Search results for: Regression method
Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 8613

Search results for: Regression method

8223 Electrical Field Around the Overhead Transmission Lines

Authors: S.S. Razavipour, M. Jahangiri, H. Sadeghipoor

Abstract:

In this paper, the computation of the electrical field distribution around AC high-voltage lines is demonstrated. The advantages and disadvantages of two different methods are described to evaluate the electrical field quantity. The first method is a seminumerical method using the laws of electrostatic techniques to simulate the two-dimensional electric field under the high-voltage overhead line. The second method which will be discussed is the finite element method (FEM) using specific boundary conditions to compute the two- dimensional electric field distributions in an efficient way.

Keywords: Electrical field, unloaded transmission lines, finite element method, electrostatic images technique.

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8222 A Finite Point Method Based on Directional Derivatives for Diffusion Equation

Authors: Guixia Lv, Longjun Shen

Abstract:

This paper presents a finite point method based on directional derivatives for diffusion equation on 2D scattered points. To discretize the diffusion operator at a given point, a six-point stencil is derived by employing explicit numerical formulae of directional derivatives, namely, for the point under consideration, only five neighbor points are involved, the number of which is the smallest for discretizing diffusion operator with first-order accuracy. A method for selecting neighbor point set is proposed, which satisfies the solvability condition of numerical derivatives. Some numerical examples are performed to show the good performance of the proposed method.

Keywords: Finite point method, directional derivatives, diffusionequation, method for selecting neighbor point set.

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8221 A Method for Quality Inspection of Motors by Detecting Abnormal Sound

Authors: Tadatsugu Kitamoto

Abstract:

Recently, a quality of motors is inspected by human ears. In this paper, I propose two systems using a method of speech recognition for automation of the inspection. The first system is based on a method of linear processing which uses K-means and Nearest Neighbor method, and the second is based on a method of non-linear processing which uses neural networks. I used motor sounds in these systems, and I successfully recognize 86.67% of motor sounds in the linear processing system and 97.78% in the non-linear processing system.

Keywords: Acoustical diagnosis, Neural networks, K-means, Short-time Fourier transformation

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8220 A New Approach for Mobile Agent Security

Authors: R. Haghighat far, H. Yarahmadi

Abstract:

A mobile agent is a software which performs an action autonomously and independently as a person or an organizations assistance. Mobile agents are used for searching information, retrieval information, filtering, intruder recognition in networks, and so on. One of the important issues of mobile agent is their security. It must consider different security issues in effective and secured usage of mobile agent. One of those issues is the integrity-s protection of mobile agents. In this paper, the advantages and disadvantages of each method, after reviewing the existing methods, is examined. Regarding to this matter that each method has its own advantage or disadvantage, it seems that by combining these methods, one can reach to a better method for protecting the integrity of mobile agents. Therefore, this method is provided in this paper and then is evaluated in terms of existing method. Finally, this method is simulated and its results are the sign of improving the possibility of integrity-s protection of mobile agents.

Keywords: Integrity, Mobile Agent, Security.

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8219 Predictive Analysis for Big Data: Extension of Classification and Regression Trees Algorithm

Authors: Ameur Abdelkader, Abed Bouarfa Hafida

Abstract:

Since its inception, predictive analysis has revolutionized the IT industry through its robustness and decision-making facilities. It involves the application of a set of data processing techniques and algorithms in order to create predictive models. Its principle is based on finding relationships between explanatory variables and the predicted variables. Past occurrences are exploited to predict and to derive the unknown outcome. With the advent of big data, many studies have suggested the use of predictive analytics in order to process and analyze big data. Nevertheless, they have been curbed by the limits of classical methods of predictive analysis in case of a large amount of data. In fact, because of their volumes, their nature (semi or unstructured) and their variety, it is impossible to analyze efficiently big data via classical methods of predictive analysis. The authors attribute this weakness to the fact that predictive analysis algorithms do not allow the parallelization and distribution of calculation. In this paper, we propose to extend the predictive analysis algorithm, Classification And Regression Trees (CART), in order to adapt it for big data analysis. The major changes of this algorithm are presented and then a version of the extended algorithm is defined in order to make it applicable for a huge quantity of data.

Keywords: Predictive analysis, big data, predictive analysis algorithms. CART algorithm.

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8218 A Formatting Method for Transforming XML Data into HTML

Authors: Zhe JIN, Motomichi TOYAMA

Abstract:

In this paper, we propose a fixed formatting method of PPX(Pretty Printer for XML). PPX is a query language for XML database which has extensive formatting capability that produces HTML as the result of a query. The fixed formatting method is to completely specify the combination of variables and layout specification operators within the layout expression of the GENERATE clause of PPX. In the experiment, a quick comparison shows that PPX requires far less description compared to XSLT or XQuery programs doing the same tasks.

Keywords: PPX, XML, HTML, XSLT, XQuery, fixed formatting method.

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8217 Containment/Penetration Analysis for the Protection of Aircraft Engine External Configuration and Nuclear Power Plant Structures

Authors: Dong Wook Lee, Adrian Mistreanu

Abstract:

The authors have studied a method for analyzing containment and penetration using an explicit nonlinear Finite Element Analysis. This method may be used in the stage of concept design for the protection of external configurations or components of aircraft engines and nuclear power plant structures. This paper consists of the modeling method, the results obtained from the method and the comparison of the results with those calculated from simple analytical method. It shows that the containment capability obtained by proposed method matches well with analytically calculated containment capability.

Keywords: Computer Aided Engineering, CAE, containment analysis, Finite Element Analysis, FEA, impact analysis, penetration analysis.

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8216 Simplex Method for Solving Linear Programming Problems with Fuzzy Numbers

Authors: S. H. Nasseri, E. Ardil, A. Yazdani, R. Zaefarian

Abstract:

The fuzzy set theory has been applied in many fields, such as operations research, control theory, and management sciences, etc. In particular, an application of this theory in decision making problems is linear programming problems with fuzzy numbers. In this study, we present a new method for solving fuzzy number linear programming problems, by use of linear ranking function. In fact, our method is similar to simplex method that was used for solving linear programming problems in crisp environment before.

Keywords: Fuzzy number linear programming, rankingfunction, simplex method.

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8215 Inverse Heat Transfer Analysis of a Melting Furnace Using Levenberg-Marquardt Method

Authors: Mohamed Hafid, Marcel Lacroix

Abstract:

This study presents a simple inverse heat transfer procedure for predicting the wall erosion and the time-varying thickness of the protective bank that covers the inside surface of the refractory brick wall of a melting furnace. The direct problem is solved by using the Finite-Volume model. The melting/solidification process is modeled using the enthalpy method. The inverse procedure rests on the Levenberg-Marquardt method combined with the Broyden method. The effect of the location of the temperature sensors and of the measurement noise on the inverse predictions is investigated. Recommendations are made concerning the location of the temperature sensor.

Keywords: Melting furnace, inverse heat transfer, enthalpy method, Levenberg–Marquardt Method.

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8214 Quartic Nonpolynomial Spline Solutions for Third Order Two-Point Boundary Value Problem

Authors: Talaat S. El-Danaf

Abstract:

In this paper, we develop quartic nonpolynomial spline method for the numerical solution of third order two point boundary value problems. It is shown that the new method gives approximations, which are better than those produced by other spline methods. Convergence analysis of the method is discussed through standard procedures. Two numerical examples are given to illustrate the applicability and efficiency of the novel method.

Keywords: Quartic nonpolynomial spline, Two-point boundary value problem.

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8213 Increased Signal to Noise Ratio in P300 Potentials by the Method of Coherent Self-Averaging in BCI Systems

Authors: Ricardo Espinosa

Abstract:

The coherent Self-Averaging (CSA), is a new method proposed in this work; applied to simulated signals evoked potentials related to events (ERP) to find the wave P300, useful systems in the brain computer interface (BCI). The CSA method cleans signal in the time domain of white noise through of successive averaging of a single signal. The method is compared with the traditional method, coherent averaging or synchronized (CA), showing optimal results in the improvement of the signal to noise ratio (SNR). The method of CSA is easy to implement, robust and applicable to any physiological time series contaminated with white noise

Keywords: Evoked potentials, wave P300, Coherent Self-averaging, brain - computer interface (BCI).

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8212 An Internet of Things-Based Weight Monitoring System for Honey

Authors: Zheng-Yan Ruan, Chien-Hao Wang, Hong-Jen Lin, Chien-Peng Huang, Ying-Hao Chen, En-Cheng Yang, Chwan-Lu Tseng, Joe-Air Jiang

Abstract:

Bees play a vital role in pollination. This paper focuses on the weighing process of honey. Honey is usually stored at the comb in a hive. Bee farmers brush bees away from the comb and then collect honey, and the collected honey is weighed afterward. However, such a process brings strong negative influences on bees and even leads to the death of bees. This paper therefore presents an Internet of Things-based weight monitoring system which uses weight sensors to measure the weight of honey and simplifies the whole weighing procedure. To verify the system, the weight measured by the system is compared to the weight of standard weights used for calibration by employing a linear regression model. The R2 of the regression model is 0.9788, which suggests that the weighing system is highly reliable and is able to be applied to obtain actual weight of honey. In the future, the weight data of honey can be used to find the relationship between honey production and different ecological parameters, such as bees’ foraging behavior and weather conditions. It is expected that the findings can serve as critical information for honey production improvement.

Keywords: Internet of Things, weight, honey, bee.

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8211 Performance Evaluation of Minimum Quantity Lubrication on EN3 Mild Steel Turning

Authors: Swapnil Rajan Jadhav, Ajay Vasantrao Kashikar

Abstract:

Lubrication, cooling and chip removal are the desired functions of any cutting fluid. Conventional or flood lubrication requires high volume flow rate and cost associated with this is higher. In addition, flood lubrication possesses health risks to machine operator. To avoid these consequences, dry machining and minimum quantity are two alternatives. Dry machining cannot be a suited alternative as it can generate greater heat and poor surface finish. Here, turning work is carried out on a Lathe machine using EN3 Mild steel. Variable cutting speeds and depth of cuts are provided and corresponding temperatures and surface roughness values were recorded. Experimental results are analyzed by Minitab software. Regression analysis, main effect plot, and interaction plot conclusion are drawn by using ANOVA. There is a 95.83% reduction in the use of cutting fluid. MQL gives a 9.88% reduction in tool temperature, this will improve tool life. MQL produced a 17.64% improved surface finish. MQL appears to be an economical and environmentally compatible lubrication technique for sustainable manufacturing.

Keywords: ANOVA, MQL, regression analysis, surface roughness

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8210 Performance Evaluation of Minimum Quantity Lubrication on EN3 Mild Steel Turning

Authors: Swapnil Rajan Jadhav, Ajay Vasantrao Kashikar

Abstract:

Lubrication, cooling and chip removal are the desired functions of any cutting fluid. Conventional or flood lubrication requires high volume flow rate and cost associated with this is higher. In addition, flood lubrication possesses health risks to machine operator. To avoid these consequences, dry machining and minimum quantity are two alternatives. Dry machining cannot be a suited alternative as it can generate greater heat and poor surface finish. Here, turning work is carried out on a Lathe machine using EN3 Mild steel. Variable cutting speeds and depth of cuts are provided and corresponding temperatures and surface roughness values were recorded. Experimental results are analyzed by Minitab software. Regression analysis, main effect plot, and interaction plot conclusion are drawn by using ANOVA. There is a 95.83% reduction in the use of cutting fluid. MQL gives a 9.88% reduction in tool temperature, this will improve tool life. MQL produced a 17.64% improved surface finish. MQL appears to be an economical and environmentally compatible lubrication technique for sustainable manufacturing.

Keywords: ANOVA, MQL, regression analysis, surface roughness

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8209 Evaluating Factors Influencing Information Quality in Large Firms

Authors: B. E. Narkhede, S. K. Mahajan, B. T. Patil, R. D. Raut

Abstract:

Information quality is a major performance measure for an Enterprise Resource Planning (ERP) system of any firm. This study identifies various critical success factors of information quality. The effect of various critical success factors like project management, reengineering efforts and interdepartmental communications on information quality is analyzed using a multiple regression model. Here quantitative data are collected from respondents from various firms through structured questionnaire for assessment of the information quality, project management, reengineering efforts and interdepartmental communications. The validity and reliability of the data are ensured using techniques like factor analysis, computing of Cronbach’s alpha. This study gives relative importance of each of the critical success factors. The findings suggest that among the various factors influencing information quality careful reengineering efforts are the most influencing factor. This paper gives clear insight to managers and practitioners regarding the relative importance of critical success factors influencing information quality so that they can formulate a strategy at the beginning of ERP system implementation.

Keywords: Enterprise resource planning, information systems, multiple regression, information quality.

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8208 A New Inversion-free Method for Hermitian Positive Definite Solution of Matrix Equation

Authors: Minghui Wang, Juntao Zhang

Abstract:

An inversion-free iterative algorithm is presented for solving nonlinear matrix equation with a stepsize parameter t. The existence of the maximal solution is discussed in detail, and the method for finding it is proposed. Finally, two numerical examples are reported that show the efficiency of the method.

Keywords: Inversion-free method, Hermitian positive definite solution, Maximal solution, Convergence.

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8207 Wavelet and K-L Seperability Based Feature Extraction Method for Functional Data Classification

Authors: Jun Wan, Zehua Chen, Yingwu Chen, Zhidong Bai

Abstract:

This paper proposes a novel feature extraction method, based on Discrete Wavelet Transform (DWT) and K-L Seperability (KLS), for the classification of Functional Data (FD). This method combines the decorrelation and reduction property of DWT and the additive independence property of KLS, which is helpful to extraction classification features of FD. It is an advanced approach of the popular wavelet based shrinkage method for functional data reduction and classification. A theory analysis is given in the paper to prove the consistent convergence property, and a simulation study is also done to compare the proposed method with the former shrinkage ones. The experiment results show that this method has advantages in improving classification efficiency, precision and robustness.

Keywords: classification, functional data, feature extraction, K-Lseperability, wavelet.

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8206 Modified Levenberg-Marquardt Method for Neural Networks Training

Authors: Amir Abolfazl Suratgar, Mohammad Bagher Tavakoli, Abbas Hoseinabadi

Abstract:

In this paper a modification on Levenberg-Marquardt algorithm for MLP neural network learning is proposed. The proposed algorithm has good convergence. This method reduces the amount of oscillation in learning procedure. An example is given to show usefulness of this method. Finally a simulation verifies the results of proposed method.

Keywords: Levenberg-Marquardt, modification, neural network, variable learning rate.

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8205 Derivative Spectrophotometry Applied to the Determination of Triprolidine Hydrochloride and Pseudoephedrine Hydrochloride in Tablets and Dissolution Testing

Authors: L. Sriphong, A. Chaidedgumjorn, K. Chaisuroj

Abstract:

A spectrophotometric method was developed for simultaneous quantification of pseudoephedrine hydrochloride (PSE) triprolidine hydrochloride (TRI) using second derivative method (zero-crossing technique). The second derivative amplitudes of PSE and TRI were measured at 271 and 321 nm, respectively. The calibration curves were linear in the range of 200 to 1,000 g/ml for PSE and 10 to 50 g/ml for TRI. The method was validated for specificity, accuracy, precision, limit of detection and limit of quantitation. The proposed method was applied to the assaying and dissolution of PSE and TRI in commercial tablets without any chemical separation. The results were compared with those obtained by the official USP31 method and statistical tests showed that there is no significant between the methods at 95% confidence level. The proposed method is simple, rapid and suitable for the routine quality control application. KeywordsTriprolidine, Pseudoephedrine, Derivative spectrophotometry, Dissolution testing.

Keywords: Triprolidine, Pseudoephedrine, Derivative spectrophotometry, Dissolution testing.

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8204 Parallel Direct Integration Variable Step Block Method for Solving Large System of Higher Order Ordinary Differential Equations

Authors: Zanariah Abdul Majid, Mohamed Suleiman

Abstract:

The aim of this paper is to investigate the performance of the developed two point block method designed for two processors for solving directly non stiff large systems of higher order ordinary differential equations (ODEs). The method calculates the numerical solution at two points simultaneously and produces two new equally spaced solution values within a block and it is possible to assign the computational tasks at each time step to a single processor. The algorithm of the method was developed in C language and the parallel computation was done on a parallel shared memory environment. Numerical results are given to compare the efficiency of the developed method to the sequential timing. For large problems, the parallel implementation produced 1.95 speed-up and 98% efficiency for the two processors.

Keywords: Numerical methods, parallel method, block method, higher order ODEs.

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8203 An Efficient Method for Load−Flow Solution of Radial Distribution Networks

Authors: Smarajit Ghosh , Karma Sonam Sherpa

Abstract:

This paper reports a new and accurate method for load-flow solution of radial distribution networks with minimum data preparation. The node and branch numbering need not to be sequential like other available methods. The proposed method does not need sending-node, receiving-node and branch numbers if these are sequential. The proposed method uses the simple equation to compute the voltage magnitude and has the capability to handle composite load modelling. The proposed method uses the set of nodes of feeder, lateral(s) and sub lateral(s). The effectiveness of the proposed method is compared with other methods using two examples. The detailed load-flow results for different kind of load-modellings are also presented.

Keywords: Load−flow, Feeder, Lateral, Power, Voltage, Composite, Exponential

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8202 Simplex Method for Fuzzy Variable Linear Programming Problems

Authors: S.H. Nasseri, E. Ardil

Abstract:

Fuzzy linear programming is an application of fuzzy set theory in linear decision making problems and most of these problems are related to linear programming with fuzzy variables. A convenient method for solving these problems is based on using of auxiliary problem. In this paper a new method for solving fuzzy variable linear programming problems directly using linear ranking functions is proposed. This method uses simplex tableau which is used for solving linear programming problems in crisp environment before.

Keywords: Fuzzy variable linear programming, fuzzy number, ranking function, simplex method.

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8201 A New Splitting H1-Galerkin Mixed Method for Pseudo-hyperbolic Equations

Authors: Yang Liu, Jinfeng Wang, Hong Li, Wei Gao, Siriguleng He

Abstract:

A new numerical scheme based on the H1-Galerkin mixed finite element method for a class of second-order pseudohyperbolic equations is constructed. The proposed procedures can be split into three independent differential sub-schemes and does not need to solve a coupled system of equations. Optimal error estimates are derived for both semidiscrete and fully discrete schemes for problems in one space dimension. And the proposed method dose not requires the LBB consistency condition. Finally, some numerical results are provided to illustrate the efficacy of our method.

Keywords: Pseudo-hyperbolic equations, splitting system, H1-Galerkin mixed method, error estimates.

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8200 Select-Low and Select-High Methods for the Wheeled Robot Dynamic States Control

Authors: Bogusław Schreyer

Abstract:

The paper enquires on the two methods of the wheeled robot braking torque control. Those two methods are applied when the adhesion coefficient under left side wheels is different from the adhesion coefficient under the right side wheels. In case of the select-low (SL) method the braking torque on both wheels is controlled by the signals originating from the wheels on the side of the lower adhesion. In the select-high (SH) method the torque is controlled by the signals originating from the wheels on the side of the higher adhesion. The SL method is securing stable and secure robot behaviors during the braking process. However, the efficiency of this method is relatively low. The SH method is more efficient in terms of time and braking distance but in some situations may cause wheels blocking. It is important to monitor the velocity of all wheels and then take a decision about the braking torque distribution accordingly. In case of the SH method the braking torque slope may require significant decrease in order to avoid wheel blocking.

Keywords: Select-high method, select-low method, torque distribution, wheeled robot.

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8199 Consumer Online Shopping Behavior: The Effect of Internet Marketing Environment, Product Characteristics, Familiarity and Confidence, and Promotional Offer

Authors: Norazah Mohd Suki, Norbayah Mohd Suki

Abstract:

Online shopping enables consumers to search for information and purchase products or services through direct interaction with online store. This study aims to examine the effect of Internet marketing environment, product characteristics, familiarity and confidence, and promotional offers on consumer online shopping behavior. 200 questionnaires were distributed to the respondents, who are students and staff at a public university in the Federal Territory of Labuan, Malaysia, following simple random sampling as a means of data collection. Multiple regression analysis was used as a statistical measure to determine the strength of the relationship between one dependent variable and a series of other independent variables. Results revealed that familiarity and confidence was found to greatly influence consumer online shopping behavior followed by promotional offers. A clear understanding of consumer online shopping behavior can help marketing managers predict the online shopping rate and evaluate the future growth of online commerce.

Keywords: Internet Marketing Environment, Product Characteristics, Multiple Regression Analysis, Malaysia.

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8198 Self-adaptation of Ontologies to Folksonomies in Semantic Web

Authors: Francisco Echarte, José Javier Astrain, Alberto Córdoba, Jesús Villadangos

Abstract:

Ontologies and tagging systems are two different ways to organize the knowledge present in the current Web. In this paper we propose a simple method to model folksonomies, as tagging systems, with ontologies. We show the scalability of the method using real data sets. The modeling method is composed of a generic ontology that represents any folksonomy and an algorithm to transform the information contained in folksonomies to the generic ontology. The method allows representing folksonomies at any instant of time.

Keywords: Folksonomies, ontologies, OWL, semantic web.

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8197 A Statistical Approach for Predicting and Optimizing Depth of Cut in AWJ Machining for 6063-T6 Al Alloy

Authors: Farhad Kolahan, A. Hamid Khajavi

Abstract:

In this paper, a set of experimental data has been used to assess the influence of abrasive water jet (AWJ) process parameters in cutting 6063-T6 aluminum alloy. The process variables considered here include nozzle diameter, jet traverse rate, jet pressure and abrasive flow rate. The effects of these input parameters are studied on depth of cut (h); one of most important characteristics of AWJ. The Taguchi method and regression modeling are used in order to establish the relationships between input and output parameters. The adequacy of the model is evaluated using analysis of variance (ANOVA) technique. In the next stage, the proposed model is embedded into a Simulated Annealing (SA) algorithm to optimize the AWJ process parameters. The objective is to determine a suitable set of process parameters that can produce a desired depth of cut, considering the ranges of the process parameters. Computational results prove the effectiveness of the proposed model and optimization procedure.

Keywords: AWJ machining, Mathematical modeling, Simulated Annealing, Optimization

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8196 Significance of Splitting Method in Non-linear Grid system for the Solution of Navier-Stokes Equation

Authors: M. Zamani, O. Kahar

Abstract:

Solution to unsteady Navier-Stokes equation by Splitting method in physical orthogonal algebraic curvilinear coordinate system, also termed 'Non-linear grid system' is presented. The linear terms in Navier-Stokes equation are solved by Crank- Nicholson method while the non-linear term is solved by the second order Adams-Bashforth method. This work is meant to bring together the advantage of Splitting method as pressure-velocity solver of higher efficiency with the advantage of consuming Non-linear grid system which produce more accurate results in relatively equal number of grid points as compared to Cartesian grid. The validation of Splitting method as a solution of Navier-Stokes equation in Nonlinear grid system is done by comparison with the benchmark results for lid driven cavity flow by Ghia and some case studies including Backward Facing Step Flow Problem.

Keywords: Navier-Stokes, 'Non-linear grid system', Splitting method.

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8195 Prediction of Soil Exchangeable Sodium Ratio Based on Soil Sodium Adsorption Ratio

Authors: M. Siosemarde, F. Kave, E. Pazira, H. Sedghi, S. J. Ghaderi

Abstract:

Researchers have long had trouble in measurement of Exchangeable Sodium Ratio (ESR) at salt-affected soils. this parameter are often determined using laborious and time consuming laboratory tests, but it may be more appropriate and economical to develop a method which uses a more simple soil salinity index. The aim of this study was to determine the relationship between exchangeable sodium ratio (ESR) and sodium adsorption ratio (SAR) in some salt-affected soils of Khuzestan plain. To this purpose, two experimental areas (S1, S2) of Khuzestan province-IRAN were selected and four treatments with three replications by series of double rings were applied. The treatments were included 25cm, 50cm, 75cm and 100cm water application. The statistical results of the study indicated that in order to predict soil ESR based on soil SAR the linear regression model ESR=0.2048+0.0066 SAR (R2=0.53) & ESR=0.0564+0.0171 SAR (R2=0.76) can be recommended in Pilot S1 and S2 respectively.

Keywords: exchangeable sodium ratio, Khuzestan plain, saltaffectedsoils and sodium adsorption ratio.

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8194 Development of Variable Stepsize Variable Order Block Method in Divided Difference Form for the Numerical Solution of Delay Differential Equations

Authors: Fuziyah Ishak, Mohamed B. Suleiman, Zanariah A. Majid, Khairil I. Othman

Abstract:

This paper considers the development of a two-point predictor-corrector block method for solving delay differential equations. The formulae are represented in divided difference form and the algorithm is implemented in variable stepsize variable order technique. The block method produces two new values at a single integration step. Numerical results are compared with existing methods and it is evident that the block method performs very well. Stability regions of the block method are also investigated.

Keywords: block method, delay differential equations, predictor-corrector, stability region, variable stepsize variable order.

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