Search results for: Boundary scan
Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 825

Search results for: Boundary scan

435 Viscoelastic Modeling of Brain MRE Data Using FE Method

Authors: H. Ajabi Naeeni, M. Haghpanahi

Abstract:

Dynamic shear test on simulated phantom can be used to validate magnetic resonance elastography (MRE) measurements. Phantom gel has been usually utilized for the cell culture of cartilage and soft tissue and also been used for mechanical property characterization using imaging systems. The viscoelastic property of the phantom would be important for dynamic experiments and analyses. In this study, An axisymmetric FE model is presented for determining the dynamic shear behaviour of brain simulated phantom using ABAQUS. The main objective of this study was to investigate the effect of excitation frequencies and boundary conditions on shear modulus and shear viscosity in viscoelastic media.

Keywords: Viscoelastic, MR Elastography, Finite Element, Brain.

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434 Accuracy of Divergence Measures for Detection of Abrupt Changes

Authors: P. Bergl

Abstract:

Numerous divergence measures (spectral distance, cepstral distance, difference of the cepstral coefficients, Kullback-Leibler divergence, distance given by the General Likelihood Ratio, distance defined by the Recursive Bayesian Changepoint Detector and the Mahalanobis measure) are compared in this study. The measures are used for detection of abrupt spectral changes in synthetic AR signals via the sliding window algorithm. Two experiments are performed; the first is focused on detection of single boundary while the second concentrates on detection of a couple of boundaries. Accuracy of detection is judged for each method; the measures are compared according to results of both experiments.

Keywords: Abrupt changes detection, autoregressive model, divergence measure.

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433 Variational Evolutionary Splines for Solving a Model of Temporomandibular Disorders

Authors: Alberto Hananel

Abstract:

The aim of this work is to modelize the occlusion of a person with temporomandibular disorders as an evolutionary equation and approach its solution by the construction and characterizing of discrete variational splines. To formulate the problem, certain boundary conditions have been considered. After showing the existence and the uniqueness of the solution of such a problem, a convergence result of a discrete variational evolutionary spline is shown. A stress analysis of the occlusion of a human jaw with temporomandibular disorders by finite elements is carried out in FreeFem++ in order to prove the validity of the presented method.

Keywords: Approximation, evolutionary PDE, finite element method, temporomandibular disorders, variational spline.

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432 New High Order Group Iterative Schemes in the Solution of Poisson Equation

Authors: Sam Teek Ling, Norhashidah Hj. Mohd. Ali

Abstract:

We investigate the formulation and implementation of new explicit group iterative methods in solving the two-dimensional Poisson equation with Dirichlet boundary conditions. The methods are derived from a fourth order compact nine point finite difference discretization. The methods are compared with the existing second order standard five point formula to show the dramatic improvement in computed accuracy. Numerical experiments are presented to illustrate the effectiveness of the proposed methods.

Keywords: Explicit group iterative method, finite difference, fourth order compact, Poisson equation.

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431 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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430 A Novel QoS Optimization Architecture for 4G Networks

Authors: Aaqif Afzaal Abbasi, Javaid Iqbal, Akhtar Nawaz Malik

Abstract:

4G Communication Networks provide heterogeneous wireless technologies to mobile subscribers through IP based networks and users can avail high speed access while roaming across multiple wireless channels; possible by an organized way to manage the Quality of Service (QoS) functionalities in these networks. This paper proposes the idea of developing a novel QoS optimization architecture that will judge the user requirements and knowing peak times of services utilization can save the bandwidth/cost factors. The proposed architecture can be customized according to the network usage priorities so as to considerably improve a network-s QoS performance.

Keywords: QoS, Network Coverage Boundary, ServicesArchives Units (SAU), Cumulative Services Archives Units (CSAU).

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429 Establishment of Kinetic Zone Diagrams via Simulated Linear Sweep Voltammograms for Soluble-Insoluble Systems

Authors: Imene Atek, Abed M. Affoune, Hubert Girault, Pekka Peljo

Abstract:

Due to the need for a rigorous mathematical model that can help to estimate kinetic properties for soluble-insoluble systems, through voltammetric experiments, a Nicholson Semi Analytical Approach was used in this work for modeling and prediction of theoretical linear sweep voltammetry responses for reversible, quasi reversible or irreversible electron transfer reactions. The redox system of interest is a one-step metal electrodeposition process. A rigorous analysis of simulated linear scan voltammetric responses following variation of dimensionless factors, the rate constant and charge transfer coefficients in a broad range was studied and presented in the form of the so called kinetic zones diagrams. These kinetic diagrams were divided into three kinetics zones. Interpreting these zones leads to empirical mathematical models which can allow the experimenter to determine electrodeposition reactions kinetics whatever the degree of reversibility. The validity of the obtained results was tested and an excellent experiment–theory agreement has been showed.

Keywords: Electrodeposition, kinetics diagrams, modeling, voltammetry.

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428 Effect of Adverse Pressure Gradient on a Fluctuating Velocity over the Co-Flow Jet Airfoil

Authors: Morteza Mirhosseini, Amir B. Khoshnevis

Abstract:

The boundary layer separation and new active flow control of a NACA 0025 airfoil were studied experimentally. This new flow control is sometimes known as a co-flow jet (cfj) airfoil. This paper presents the fluctuating velocity in a wall jet over the co-flow jet airfoil subjected to an adverse pressure gradient and a curved surface. In these results, the fluctuating velocity at the inner part increasing by increased the angle of attack up to 12o and this has due to the jet energized, while the angle of attack 20o has different. The airfoil cord based Reynolds number has 105.

Keywords: Adverse pressure gradient, fluctuating velocity, wall jet, co-flow jet airfoil.

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427 Integral Methods in the Determination of Temperature Fields of Cooled Blades of Gas Turbines

Authors: C. Ardil

Abstract:

A mathematical model and an effective numerical method for calculating the temperature field of the profile part of convection cooled blades have been developed. The theoretical substantiation of the method is proved by corresponding theorems. To this end, convergent quadrature processes were developed and error estimates were obtained in terms of the Zygmund continuity moduli.The boundary conditions for heat exchange are determined from the solution of the corresponding integral equations and empirical relations.The reliability of the developed methods is confirmed by the calculation-experimental studies of the thermohydraulic characteristics of the nozzle apparatus of the first stage of a gas turbine.

Keywords: Integral methods, determination of temperature fields, cooled blades, gas turbines.

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426 Numerical Modeling of Temperature Fields in Aviation Gas Turbine Elements

Authors: A. M. Pashaev, R. A. Sadihov, A. S. Samedov, C. Ardil

Abstract:

A mathematical model and a numerical method for computing the temperature field of the profile part of convectionally cooled blades are developed. The theoretical substantiation of the method is proved by corresponding theorems. To this end, convergent quadrature processes were developed and error estimates were obtained in terms of the Zygmund continuity moduli. The boundary conditions for heat exchange are determined from the solution of the corresponding integral equations and empirical relations. The reliability of the developed methods is confirmed by calculation and experimental studies of the thermohydraulic characteristics of the nozzle apparatus of the first stage of the gas turbine.

Keywords: Aviation gas turbine, temperature field, cooled blades, numerical modeling.

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425 Characterizations of Star-Shaped, L-Convex, and Convex Polygons

Authors: Thomas Shermer, Godfried T. Toussaint

Abstract:

A chord of a simple polygon P is a line segment [xy] that intersects the boundary of P only at both endpoints x and y. A chord of P is called an interior chord provided the interior of [xy] lies in the interior of P. P is weakly visible from [xy] if for every point v in P there exists a point w in [xy] such that [vw] lies in P. In this paper star-shaped, L-convex, and convex polygons are characterized in terms of weak visibility properties from internal chords and starshaped subsets of P. A new Krasnoselskii-type characterization of isothetic star-shaped polygons is also presented.

Keywords: Convex polygons, L-convex polygons, star-shaped polygons, chords, weak visibility, discrete and computational geometry

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424 Local Dynamic Mechanical Properties of Native Porcine Endplate

Authors: J. Sepitka, J. Lukes, J. Reznicek

Abstract:

Hysitron TriboIndenterTM TI 950 system has been used for studying the local viscoelastic properties of porcine intervertebral disc end plate by means of nanoscale mechanical dynamic analysis. The specimen of an endplate was cut from fresh porcine vertebra dissected from 16 month animal. The lumbar spine motion segments were dissected and 5 millimeter thick plates of vertebral body, endplate and annulus fibrosus were prepared for nanoindentation. The surface of the sample was kept in physiological solution during nanoindentation experiment. We obtained mechanical characteristics of different areas of native endplate (endplate middle and vertebra and annulus fibrosus boundary).

Keywords: nanoindentation, DMA, endplate, cartilage

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423 Lamb Waves in Plates Subjected to Uniaxial Stresses

Authors: Munawwar Mohabuth, Andrei Kotousov, Ching-Tai Ng

Abstract:

On the basis of the theory of nonlinear elasticity, the effect of homogeneous stress on the propagation of Lamb waves in an initially isotropic hyperelastic plate is analysed. The equations governing the propagation of small amplitude waves in the prestressed plate are derived using the theory of small deformations superimposed on large deformations. By enforcing traction free boundary conditions at the upper and lower surfaces of the plate, acoustoelastic dispersion equations for Lamb wave propagation are obtained, which are solved numerically. Results are given for an aluminum plate subjected to a range of applied stresses.

Keywords: Acoustoelasticity, dispersion, finite deformation, lamb waves.

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422 Spatial Variability of Brahmaputra River Flow Characteristics

Authors: Hemant Kumar

Abstract:

Brahmaputra River is known according to the Hindu mythology the son of the Lord Brahma. According to this name, the river Brahmaputra creates mass destruction during the monsoon season in Assam, India. It is a state situated in North-East part of India. This is one of the essential states out of the seven countries of eastern India, where almost all entire Brahmaputra flow carried out. The other states carry their tributaries. In the present case study, the spatial analysis performed in this specific case the number of MODIS data are acquired. In the method of detecting the change, the spray content was found during heavy rainfall and in the flooded monsoon season. By this method, particularly the analysis over the Brahmaputra outflow determines the flooded season. The charged particle-associated in aerosol content genuinely verifies the heavy water content below the ground surface, which is validated by trend analysis through rainfall spectrum data. This is confirmed by in-situ sampled view data from a different position of Brahmaputra River. Further, a Hyperion Hyperspectral 30 m resolution data were used to scan the sediment deposits, which is also confirmed by in-situ sampled view data from a different position.

Keywords: Spatial analysis, change detection, aerosol, trend analysis.

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421 Numerical Grid Generation of Oceanic Model for the Andaman Sea

Authors: Nitima Aschariyaphotha, Pratan Sakkaplangkul, Anirut Luadsong

Abstract:

The study of the Andaman Sea can be studied by using the oceanic model; therefore the grid covering the study area should be generated. This research aims to generate grid covering the Andaman Sea, situated between longitudes 90◦E to 101◦E and latitudes 1◦N to 18◦N. A horizontal grid is an orthogonal curvilinear with 87 × 217 grid points. The methods used in this study are cubic spline and bilinear interpolations. The boundary grid points are generated by spline interpolation while the interior grid points have to be specified by bilinear interpolation method. A vertical grid is sigma coordinate with 15 layers of water column.

Keywords: Sigma Coordinate, Curvilinear Coordinate, AndamanSea.

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420 Lattice Boltzmann Simulation of the Carbonization of Wood Particle

Authors: Ahmed Mahmoudi, Imen Mejri, Mohamed A. Abbassi, Ahmed Omri

Abstract:

A numerical study based on the Lattice Boltzmann Method (LBM) is proposed to solve one, two and three dimensional heat and mass transfer for isothermal carbonization of thick wood particles. To check the validity of the proposed model, computational results have been compared with the published data and a good agreement is obtained. Then, the model is used to study the effect of reactor temperature and thermal boundary conditions, on the evolution of the local temperature and the mass distributions of the wood particle during carbonization

Keywords: Lattice Boltzmann Method, pyrolysis conduction, carbonization, Heat and mass transfer.

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419 Computational Study of Blood Flow Analysis for Coronary Artery Disease

Authors: Radhe Tado, Ashish B. Deoghare, K. M. Pandey

Abstract:

The aim of this study is to estimate the effect of blood flow through the coronary artery in human heart so as to assess the coronary artery disease.Velocity, wall shear stress (WSS), strain rate and wall pressure distribution are some of the important hemodynamic parameters that are non-invasively assessed with computational fluid dynamics (CFD). These parameters are used to identify the mechanical factors responsible for the plaque progression and/or rupture in left coronary arteries (LCA) in coronary arteries.The initial step for CFD simulations was the construction of a geometrical model of the LCA. Patient specific artery model is constructed using computed tomography (CT) scan data with the help of MIMICS Research 19.0. For CFD analysis ANSYS FLUENT-14.5 is used.Hemodynamic parameters were quantified and flow patterns were visualized both in the absence and presence of coronary plaques. The wall pressure continuously decreased towards distal segments and showed pressure drops in stenotic segments. Areas of high WSS and high flow velocities were found adjacent to plaques deposition.

Keywords: Computational fluid dynamics, hemodynamics, velocity, strain rate, wall pressure, wall shear stress.

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418 Flow Behavior and Performances of Centrifugal Compressor Stage Vaneless Diffusers

Authors: Y. Galerkin, O. Solovieva

Abstract:

Parameters of flow are calculated in vaneless diffusers with relative width 0,014–0,10. Inlet angles of flow and similarity criteria were varied. There is information on flow separation, boundary layer development, configuration of streamlines. Polytrophic efficiency, loss coefficient and recovery coefficient are used to compare effectiveness of diffusers. The sample of optimization of narrow diffuser with conical walls is presented. Three wide diffusers with narrowing walls are compared. The work is made in the R&D laboratory “Gas dynamics of turbo machines” of the TU SPb.

Keywords: Vaneless diffuser, relative width, flow angle, flow separation, loss coefficient, similarity criteria.

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417 Heat and Mass Transfer for Viscous Flow with Radiation Effect past a Nonlinearly Stretching Sheet

Authors: Kai-Long Hsiao

Abstract:

In this study, an analysis has been performed for heat and mass transfer of a steady laminar boundary-layer flow of a viscous flow past a nonlinearly stretching sheet. Parameters n, Ec, k0, Sc represent the dominance of the nonlinearly effect, viscous effect, radiation effect and mass transfer effect which have presented in governing equations, respectively. The similarity transformation and the finite-difference method have been used to analyze the present problem.

Keywords: Nonlinearly stretching sheet, heat and mass transfer, radiation effect, viscous effect.

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416 Unsteady Stagnation-Point Flow towards a Shrinking Sheet with Radiation Effect

Authors: F. M. Ali, R. Nazar, N. M. Arifin, I. Pop

Abstract:

In this paper, the problem of unsteady stagnation-point flow and heat transfer induced by a shrinking sheet in the presence of radiation effect is studied. The transformed boundary layer equations are solved numerically by the shooting method. The influence of radiation, unsteadiness and shrinking parameters, and the Prandtl number on the reduced skin friction coefficient and the heat transfer coefficient, as well as the velocity and temperature profiles are presented and discussed in detail. It is found that dual solutions exist and the temperature distribution becomes less significant with radiation parameter.

Keywords: Heat transfer, Radiation effect, Shrinking sheet Unsteady flow.

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415 Unsupervised Texture Segmentation via Applying Geodesic Active Regions to Gaborian Feature Space

Authors: Yuan He, Yupin Luo, Dongcheng Hu

Abstract:

In this paper, we propose a novel variational method for unsupervised texture segmentation. We use a Gabor filter bank to extract texture features. Some of the filtered channels form a multidimensional Gaborian feature space. To avoid deforming contours directly in a vector-valued space we use a Gaussian mixture model to describe the statistical distribution of this space and get the boundary and region probabilities. Then a framework of geodesic active regions is applied based on them. In the end, experimental results are presented, and show that this method can obtain satisfied boundaries between different texture regions.

Keywords: Texture segmentation, Gabor filter, snakes, Geodesicactive regions

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414 Safety Compliance of Substation Earthing Design

Authors: A. Hellany, M.Nagrial, M. Nassereddine, J. Rizk

Abstract:

As new challenges emerge in power electrical workplace safety, it is the responsibility of the systems designer to seek out new approaches and solutions that address them. Design decisions made today will impact cost, safety and serviceability of the installed systems for 40 or 50 years during the useful life for the owner. Studies have shown that this cost is an order of magnitude of 7 to 10 times the installed cost of the power distribution equipment. This paper reviews some aspects of earthing system design in power substation surrounded by residential houses. The electrical potential rise and split factors are discussed and a few recommendations are provided to achieve a safety voltage in the area beyond the boundary of the substation.

Keywords: EPR, Split Factor, Earthing Design

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413 Fish Locomotion for Innovative Marine Propulsion Systems

Authors: Omar B. Yaakob, Yasser M. Ahmed, Ahmad F. Said

Abstract:

There is an essential need for obtaining the mathematical representation of fish body undulations, which can be used for designing and building new innovative types of marine propulsion systems with less environmental impact. This research work presents a case study to derive the mathematical model for fish body movement. Observation and capturing image methods were used in this study in order to obtain a mathematical representation of Clariasbatrachus fish (catfish). An experiment was conducted by using an aquarium with dimension 0.609 m x 0.304 m x 0.304 m, and a 0.5 m ruler was attached at the base of the aquarium. Progressive Scan Monochrome Camera was positioned at 1.8 m above the base of the aquarium to provide swimming sequences. Seven points were marked on the fish body using white marker to indicate the fish movement and measuring the amplitude of undulation. Images from video recordings (20 frames/s) were analyzed frame by frame using local coordinate system, with time interval 0.05 s. The amplitudes of undulations were obtained for image analysis from each point that has been marked on fish body. A graph of amplitude of undulations versus time was plotted by using computer to derive a mathematical fit. The function for the graph is polynomial with nine orders.

Keywords: Fish locomotion, body undulation, steady and unsteady swimming modes.

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412 An Efficient Approach to Mining Frequent Itemsets on Data Streams

Authors: Sara Ansari, Mohammad Hadi Sadreddini

Abstract:

The increasing importance of data stream arising in a wide range of advanced applications has led to the extensive study of mining frequent patterns. Mining data streams poses many new challenges amongst which are the one-scan nature, the unbounded memory requirement and the high arrival rate of data streams. In this paper, we propose a new approach for mining itemsets on data stream. Our approach SFIDS has been developed based on FIDS algorithm. The main attempts were to keep some advantages of the previous approach and resolve some of its drawbacks, and consequently to improve run time and memory consumption. Our approach has the following advantages: using a data structure similar to lattice for keeping frequent itemsets, separating regions from each other with deleting common nodes that results in a decrease in search space, memory consumption and run time; and Finally, considering CPU constraint, with increasing arrival rate of data that result in overloading system, SFIDS automatically detect this situation and discard some of unprocessing data. We guarantee that error of results is bounded to user pre-specified threshold, based on a probability technique. Final results show that SFIDS algorithm could attain about 50% run time improvement than FIDS approach.

Keywords: Data stream, frequent itemset, stream mining.

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411 Simulation Design of Separator for the Treatment of Emulsions

Authors: Irena Markovska, Dimitar Rusev, Nikolai Zaicev, Bogdan Bogdanov, Dimitar Georgiev, Yancho Hristov

Abstract:

A prototype model of an emulsion separator was designed and manufactured. Generally, it is a cylinder filled with different fractal modules. The emulsion was fed into the reactor by a peristaltic pump through an inlet placed at the boundary between the two phases. For hydrodynamic design and sizing of the reactor the assumptions of the theory of filtration were used and methods to describe the separation process were developed. Based on this methodology and using numerical methods and software of Autodesk the process is simulated in different operating modes. The basic hydrodynamic characteristics - speed and performance for different types of fractal systems and decisions to optimize the design of the reactor were also defined.

Keywords: fractal systems, reactor, separation, emulsions

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410 Random Subspace Neural Classifier for Meteor Recognition in the Night Sky

Authors: Carlos Vera, Tetyana Baydyk, Ernst Kussul, Graciela Velasco, Miguel Aparicio

Abstract:

This article describes the Random Subspace Neural Classifier (RSC) for the recognition of meteors in the night sky. We used images of meteors entering the atmosphere at night between 8:00 p.m.-5: 00 a.m. The objective of this project is to classify meteor and star images (with stars as the image background). The monitoring of the sky and the classification of meteors are made for future applications by scientists. The image database was collected from different websites. We worked with RGB-type images with dimensions of 220x220 pixels stored in the BitMap Protocol (BMP) format. Subsequent window scanning and processing were carried out for each image. The scan window where the characteristics were extracted had the size of 20x20 pixels with a scanning step size of 10 pixels. Brightness, contrast and contour orientation histograms were used as inputs for the RSC. The RSC worked with two classes and classified into: 1) with meteors and 2) without meteors. Different tests were carried out by varying the number of training cycles and the number of images for training and recognition. The percentage error for the neural classifier was calculated. The results show a good RSC classifier response with 89% correct recognition. The results of these experiments are presented and discussed.

Keywords: Contour orientation histogram, meteors, night sky, RSC neural classifier, stars.

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409 On the Approximate Solution of Continuous Coefficients for Solving Third Order Ordinary Differential Equations

Authors: A. M. Sagir

Abstract:

This paper derived four newly schemes which are combined in order to form an accurate and efficient block method for parallel or sequential solution of third order ordinary differential equations of the form y''' = f(x, y, y', y''), y(α)=y0, y'(α)=β, y''(α)=η with associated initial or boundary conditions. The implementation strategies of the derived method have shown that the block method is found to be consistent, zero stable and hence convergent. The derived schemes were tested on stiff and non – stiff ordinary differential equations, and the numerical results obtained compared favorably with the exact solution.

Keywords: Block Method, Hybrid, Linear Multistep, Self starting, Third Order Ordinary Differential Equations.

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408 Study of a Fabry-Perot Resonator

Authors: F. Hadjaj, A. Belghachi, A. Halmaoui, M. Belhadj, H. Mazouz

Abstract:

A laser is essentially an optical oscillator consisting of a resonant cavity, an amplifying medium and a pumping source. In semiconductor diode lasers, the cavity is created by the boundary between the cleaved face of the semiconductor crystal and air, and has reflective properties as a result of the differing refractive indices of the two media. For a GaAs-air interface a reflectance of 0.3 is typical and therefore the length of the semiconductor junction forms the resonant cavity. To prevent light being emitted in unwanted directions from the junction, sides perpendicular to the required direction are roughened. The objective of this work is to simulate the optical resonator Fabry-Perot and explore its main characteristics, such as FSR, finesse, linewidth, transmission and so on, that describe the performance of resonator.

Keywords: Fabry-Perot Resonator, laser diode.

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407 A Modified Run Length Coding Technique for Test Data Compression Based on Multi-Level Selective Huffman Coding

Authors: C. Kalamani, K. Paramasivam

Abstract:

Test data compression is an efficient method for reducing the test application cost. The problem of reducing test data has been addressed by researchers in three different aspects: Test Data Compression, Built-in-Self-Test (BIST) and Test set compaction. The latter two methods are capable of enhancing fault coverage with cost of hardware overhead. The drawback of the conventional methods is that they are capable of reducing the test storage and test power but when test data have redundant length of runs, no additional compression method is followed. This paper presents a modified Run Length Coding (RLC) technique with Multilevel Selective Huffman Coding (MLSHC) technique to reduce test data volume, test pattern delivery time and power dissipation in scan test applications where redundant length of runs is encountered then the preceding run symbol is replaced with tiny codeword. Experimental results show that the presented method not only improves the test data compression but also reduces the overall test data volume compared to recent schemes. Experiments for the six largest ISCAS-98 benchmarks show that our method outperforms most known techniques.

Keywords: Modified run length coding, multilevel selective Huffman coding, built-in-self-test modified selective Huffman coding, automatic test equipment.

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406 Bifurcation Method for Solving Positive Solutions to a Class of Semilinear Elliptic Equations and Stability Analysis of Solutions

Authors: Hailong Zhu, Zhaoxiang Li

Abstract:

Semilinear elliptic equations are ubiquitous in natural sciences. They give rise to a variety of important phenomena in quantum mechanics, nonlinear optics, astrophysics, etc because they have rich multiple solutions. But the nontrivial solutions of semilinear equations are hard to be solved for the lack of stabilities, such as Lane-Emden equation, Henon equation and Chandrasekhar equation. In this paper, bifurcation method is applied to solving semilinear elliptic equations which are with homogeneous Dirichlet boundary conditions in 2D. Using this method, nontrivial numerical solutions will be computed and visualized in many different domains (such as square, disk, annulus, dumbbell, etc).

Keywords: Semilinear elliptic equations, positive solutions, bifurcation method, isotropy subgroups.

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