Search results for: Backstepping method
7976 Analytical solution of Gas Flow Through a Micro-Nano Porous Media by Homotopy Perturbation method
Authors: Jamal Amani Rad, Kourosh Parand
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In this paper, we have applied the homotopy perturbation method (HPM) for obtaining the analytical solution of unsteady flow of gas through a porous medium and we have also compared the findings of this research with some other analytical results. Results showed a very good agreement between results of HPM and the numerical solutions of the problem rather than other analytical solutions which have previously been applied. The results of homotopy perturbation method are of high accuracy and the method is very effective and succinct.Keywords: Unsteady gas equation, Homotopy perturbation method(HPM), Porous medium, Nonlinear ODE
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 18857975 Electrical Field Around the Overhead Transmission Lines
Authors: S.S. Razavipour, M. Jahangiri, H. Sadeghipoor
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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.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 83697974 A Finite Point Method Based on Directional Derivatives for Diffusion Equation
Authors: Guixia Lv, Longjun Shen
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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.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 13507973 A Method for Quality Inspection of Motors by Detecting Abnormal Sound
Authors: Tadatsugu Kitamoto
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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
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 16997972 A New Approach for Mobile Agent Security
Authors: R. Haghighat far, H. Yarahmadi
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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.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 17587971 A Formatting Method for Transforming XML Data into HTML
Authors: Zhe JIN, Motomichi TOYAMA
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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.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 13637970 Containment/Penetration Analysis for the Protection of Aircraft Engine External Configuration and Nuclear Power Plant Structures
Authors: Dong Wook Lee, Adrian Mistreanu
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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.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 5397969 Simplex Method for Solving Linear Programming Problems with Fuzzy Numbers
Authors: S. H. Nasseri, E. Ardil, A. Yazdani, R. Zaefarian
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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.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 35257968 Inverse Heat Transfer Analysis of a Melting Furnace Using Levenberg-Marquardt Method
Authors: Mohamed Hafid, Marcel Lacroix
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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.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 13177967 Quartic Nonpolynomial Spline Solutions for Third Order Two-Point Boundary Value Problem
Authors: Talaat S. El-Danaf
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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.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 20077966 Increased Signal to Noise Ratio in P300 Potentials by the Method of Coherent Self-Averaging in BCI Systems
Authors: Ricardo Espinosa
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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).
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 21447965 A New Inversion-free Method for Hermitian Positive Definite Solution of Matrix Equation
Authors: Minghui Wang, Juntao Zhang
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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.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 16057964 Wavelet and K-L Seperability Based Feature Extraction Method for Functional Data Classification
Authors: Jun Wan, Zehua Chen, Yingwu Chen, Zhidong Bai
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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.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 14657963 Modified Levenberg-Marquardt Method for Neural Networks Training
Authors: Amir Abolfazl Suratgar, Mohammad Bagher Tavakoli, Abbas Hoseinabadi
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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.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 50467962 Derivative Spectrophotometry Applied to the Determination of Triprolidine Hydrochloride and Pseudoephedrine Hydrochloride in Tablets and Dissolution Testing
Authors: L. Sriphong, A. Chaidedgumjorn, K. Chaisuroj
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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.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 22507961 Parallel Direct Integration Variable Step Block Method for Solving Large System of Higher Order Ordinary Differential Equations
Authors: Zanariah Abdul Majid, Mohamed Suleiman
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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.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 13817960 An Efficient Method for Load−Flow Solution of Radial Distribution Networks
Authors: Smarajit Ghosh , Karma Sonam Sherpa
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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
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 57057959 Simplex Method for Fuzzy Variable Linear Programming Problems
Authors: S.H. Nasseri, E. Ardil
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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.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 33497958 A New Splitting H1-Galerkin Mixed Method for Pseudo-hyperbolic Equations
Authors: Yang Liu, Jinfeng Wang, Hong Li, Wei Gao, Siriguleng He
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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.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 15027957 Select-Low and Select-High Methods for the Wheeled Robot Dynamic States Control
Authors: Bogusław Schreyer
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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.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 4897956 Self-adaptation of Ontologies to Folksonomies in Semantic Web
Authors: Francisco Echarte, José Javier Astrain, Alberto Córdoba, Jesús Villadangos
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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.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 16267955 Significance of Splitting Method in Non-linear Grid system for the Solution of Navier-Stokes Equation
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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.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 15277954 A Novel Method for the Characterization of Synchronization and Coupling in Multichannel EEG and ECoG
Authors: Manfred Hartmann, Andreas Graef, Hannes Perko, Christoph Baumgartner, Tilmann Kluge
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In this paper we introduce a novel method for the characterization of synchronziation and coupling effects in multivariate time series that can be used for the analysis of EEG or ECoG signals recorded during epileptic seizures. The method allows to visualize the spatio-temporal evolution of synchronization and coupling effects that are characteristic for epileptic seizures. Similar to other methods proposed for this purpose our method is based on a regression analysis. However, a more general definition of the regression together with an effective channel selection procedure allows to use the method even for time series that are highly correlated, which is commonly the case in EEG/ECoG recordings with large numbers of electrodes. The method was experimentally tested on ECoG recordings of epileptic seizures from patients with temporal lobe epilepsies. A comparision with the results from a independent visual inspection by clinical experts showed an excellent agreement with the patterns obtained with the proposed method.Keywords: EEG, epilepsy, regression analysis, seizurepropagation.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 14317953 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
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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.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 14747952 An Efficient Segmentation Method Based on Local Entropy Characteristics of Iris Biometrics
Authors: Ali Shojaee Bakhtiari, Ali Asghar Beheshti Shirazi, Amir Sepasi Zahmati
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An efficient iris segmentation method based on analyzing the local entropy characteristic of the iris image, is proposed in this paper and the strength and weaknesses of the method are analyzed for practical purposes. The method shows special strength in providing designers with an adequate degree of freedom in choosing the proper sections of the iris for their application purposes.Keywords: Iris segmentation, entropy, biocryptosystem, biometric identification.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 14277951 A Novel Eccentric Lapping Method with Two Rotatable Lapping Plates for Finishing Cemented Carbide Balls
Authors: C. C. Lv, Y. L. Sun, D. W. Zuo
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Cemented carbide balls are usually implemented in industry under the environment of high speed, high temperature, corrosiveness and strong collisions. However, its application is limited due to high fabrication cost, processing efficiency and quality. A novel eccentric lapping method with two rotatable lapping plates was proposed in this paper. A mathematical model was constructed to analyze the influence of each design parameter on this lapping method. To validate this new lapping method, an orthogonal experiment was conducted with cemented carbide balls (YG6). The simulation model was verified and the optimal lapping parameters were derived. The results show that the surface roundness of the balls reaches to 0.65um from 2um in 1 hour using this lapping method. So, using this novel lapping method, it can effectively improve the machining precision and efficiency of cemented carbide balls.
Keywords: Cemented carbide balls, eccentric lapping, high precision, lapping tracks, V-groove.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 25197950 Radiation Heat Transfer Effect in Solid Oxide Fuel Cell: Application of the Lattice Boltzmann Method
Authors: Imen Mejri, Ahmed Mahmoudi, Mohamed A. Abbassi, Ahmed Omri
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The radiation effect within the solid anode, electrolyte, and cathode SOFC layers problem has been investigated in this paper. Energy equation is solved by the Lattice Boltzmann method (LBM). The Rosseland method is used to model the radiative transfer in the electrodes. The Schuster-Schwarzschild method is used to model the radiative transfer in the electrolyte. Without radiative effect, the found results are in good agreement with those published. The obtained results show that the radiative effect can be neglected.
Keywords: SOFC, lattice Boltzmann method, conduction, radiation.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 24517949 Dynamics and Feedback Control for a New Hyperchaotic System
Authors: Kejun Zhuang, Hailong Zhu
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In this paper, stability and Hopf bifurcation analysis of a novel hyperchaotic system are investigated. Four feedback control strategies, the linear feedback control method, enhancing feedback control method, speed feedback control method and delayed feedback control method, are used to control the hyperchaotic attractor to unstable equilibrium. Moreover numerical simulations are given to verify the theoretical results.Keywords: Feedback control, Hopf bifurcation, hyperchaotic system, stability.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 17587948 The Method of Evaluation Artery Diameter from Ultrasound Video
Authors: U. Rubins, Z. Marcinkevics, K.Volceka
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The cardiovascular system has become the most important subject of clinical research, particularly measurement of arterial blood flow. Therefore correct determination of arterial diameter is crucial. We propose a novel, semi-automatic method for artery lumen detection. The method is based on Gaussian probability function. Usability of our proposed method was assessed by analyzing ultrasound B-mode CFA video sequences acquired from eleven healthy volunteers. The correlation coefficient between the manual and semi-automatic measurement of arterial diameter was 0.996. Our proposed method for detecting artery boundary is novel and accurate enough for the measurement of artery diameter.Keywords: Ultrasound, boundary detection, artery diameter, curve fitting.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 15927947 Generalized Chebyshev Collocation Method
Authors: Junghan Kim, Wonkyu Chung, Sunyoung Bu, Philsu Kim
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In this paper, we introduce a generalized Chebyshev collocation method (GCCM) based on the generalized Chebyshev polynomials for solving stiff systems. For employing a technique of the embedded Runge-Kutta method used in explicit schemes, the property of the generalized Chebyshev polynomials is used, in which the nodes for the higher degree polynomial are overlapped with those for the lower degree polynomial. The constructed algorithm controls both the error and the time step size simultaneously and further the errors at each integration step are embedded in the algorithm itself, which provides the efficiency of the computational cost. For the assessment of the effectiveness, numerical results obtained by the proposed method and the Radau IIA are presented and compared.
Keywords: Generalized Chebyshev Collocation method, Generalized Chebyshev Polynomial, Initial value problem.
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