of the gravity gradient sensor by Newton’s law, and then considers the relative motion between inertial and non-inertial systems to build a relatively adequate mathematical model, laying a foundation for the measurement error calibration, measurement accuracy improvement.Keywords: Gravity gradient, accelerometer, gravity gradient sensor, single-axis rotation modulation.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 10507594 A Bi-Objective Model to Address Simultaneous Formulation of Project Scheduling and Material Ordering
Authors: Babak H. Tabrizi, Seyed Farid Ghaderi
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Concurrent planning of project scheduling and material ordering has been increasingly addressed within last decades as an approach to improve the project execution costs. Therefore, we have taken the problem into consideration in this paper, aiming to maximize schedules quality robustness, in addition to minimize the relevant costs. In this regard, a bi-objective mathematical model is developed to formulate the problem. Moreover, it is possible to utilize the all-unit discount for materials purchasing. The problem is then solved by the E-constraint method, and the Pareto front is obtained for a variety of robustness values. The applicability and efficiency of the proposed model is tested by different numerical instances, finally.Keywords: E-constraint method, material ordering, project management, project scheduling.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 20057593 Evaluation of Hydrogen Particle Volume on Surfaces of Selected Nanocarbons
Authors: M. Ziółkowska, J. T. Duda, J. Milewska-Duda
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This paper describes an approach to the adsorption phenomena modeling aimed at specifying the adsorption mechanisms on localized or nonlocalized adsorbent sites, when applied to the nanocarbons. The concept comes from the fundamental thermodynamic description of adsorption equilibrium and is based on numerical calculations of the hydrogen adsorbed particles volume on the surface of selected nanocarbons: single-walled nanotube and nanocone. This approach enables to obtain information on adsorption mechanism and then as a consequence to take appropriate mathematical adsorption model, thus allowing for a more reliable identification of the material porous structure. Theoretical basis of the approach is discussed and newly derived results of the numerical calculations are presented for the selected nanocarbons.
Keywords: Adsorption, mathematical modeling, nanocarbons, numerical analysis.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 18957592 The Fundamental Reliance of Iterative Learning Control on Stability Robustness
Authors: Richard W. Longman
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Iterative learning control aims to achieve zero tracking error of a specific command. This is accomplished by iteratively adjusting the command given to a feedback control system, based on the tracking error observed in the previous iteration. One would like the iterations to converge to zero tracking error in spite of any error present in the model used to design the learning law. First, this need for stability robustness is discussed, and then the need for robustness of the property that the transients are well behaved. Methods of producing the needed robustness to parameter variations and to singular perturbations are presented. Then a method involving reverse time runs is given that lets the world behavior produce the ILC gains in such a way as to eliminate the need for a mathematical model. Since the real world is producing the gains, there is no issue of model error. Provided the world behaves linearly, the approach gives an ILC law with both stability robustness and good transient robustness, without the need to generate a model.Keywords: Iterative learning control, stability robustness, monotonic convergence.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 15897591 Mathematical Modelling of Venturi Scrubber for Ammonia Absorption
Authors: S.Mousavian, D.Ashouri, M.abdolahi, M.H.Vakili, Y.Rahnama
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In this study, the dispersed model is used to predict gas phase concentration, liquid drop concentration. The venturi scrubber efficiency is calculated by gas phase concentration. The modified model has been validated with available experimental data of Johnstone, Field and Tasler for a range of throat gas velocities, liquid to gas ratios and particle diameters and is used to study the effect of some design parameters on collection efficiency.Keywords: Ammonia, Modelling, Purge gas, Removal efficiency, Venturi scrubber
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 24527590 Mathematical Programming Models for Portfolio Optimization Problem: A Review
Authors: M. Mokhtar, A. Shuib, D. Mohamad
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Portfolio optimization problem has received a lot of attention from both researchers and practitioners over the last six decades. This paper provides an overview of the current state of research in portfolio optimization with the support of mathematical programming techniques. On top of that, this paper also surveys the solution algorithms for solving portfolio optimization models classifying them according to their nature in heuristic and exact methods. To serve these purposes, 40 related articles appearing in the international journal from 2003 to 2013 have been gathered and analyzed. Based on the literature review, it has been observed that stochastic programming and goal programming constitute the highest number of mathematical programming techniques employed to tackle the portfolio optimization problem. It is hoped that the paper can meet the needs of researchers and practitioners for easy references of portfolio optimization.
Keywords: Portfolio optimization, Mathematical programming, Multi-objective programming, Solution approaches.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 65567589 A new Heuristic Algorithm for the Dynamic Facility Layout Problem with Budget Constraint
Authors: Parham Azimi, Hamid Reza Charmchi
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In this research, we have developed a new efficient heuristic algorithm for the dynamic facility layout problem with budget constraint (DFLPB). This heuristic algorithm combines two mathematical programming methods such as discrete event simulation and linear integer programming (IP) to obtain a near optimum solution. In the proposed algorithm, the non-linear model of the DFLP has been changed to a pure integer programming (PIP) model. Then, the optimal solution of the PIP model has been used in a simulation model that has been designed in a similar manner as the DFLP for determining the probability of assigning a facility to a location. After a sufficient number of runs, the simulation model obtains near optimum solutions. Finally, to verify the performance of the algorithm, several test problems have been solved. The results show that the proposed algorithm is more efficient in terms of speed and accuracy than other heuristic algorithms presented in previous works found in the literature.Keywords: Budget constraint, Dynamic facility layout problem, Integer programming, Simulation
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 19577588 A Study of Two Disease Models: With and Without Incubation Period
Authors: H. C. Chinwenyi, H. D. Ibrahim, J. O. Adekunle
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The incubation period is defined as the time from infection with a microorganism to development of symptoms. In this research, two disease models: one with incubation period and another without incubation period were studied. The study involves the use of a mathematical model with a single incubation period. The test for the existence and stability of the disease free and the endemic equilibrium states for both models were carried out. The fourth order Runge-Kutta method was used to solve both models numerically. Finally, a computer program in MATLAB was developed to run the numerical experiments. From the results, we are able to show that the endemic equilibrium state of the model with incubation period is locally asymptotically stable whereas the endemic equilibrium state of the model without incubation period is unstable under certain conditions on the given model parameters. It was also established that the disease free equilibrium states of the model with and without incubation period are locally asymptotically stable. Furthermore, results from numerical experiments using empirical data obtained from Nigeria Centre for Disease Control (NCDC) showed that the overall population of the infected people for the model with incubation period is higher than that without incubation period. We also established from the results obtained that as the transmission rate from susceptible to infected population increases, the peak values of the infected population for the model with incubation period decrease and are always less than those for the model without incubation period.
Keywords: Asymptotic stability, incubation period, Routh-Hurwitz criterion, Runge Kutta method.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 6777587 Modeling of Cross Flow Classifier with Water Injection
Authors: E. Pikushchak, J. Dueck, L. Minkov
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In hydrocyclones, the particle separation efficiency is limited by the suspended fine particles, which are discharged with the coarse product in the underflow. It is well known that injecting water in the conical part of the cyclone reduces the fine particle fraction in the underflow. This paper presents a mathematical model that simulates the water injection in the conical component. The model accounts for the fluid flow and the particle motion. Particle interaction, due to hindered settling caused by increased density and viscosity of the suspension, and fine particle entrainment by settling coarse particles are included in the model. Water injection in the conical part of the hydrocyclone is performed to reduce fine particle discharge in the underflow. The model demonstrates the impact of the injection rate, injection velocity, and injection location on the shape of the partition curve. The simulations are compared with experimental data of a 50-mm cyclone.Keywords: Classification, fine particle processing, hydrocyclone, water injection.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 19457586 Practical Problems as Tools for the Development of Secondary School Students’ Motivation to Learn Mathematics
Authors: M. Rodionov, Z. Dedovets
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This article discusses plausible reasoning use for solution to practical problems. Such reasoning is the major driver of motivation and implementation of mathematical, scientific and educational research activity. A general, practical problem solving algorithm is presented which includes an analysis of specific problem content to build, solve and interpret the underlying mathematical model. The author explores the role of practical problems such as the stimulation of students' interest, the development of their world outlook and their orientation in the modern world at the different stages of learning mathematics in secondary school. Particular attention is paid to the characteristics of those problems which were systematized and presented in the conclusions.
Keywords: Mathematics, motivation, secondary school, student, practical problem.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 10577585 Gas-Solid Nitrocarburizing of Steels: Kinetic Modeling and Experimental Validation
Authors: L. Torchane
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The study is devoted to define the optimal conditions for the nitriding of pure iron at atmospheric pressure by using NH3- Ar-C3H8 gas mixtures. After studying the mechanisms of phase formation and mass transfer at the gas-solid interface, a mathematical model is developed in order to predict the nitrogen transfer rate in the solid, the ε-carbonitride layer growth rate and the nitrogen and carbon concentration profiles. In order to validate the model and to show its possibilities, it is compared with thermogravimetric experiments, analyses and metallurgical observations (X-ray diffraction, optical microscopy and electron microprobe analysis). Results obtained allow us to demonstrate the sound correlation between the experimental results and the theoretical predictions.
Keywords: Gaseous Nitrocarburizing, Kinetic Model, Diffusion, Layer Growth Kinetic.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 21727584 Image Segmentation by Mathematical Morphology: An Approach through Linear, Bilinear and Conformal Transformation
Authors: Dibyendu Ghoshal, Pinaki Pratim Acharjya
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Image segmentation process based on mathematical morphology has been studied in the paper. It has been established from the first principles of the morphological process, the entire segmentation is although a nonlinear signal processing task, the constituent wise, the intermediate steps are linear, bilinear and conformal transformation and they give rise to a non linear affect in a cumulative manner.
Keywords: Image segmentation, linear transform, bilinear transform, conformal transform, mathematical morphology.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 21767583 A Model for Analyzing the Startup Dynamics of a Belt Transmission Driven by a DC Motor
Authors: Giovanni Incerti
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In this paper the vibration of a synchronous belt drive during start-up is analyzed and discussed. Besides considering the belt elasticity, the model here proposed also takes into consideration the electromagnetic response of the DC motor. The solution of the motion equations is obtained by means of the modal analysis in state space, which allows to obtain the decoupling of all equations, without introducing the hypothesis of proportional damping. The mathematical model of the transmission and the solution algorithms have been implemented within a computing software that allows the user to simulate the dynamics of the system and to evaluate the effects due to the elasticity of the belt branches and to the electromagnetic behavior of the DC motor. In order to show the details of the calculation procedure, the paper presents a case study developed with the aid of the above-mentioned software.
Keywords: Belt drive, Vibrations, Startup, DC motor.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 30897582 Parametric Characterization of Load Capacity of Infinitely Wide Parabolic Slider Bearing with Couple Stress Fluids
Authors: Oladeinde Mobolaji Humphrey, Akpobi John
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A mathematical model for the hydrodynamic lubrication of parabolic slider bearings with couple stress lubricants is presented. A numerical solution for the mathematical model using finite element scheme is obtained using three nodes isoparametric quadratic elements. Stiffness integrals obtained from the weak form of the governing equations were solved using Gauss Quadrature to obtain a finite number of stiffness matrices. The global system of equations was obtained for the bearing and solved using Gauss Seidel iterative scheme. The converged pressure solution was used to obtain the load capacity of the bearing. Parametric studies were carried out and it was shown that the effect of couple stresses and profile parameter are to increase the load carrying capacity of the parabolic slider bearing. Numerical experiments reveal that the magnitude of the profile parameter at which maximum load is obtained increases with decrease in couple stress parameter. The results are presented in graphical form.Keywords: Finite element, numerical, parabolic slider.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 20747581 Study on Cross-flow Heat Transfer in Fixed Bed
Authors: Hong-fang Ma, Hai-tao Zhang, Wei-yong Ying, Ding-ye Fang
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Radial flow reactor was focused for large scale methanol synthesis and in which the heat transfer type was cross-flow. The effects of operating conditions including the reactor inlet air temperature, the heating pipe temperature and the air flow rate on the cross-flow heat transfer was investigated and the results showed that the temperature profile of the area in front of the heating pipe was slightly affected by all the operating conditions. The main area whose temperature profile was influenced was the area behind the heating pipe. The heat transfer direction according to the air flow directions. In order to provide the basis for radial flow reactor design calculation, the dimensionless number group method was used for data fitting of the bed effective thermal conductivity and the wall heat transfer coefficient which was calculated by the mathematical model with the product of Reynolds number and Prandtl number. The comparison of experimental data and calculated value showed that the calculated value fit the experimental data very well and the formulas could be used for reactor designing calculation.Keywords: Cross-flow, Heat transfer, Fixed bed, Mathematical model
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1860