Search results for: embedded atom method.
Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 8449

Search results for: embedded atom method.

8209 Quantum Statistical Mechanical Formulations of Three-Body Problems via Non-Local Potentials

Authors: A. Maghari, V. H. Maleki

Abstract:

In this paper, we present a quantum statistical mechanical formulation from our recently analytical expressions for partial-wave transition matrix of a three-particle system. We report the quantum reactive cross sections for three-body scattering processes 1+(2,3)→1+(2,3) as well as recombination 1+(2,3)→1+(3,1) between one atom and a weakly-bound dimer. The analytical expressions of three-particle transition matrices and their corresponding cross-sections were obtained from the threedimensional Faddeev equations subjected to the rank-two non-local separable potentials of the generalized Yamaguchi form. The equilibrium quantum statistical mechanical properties such partition function and equation of state as well as non-equilibrium quantum statistical properties such as transport cross-sections and their corresponding transport collision integrals were formulated analytically. This leads to obtain the transport properties, such as viscosity and diffusion coefficient of a moderate dense gas.

Keywords: Statistical mechanics, Nonlocal separable potential, three-body interaction, Faddeev equations.

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8208 Robotics and Embedded Systems Applied to the Buried Pipeline Inspection

Authors: Robson C. Santos, Julio C. P. Ribeiro, Iorran M. de Castro, Luan C. F. Rodrigues, Sandro R. L. Silva, Diego M. Quesada

Abstract:

The work aims to develop a robot in the form of autonomous vehicle to detect, inspection and mapping of underground pipelines through the ATmega328 Arduino platform. Hardware prototyping is very similar to C / C ++ language that facilitates its use in robotics open source, resembles PLC used in large industrial processes. The robot will traverse the surface independently of direct human action, in order to automate the process of detecting buried pipes, guided by electromagnetic induction. The induction comes from coils that send the signal to the Arduino microcontroller contained in that will make the difference in intensity and the treatment of the information, and then this determines actions to electrical components such as relays and motors, allowing the prototype to move on the surface and getting the necessary information. This change of direction is performed by a stepper motor with a servo motor. The robot was developed by electrical and electronic assemblies that allowed test your application. The assembly is made up of metal detector coils, circuit boards and microprocessor, which interconnected circuits previously developed can determine, process control and mechanical actions for a robot (autonomous car) that will make the detection and mapping of buried pipelines plates. This type of prototype can prevent and identifies possible landslides and they can prevent the buried pipelines suffer an external pressure on the walls with the possibility of oil leakage and thus pollute the environment.

Keywords: Robotic, metal detector, embedded system, pipeline.

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8207 Numerical Investigations on Group Piles’ Lateral Bearing Capacity Considering Interaction of Soil and Structure

Authors: Mahdi Sadeghian, Mahmoud Hassanlourad, Alireza Ardakani, Reza Dinarvand

Abstract:

In this research, the behavior of monopiles, under lateral loads, was investigated with vertical and oblique piles by Finite Element Method. In engineering practice when soil-pile interaction comes to the picture some simplifications are applied to reduce the design time. As a simplified replacement of soil and pile interaction analysis, pile could be replaced by a column. The height of the column would be equal to the free length of the pile plus a portion of the embedded length of it. One of the important factors studied in this study was that columns with an equivalent length (free length plus a part of buried depth) could be used instead of soil and pile modeling. The results of the analysis show that the more internal friction angle of the soil increases, the more the bearing capacity of the soil is achieved. This additional length is 6 to 11 times of the pile diameter in dense soil although in loose sandy soil this range might increase.

Keywords: Lateral bearing capacity, pile group, oblique pile, soil-structure interaction, depth of fixity.

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8206 Generalized Rough Sets Applied to Graphs Related to Urban Problems

Authors: Mihai Rebenciuc, Simona Mihaela Bibic

Abstract:

Branch of modern mathematics, graphs represent instruments for optimization and solving practical applications in various fields such as economic networks, engineering, network optimization, the geometry of social action, generally, complex systems including contemporary urban problems (path or transport efficiencies, biourbanism, & c.). In this paper is studied the interconnection of some urban network, which can lead to a simulation problem of a digraph through another digraph. The simulation is made univoc or more general multivoc. The concepts of fragment and atom are very useful in the study of connectivity in the digraph that is simulation - including an alternative evaluation of k- connectivity. Rough set approach in (bi)digraph which is proposed in premier in this paper contribute to improved significantly the evaluation of k-connectivity. This rough set approach is based on generalized rough sets - basic facts are presented in this paper.

Keywords: (Bi)digraphs, rough set theory, systems of interacting agents, complex systems.

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8205 Application of He’s Parameter-Expansion Method to a Coupled Van Der Pol oscillators with Two Kinds of Time-delay Coupling

Authors: Mohammad Taghi Darvishi, Samad Kheybari

Abstract:

In this paper, the dynamics of a system of two van der Pol oscillators with delayed position and velocity is studied. We provide an approximate solution for this system using parameterexpansion method. Also, we obtain approximate values for frequencies of the system. The parameter-expansion method is more efficient than the perturbation method for this system because the method is independent of perturbation parameter assumption.

Keywords: Parameter-expansion method, coupled van der pol oscillator, time-delay system.

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8204 Verification of On-Line Vehicle Collision Avoidance Warning System using DSRC

Authors: C. W. Hsu, C. N. Liang, L. Y. Ke, F. Y. Huang

Abstract:

Many accidents were happened because of fast driving, habitual working overtime or tired spirit. This paper presents a solution of remote warning for vehicles collision avoidance using vehicular communication. The development system integrates dedicated short range communication (DSRC) and global position system (GPS) with embedded system into a powerful remote warning system. To transmit the vehicular information and broadcast vehicle position; DSRC communication technology is adopt as the bridge. The proposed system is divided into two parts of the positioning andvehicular units in a vehicle. The positioning unit is used to provide the position and heading information from GPS module, and furthermore the vehicular unit is used to receive the break, throttle, and othersignals via controller area network (CAN) interface connected to each mechanism. The mobile hardware are built with an embedded system using X86 processor in Linux system. A vehicle is communicated with other vehicles via DSRC in non-addressed protocol with wireless access in vehicular environments (WAVE) short message protocol. From the position data and vehicular information, this paper provided a conflict detection algorithm to do time separation and remote warning with error bubble consideration. And the warning information is on-line displayed in the screen. This system is able to enhance driver assistance service and realize critical safety by using vehicular information from the neighbor vehicles.KeywordsDedicated short range communication, GPS, Control area network, Collision avoidance warning system.

Keywords: Dedicated short range communication, GPS, Control area network, Collision avoidance warning system.

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8203 Mathematical Reconstruction of an Object Image Using X-Ray Interferometric Fourier Holography Method

Authors: M. K. Balyan

Abstract:

The main principles of X-ray Fourier interferometric holography method are discussed. The object image is reconstructed by the mathematical method of Fourier transformation. The three methods are presented – method of approximation, iteration method and step by step method. As an example the complex amplitude transmission coefficient reconstruction of a beryllium wire is considered. The results reconstructed by three presented methods are compared. The best results are obtained by means of step by step method.

Keywords: Dynamical diffraction, hologram, object image, X-ray holography.

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8202 An Additive Watermarking Technique in Gray Scale Images Using Discrete Wavelet Transformation and Its Analysis on Watermark Strength

Authors: Kamaldeep Joshi, Rajkumar Yadav, Ashok Kumar Yadav

Abstract:

Digital Watermarking is a procedure to prevent the unauthorized access and modification of personal data. It assures that the communication between two parties remains secure and their communication should be undetected. This paper investigates the consequence of the watermark strength of the grayscale image using a Discrete Wavelet Transformation (DWT) additive technique. In this method, the gray scale host image is divided into four sub bands: LL (Low-Low), HL (High-Low), LH (Low-High), HH (High-High) and the watermark is inserted in an LL sub band using DWT technique. As the image is divided into four sub bands, a watermark of equal size of the LL sub band has been inserted and the results are discussed. LL represents the average component of the host image which contains the maximum information of the image. Two kinds of experiments are performed. In the first, the same watermark is embedded in different images and in the later on the strength of the watermark varies by a factor of s i.e. (s=10, 20, 30, 40, 50) and it is inserted in the same image.

Keywords: Watermarking, discrete wavelet transform, scaling factor, steganography.

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8201 Steepest Descent Method with New Step Sizes

Authors: Bib Paruhum Silalahi, Djihad Wungguli, Sugi Guritman

Abstract:

Steepest descent method is a simple gradient method for optimization. This method has a slow convergence in heading to the optimal solution, which occurs because of the zigzag form of the steps. Barzilai and Borwein modified this algorithm so that it performs well for problems with large dimensions. Barzilai and Borwein method results have sparked a lot of research on the method of steepest descent, including alternate minimization gradient method and Yuan method. Inspired by previous works, we modified the step size of the steepest descent method. We then compare the modification results against the Barzilai and Borwein method, alternate minimization gradient method and Yuan method for quadratic function cases in terms of the iterations number and the running time. The average results indicate that the steepest descent method with the new step sizes provide good results for small dimensions and able to compete with the results of Barzilai and Borwein method and the alternate minimization gradient method for large dimensions. The new step sizes have faster convergence compared to the other methods, especially for cases with large dimensions.

Keywords: Convergence, iteration, line search, running time, steepest descent, unconstrained optimization.

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8200 Magnetohydrodynamics Boundary Layer Flows over a Stretching Surface with Radiation Effect and Embedded in Porous Medium

Authors: Siti Khuzaimah Soid, Zanariah Mohd Yusof, Ahmad Sukri Abd Aziz, Seripah Awang Kechil

Abstract:

A steady two-dimensional magnetohydrodynamics flow and heat transfer over a stretching vertical sheet influenced by radiation and porosity is studied. The governing boundary layer equations of partial differential equations are reduced to a system of ordinary differential equations using similarity transformation. The system is solved numerically by using a finite difference scheme known as the Keller-box method for some values of parameters, namely the radiation parameter N, magnetic parameter M, buoyancy parameter l , Prandtl number Pr and permeability parameter K. The effects of the parameters on the heat transfer characteristics are analyzed and discussed. It is found that both the skin friction coefficient and the local Nusselt number decrease as the magnetic parameter M and permeability parameter K increase. Heat transfer rate at the surface decreases as the radiation parameter increases.

Keywords: Keller-box, MHD boundary layer flow, permeability stretching.

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8199 Calculation of Heating Load for an Apartment Complex with Unit Building Method

Authors: Ju-Seok Kim, Sun-Ae Moon, Tae-Gu Lee, Seung-Jae Moon, Jae-Heon Lee

Abstract:

As a simple to method estimate the plant heating energy capacity of an apartment complex, a new load calculation method has been proposed. The method which can be called as unit building method, predicts the heating load of the entire complex instead of summing up that of each apartment belonging to complex. Comparison of the unit heating load for various floor sizes between the present method and conventional approach shows a close agreement with dynamic load calculation code. Some additional calculations are performed to demonstrate it-s application examples.

Keywords: Unit Building Method, Unit Heating Load, TFMLoad.

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8198 New Laguerre-s Type Method for Solving of a Polynomial Equations Systems

Authors: Oleksandr Poliakov, Yevgen Pashkov, Marina Kolesova, Olena Chepenyuk, Mykhaylo Kalinin, Vadym Kramar

Abstract:

In this paper we present a substantiation of a new Laguerre-s type iterative method for solving of a nonlinear polynomial equations systems with real coefficients. The problems of its implementation, including relating to the structural choice of initial approximations, were considered. Test examples demonstrate the effectiveness of the method at the solving of many practical problems solving.

Keywords: Iterative method, Laguerre's method, Newton's method, polynomial equation, system of equations

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8197 Real Time Remote Monitoring and Fault Detection in Wind Turbine

Authors: Saad Chakkor, Mostafa Baghouri, Abderrahmane Hajraoui

Abstract:

In new energy development, wind power has boomed. It is due to the proliferation of wind parks and their operation in supplying the national electric grid with low cost and clean resources. Hence, there is an increased need to establish a proactive maintenance for wind turbine machines based on remote control and monitoring. That is necessary with a real-time wireless connection in offshore or inaccessible locations while the wired method has many flaws. The objective of this strategy is to prolong wind turbine lifetime and to increase productivity. The hardware of a remote control and monitoring system for wind turbine parks is designed. It takes advantage of GPRS or Wi-Max wireless module to collect data measurements from different wind machine sensors through IP based multi-hop communication. Computer simulations with Proteus ISIS and OPNET software tools have been conducted to evaluate the performance of the studied system. Study findings show that the designed device is suitable for application in a wind park.

Keywords: Embedded System, Monitoring, Wind Turbine, Faults Diagnosis, TCP/IP Protocol, Real Time, Web.

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8196 Fragile Watermarking for Color Images Using Thresholding Technique

Authors: Kuo-Cheng Liu

Abstract:

In this paper, we propose ablock-wise watermarking scheme for color image authentication to resist malicious tampering of digital media. The thresholding technique is incorporated into the scheme such that the tampered region of the color image can be recovered with high quality while the proofing result is obtained. The watermark for each block consists of its dual authentication data and the corresponding feature information. The feature information for recovery iscomputed bythe thresholding technique. In the proofing process, we propose a dual-option parity check method to proof the validity of image blocks. In the recovery process, the feature information of each block embedded into the color image is rebuilt for high quality recovery. The simulation results show that the proposed watermarking scheme can effectively proof the tempered region with high detection rate and can recover the tempered region with high quality.

Keywords: thresholding technique, tamper proofing, tamper recovery

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8195 A New Preconditioned AOR Method for Z-matrices

Authors: Guangbin Wang, Ning Zhang, Fuping Tan

Abstract:

In this paper, we present a preconditioned AOR-type iterative method for solving the linear systems Ax = b, where A is a Z-matrix. And give some comparison theorems to show that the rate of convergence of the preconditioned AOR-type iterative method is faster than the rate of convergence of the AOR-type iterative method.

Keywords: Z-matrix, AOR-type iterative method, precondition, comparison.

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8194 A Family of Improved Secant-Like Method with Super-Linear Convergence

Authors: Liang Chen

Abstract:

A family of improved secant-like method is proposed in this paper. Further, the analysis of the convergence shows that this method has super-linear convergence. Efficiency are demonstrated by numerical experiments when the choice of α is correct.

Keywords: Nonlinear equations, Secant method, Convergence order, Secant-like method.

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8193 Wind Farm Power Performance Verification Using Non-Parametric Statistical Inference

Authors: M. Celeska, K. Najdenkoski, V. Dimchev, V. Stoilkov

Abstract:

Accurate determination of wind turbine performance is necessary for economic operation of a wind farm. At present, the procedure to carry out the power performance verification of wind turbines is based on a standard of the International Electrotechnical Commission (IEC). In this paper, nonparametric statistical inference is applied to designing a simple, inexpensive method of verifying the power performance of a wind turbine. A statistical test is explained, examined, and the adequacy is tested over real data. The methods use the information that is collected by the SCADA system (Supervisory Control and Data Acquisition) from the sensors embedded in the wind turbines in order to carry out the power performance verification of a wind farm. The study has used data on the monthly output of wind farm in the Republic of Macedonia, and the time measuring interval was from January 1, 2016, to December 31, 2016. At the end, it is concluded whether the power performance of a wind turbine differed significantly from what would be expected. The results of the implementation of the proposed methods showed that the power performance of the specific wind farm under assessment was acceptable.

Keywords: Canonical correlation analysis, power curve, power performance, wind energy.

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8192 New Newton's Method with Third-order Convergence for Solving Nonlinear Equations

Authors: Osama Yusuf Ababneh

Abstract:

For the last years, the variants of the Newton-s method with cubic convergence have become popular iterative methods to find approximate solutions to the roots of non-linear equations. These methods both enjoy cubic convergence at simple roots and do not require the evaluation of second order derivatives. In this paper, we present a new Newton-s method based on contra harmonic mean with cubically convergent. Numerical examples show that the new method can compete with the classical Newton's method.

Keywords: Third-order convergence, non-linear equations, root finding, iterative method.

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8191 Improved IDR(s) Method for Gaining Very Accurate Solutions

Authors: Yusuke Onoue, Seiji Fujino, Norimasa Nakashima

Abstract:

The IDR(s) method based on an extended IDR theorem was proposed by Sonneveld and van Gijzen. The original IDR(s) method has excellent property compared with the conventional iterative methods in terms of efficiency and small amount of memory. IDR(s) method, however, has unexpected property that relative residual 2-norm stagnates at the level of less than 10-12. In this paper, an effective strategy for stagnation detection, stagnation avoidance using adaptively information of parameter s and improvement of convergence rate itself of IDR(s) method are proposed in order to gain high accuracy of the approximated solution of IDR(s) method. Through numerical experiments, effectiveness of adaptive tuning IDR(s) method is verified and demonstrated.

Keywords: Krylov subspace methods, IDR(s), adaptive tuning, stagnation of relative residual.

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8190 Denosing ECG using Translation Invariant Multiwavelet

Authors: Jeong Yup Han, Su Kyung Lee, Hong Bae Park

Abstract:

In this paper, we propose a method to reduce the various kinds of noise while gathering and recording the electrocardiogram (ECG) signal. Because of the defects of former method in the noise elimination of ECG signal, we use translation invariant (TI) multiwavelet denoising method to the noise elimination. The advantage of the proposed method is that it may not only remain the geometrical characteristics of the original ECG signal and keep the amplitudes of various ECG waveforms efficiently, but also suppress impulsive noise to some extent. The simulation results indicate that the proposed method are better than former removing noise method in aspects of remaining geometrical characteristics of ECG signal and the signal-to-noise ratio (SNR).

Keywords: ECG, TI multiwavelet, denoise.

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8189 Direct Method for Converting FIR Filter with Low Nonzero Tap into IIR Filter

Authors: Jeong Hye Moon, Byung Hoon Kang, PooGyeon Park

Abstract:

In this paper, we proposed the direct method for converting Finite-Impulse Response (FIR) filter with low nonzero tap into Infinite-Impulse Response (IIR) filter using the pre-determined table. The prony method is used by ghost cancellator which is IIR approximation to FIR filter which is better performance than IIR and have much larger calculation difference. The direct method for many ghost combination with low nonzero tap of NTSC(National Television System Committee) TV signal in Korea is described. The proposed method is illustrated with an example.

Keywords: NTSC, Ghost cancellation, FIR, IIR, Prony method.

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8188 Wavelet Based Identification of Second Order Linear System

Authors: Sudipta Majumdar, Harish Parthasarathy

Abstract:

In this paper, a wavelet based method is proposed to identify the constant coefficients of a second order linear system and is compared with the least squares method. The proposed method shows improved accuracy of parameter estimation as compared to the least squares method. Additionally, it has the advantage of smaller data requirement and storage requirement as compared to the least squares method.

Keywords: Least squares method, linear system, system identification, wavelet transform.

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8187 An Edge-based Text Region Extraction Algorithm for Indoor Mobile Robot Navigation

Authors: Jagath Samarabandu, Xiaoqing Liu

Abstract:

Using bottom-up image processing algorithms to predict human eye fixations and extract the relevant embedded information in images has been widely applied in the design of active machine vision systems. Scene text is an important feature to be extracted, especially in vision-based mobile robot navigation as many potential landmarks such as nameplates and information signs contain text. This paper proposes an edge-based text region extraction algorithm, which is robust with respect to font sizes, styles, color/intensity, orientations, and effects of illumination, reflections, shadows, perspective distortion, and the complexity of image backgrounds. Performance of the proposed algorithm is compared against a number of widely used text localization algorithms and the results show that this method can quickly and effectively localize and extract text regions from real scenes and can be used in mobile robot navigation under an indoor environment to detect text based landmarks.

Keywords: Landmarks, mobile robot navigation, scene text, text localization and extraction.

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8186 Note to the Global GMRES for Solving the Matrix Equation AXB = F

Authors: Fatemeh Panjeh Ali Beik

Abstract:

In the present work, we propose a new projection method for solving the matrix equation AXB = F. For implementing our new method, generalized forms of block Krylov subspace and global Arnoldi process are presented. The new method can be considered as an extended form of the well-known global generalized minimum residual (Gl-GMRES) method for solving multiple linear systems and it will be called as the extended Gl-GMRES (EGl- GMRES). Some new theoretical results have been established for proposed method by employing Schur complement. Finally, some numerical results are given to illustrate the efficiency of our new method.

Keywords: Matrix equation, Iterative method, linear systems, block Krylov subspace method, global generalized minimum residual (Gl-GMRES).

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8185 Direct Transient Stability Assessment of Stressed Power Systems

Authors: E. Popov, N. Yorino, Y. Zoka, Y. Sasaki, H. Sugihara

Abstract:

This paper discusses the performance of critical trajectory method (CTrj) for power system transient stability analysis under various loading settings and heavy fault condition. The method obtains Controlling Unstable Equilibrium Point (CUEP) which is essential for estimation of power system stability margins. The CUEP is computed by applying the CTrjto the boundary controlling unstable equilibrium point (BCU) method. The Proposed method computes a trajectory on the stability boundary that starts from the exit point and reaches CUEP under certain assumptions. The robustness and effectiveness of the method are demonstrated via six power system models and five loading conditions. As benchmark is used conventional simulation method whereas the performance is compared with and BCU Shadowing method.

Keywords: Power system, Transient stability, Critical trajectory method, Energy function method.

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8184 A Descent-projection Method for Solving Monotone Structured Variational Inequalities

Authors: Min Sun, Zhenyu Liu

Abstract:

In this paper, a new descent-projection method with a new search direction for monotone structured variational inequalities is proposed. The method is simple, which needs only projections and some function evaluations, so its computational load is very tiny. Under mild conditions on the problem-s data, the method is proved to converges globally. Some preliminary computational results are also reported to illustrate the efficiency of the method.

Keywords: variational inequalities, monotone function, global convergence.

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8183 Evaluation of Structural Behavior of Wide Sleepers on Asphalt Trackbed Due to Embedded Shear Keys

Authors: Seong Hyeok Lee, Jin Wook Lee, Bu Seog Ju, Woo Young Jung

Abstract:

Korea Train eXpress (KTX) is now being operated, which allows Korea being one of the countries that operates the high-speed rail system. The high-speed rail has its advantage of short time transportation of population and materials, which lead to many researches performed in this matter. In the case of high speed classical trackbed system, the maintenance and usability of gravel ballast system is costly. Recently, the concrete trackbed structure has been introduced as a replacement of classical trackbed system. In this case, the sleeper plays a critical role. Current study investigated to develop the track sleepers readily applicable to the top of the asphalt trackbed, as part of the trcakbed study utilizing the asphalt material. Among many possible shapes and design of sleepers, current study proposed two types of wide-sleepers according to the shear-key installation method. The structural behavior analysis and safety evaluation on each case was conducted using Korean design standard.

Keywords: Wide Sleepers, Asphalt, High-Speed Railway, Shear-key.

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8182 A High-Resolution Refractive Index Sensor Based on a Magnetic Photonic Crystal

Authors: Ti-An Tsai, Chun-Chih Wang, Hung-Wen Wang, I-Ling Chang, Lien-Wen Chen

Abstract:

In this study, we demonstrate a high-resolution refractive index sensor based on a Magnetic Photonic Crystal (MPC) composed of a triangular lattice array of air holes embedded in Si matrix. A microcavity is created by changing the radius of an air hole in the middle of the photonic crystal. The cavity filled with gyrotropic materials can serve as a refractive index sensor. The shift of the resonant frequency of the sensor is obtained numerically using finite difference time domain method under different ambient conditions having refractive index from n = 1.0 to n = 1.1. The numerical results show that a tiny change in refractive index of  Δn = 0.0001 is distinguishable. In addition, the spectral response of the MPC sensor is studied while an external magnetic field is present. The results show that the MPC sensor exhibits a dramatic improvement in resolution.

Keywords: Magnetic photonic crystal, refractive index sensor, sensitivity, high-resolution.

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8181 Error Propagation in the RK5GL3 Method

Authors: J.S.C. Prentice

Abstract:

The RK5GL3 method is a numerical method for solving initial value problems in ordinary differential equations, and is based on a combination of a fifth-order Runge-Kutta method and 3-point Gauss-Legendre quadrature. In this paper we describe the propagation of local errors in this method, and show that the global order of RK5GL3 is expected to be six, one better than the underlying Runge- Kutta method.

Keywords: RK5GL3, RKrGLm, Runge-Kutta, Gauss-Legendre, initial value problem, order, local error, global error.

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8180 Approximate Method of Calculation of Inviscid Hypersonic Flow

Authors: F. Sokhanvar, A. B. Khoshnevis

Abstract:

In the present work steady inviscid hypersonic flows are calculated by approximate Method. Maslens' inverse method is the chosen approximate method. For the inverse problem, parabolic shock shape is chosen for the two-dimensional flow, and the body shape and flow field are calculated using Maslen's method. For the axisymmetric inverse problem paraboloidal shock is chosen and the surface distribution of pressure is obtained.

Keywords: Hypersonic flow, Inverse problem method

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