Search results for: trial wave function
Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 2747

Search results for: trial wave function

2597 Processing Design of Miniature Casting Incorporating Stereolithography Technologies

Authors: Pei-Hsing Huang, Wei-Ju Huang

Abstract:

Investment casting is commonly used in the production of metallic components with complex shapes, due to its high dimensional precision, good surface finish, and low cost. However, the process is cumbersome, and the period between trial casting and final production can be very long, thereby limiting business opportunities and competitiveness. In this study, we replaced conventional wax injection with stereolithography (SLA) 3D printing to speed up the trial process and reduce costs. We also used silicone molds to further reduce costs to avoid the high costs imposed by photosensitive resin.

Keywords: Investment casting, stereolithography, wax molding, 3D printing.

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2596 Lattice Dynamics of (ND4Br)x(KBr)1-x Mixed Crystals

Authors: Alpana Tiwari, N. K. Gaur

Abstract:

We have incorporated the translational rotational (TR) coupling effects in the framework of three body force shell model (TSM) to develop an extended TSM (ETSM). The dynamical matrix of ETSM has been applied to compute the phonon frequencies of orientationally disordered mixed crystal (ND4Br)x(KBr)1-x in (q00), (qq0) and (qqq) symmetry directions for compositions 0.10≤x≤0.50 at T=300K.These frequencies are plotted as a function of wave vector k. An unusual acoustic mode softening is found along symmetry directions (q00) and (qq0) as a result of translation-rotation coupling.

Keywords: Orientational glass, phonons, TR-coupling.

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2595 Characterisation and Classification of Natural Transients

Authors: Ernst D. Schmitter

Abstract:

Monitoring lightning electromagnetic pulses (sferics) and other terrestrial as well as extraterrestrial transient radiation signals is of considerable interest for practical and theoretical purposes in astro- and geophysics as well as meteorology. Managing a continuous flow of data, automisation of the detection and classification process is important. Features based on a combination of wavelet and statistical methods proved efficient for analysis and characterisation of transients and as input into a radial basis function network that is trained to discriminate transients from pulse like to wave like.

Keywords: transient signals, statistics, wavelets, neural networks

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2594 Simulation of Lightning Surge Propagation in Transmission Lines Using the FDTD Method

Authors: Kokiat Aodsup, Thanatchai Kulworawanichpong

Abstract:

This paper describes a finite-difference time-domainFDTD) method to analyze lightning surge propagation in electric transmission lines. Numerical computation of solving the Telegraphist-s equations is determined and investigated its effectiveness. A source of lightning surge wave on power transmission lines is modeled by using Heidler-s surge model. The proposed method was tested against medium-voltage power transmission lines in comparison with the solution obtained by using lattice diagram. As a result, the calculation showed that the method is one of accurate methods to analyze transient lightning wave in power transmission lines.

Keywords: Traveling wave, Lightning surge, Bewley lattice diagram, Telegraphist's equations, Finite-difference time-domain (FDTD) method,

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2593 Achieving Shear Wave Elastography by a Three-element Probe for Wearable Human-machine Interface

Authors: Jipeng Yan, Xingchen Yang, Xiaowei Zhou, Mengxing Tang, Honghai Liu

Abstract:

Shear elastic modulus of skeletal muscles can be obtained by shear wave elastography (SWE) and has been linearly related to muscle force. However, SWE is currently implemented using array probes. Price and volumes of these probes and their driving equipment prevent SWE from being used in wearable human-machine interfaces (HMI). Moreover, beamforming processing for array probes reduces the real-time performance. To achieve SWE by wearable HMIs, a customized three-element probe is adopted in this work, with one element for acoustic radiation force generation and the others for shear wave tracking. In-phase quadrature demodulation and 2D autocorrelation are adopted to estimate velocities of tissues on the sound beams of the latter two elements. Shear wave speeds are calculated by phase shift between the tissue velocities. Three agar phantoms with different elasticities were made by changing the weights of agar. Values of the shear elastic modulus of the phantoms were measured as 8.98, 23.06 and 36.74 kPa at a depth of 7.5 mm respectively. This work verifies the feasibility of measuring shear elastic modulus by wearable devices.

Keywords: Shear elastic modulus, skeletal muscle, ultrasound, wearable human-machine interface.

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2592 A Transfer Function Representation of Thermo-Acoustic Dynamics for Combustors

Authors: Myunggon Yoon, Jung-Ho Moon

Abstract:

In this paper, we present a transfer function representation of a general one-dimensional combustor. The input of the transfer function is a heat rate perturbation of a burner and the output is a flow velocity perturbation at the burner. This paper considers a general combustor model composed of multiple cans with different cross sectional areas, along with a non-zero flow rate.

Keywords: Thermoacoustics, dynamics, combustor, transfer function.

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2591 Implication of the Exchange-Correlation on Electromagnetic Wave Propagation in Single-Wall Carbon Nanotubes

Authors: A. Abdikian

Abstract:

Using the linearized quantum hydrodynamic model (QHD) and by considering the role of quantum parameter (Bohm’s potential) and electron exchange-correlation potential in conjunction with Maxwell’s equations, electromagnetic wave propagation in a single-walled carbon nanotubes was studied. The electronic excitations are described. By solving the mentioned equations with appropriate boundary conditions and by assuming the low-frequency electromagnetic waves, two general expressions of dispersion relations are derived for the transverse magnetic (TM) and transverse electric (TE) modes, respectively. The dispersion relations are analyzed numerically and it was found that the dependency of dispersion curves with the exchange-correlation effects (which have been ignored in previous works) in the low frequency would be limited. Moreover, it has been realized that asymptotic behaviors of the TE and TM modes are similar in single wall carbon nanotubes (SWCNTs). The results show that by adding the function of electron exchange-correlation potential lead to the phenomena and make to extend the validity range of QHD model. The results can be important in the study of collective phenomena in nanostructures.

Keywords: Transverse magnetic, transverse electric, quantum hydrodynamic model, electron exchange-correlation potential, single-wall carbon nanotubes.

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2590 Predicting Protein Function using Decision Tree

Authors: Manpreet Singh, Parminder Kaur Wadhwa, Surinder Kaur

Abstract:

The drug discovery process starts with protein identification because proteins are responsible for many functions required for maintenance of life. Protein identification further needs determination of protein function. Proposed method develops a classifier for human protein function prediction. The model uses decision tree for classification process. The protein function is predicted on the basis of matched sequence derived features per each protein function. The research work includes the development of a tool which determines sequence derived features by analyzing different parameters. The other sequence derived features are determined using various web based tools.

Keywords: Sequence Derived Features, decision tree.

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2589 Voltage Sag Effect on Three Phase Five Leg Transformers

Authors: M. R. Dolatian, A. Jalilian

Abstract:

The behavior of three phase five leg transformer under voltage sag is studied in this paper. This paper proposes a simple, practical model of a three phase-five leg, saturated transformer with accurate performance. Transformer saturation is produced when the voltage sag is recovered and it causes inrush current in transformer. Effects of voltage sag depth, duration and initial point on wave have been analyzed in this paper. Initial point on wave can produce maximum inrush current in five leg transformers while comparing with three leg transformers. The magnetic circuit symmetry of five leg transformer produces the more symmetrical shape of inrush current curves versus initial point on wave and sag duration than three leg transformer. The simulations show that current peak has a periodical dependence on sag duration and linear dependence on sag depth. Inrush current that is produced in three phase five leg transformer is higher than three phase three leg transformer.

Keywords: Inrush current, three phase five leg transformer, saturation, voltage sag.

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2588 Assessing the Function of Light and Colorin Architectural View

Authors: Gholam Hossein Naseri, Manucher Tamizi

Abstract:

Light is one of the most important qualitative and symbolic factors and has a special position in architecture and urban development in regard to practical function. The main function of light, either natural or artificial, is lighting up the environment and the constructional forms which is called lighting. However, light is used to redefine the urban spaces by architectural genius with regard to three aesthetic, conceptual and symbolic factors. In architecture and urban development, light has a function beyond lighting up the environment, and the designers consider it as one of the basic components. The present research aims at studying the function of light and color in architectural view and their effects in buildings.

Keywords: Architectural View , Color , Light

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2587 Effect of Blade Shape on the Performance of Wells Turbine for Wave Energy Conversion

Authors: Katsuya Takasaki, Manabu Takao, Toshiaki Setoguchi

Abstract:

The effect of a 3-dimensional (3D) blade on the turbine characteristics of Wells turbine for wave energy conversion has been investigated experimentally by model testing under steady flow conditions in this study, in order to improve the peak efficiency and stall characteristics. The aim of use of 3D blade is to prevent flow separation on the suction surface near the tip. The chord length is constant with radius and the blade profile changes gradually from the mean radius to tip. The proposed blade profiles in the study are NACA0015 from the hub to mean radius and NACA0025 at the tip. The performances of Wells turbine with 3D blades has been compared with those of the original Wells turbine, i.e., the turbine with 2-dimensional (2D) blades. As a result, it was concluded that although the peak efficiency of Wells turbine can be improved by the use of the proposed 3D blade, its blade does not overcome the weakness of stalling.

Keywords: Fluid machinery, ocean engineering, stall, wave energy conversion, Wells turbine.

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2586 Particle Swarm Optimization and Quantum Particle Swarm Optimization to Multidimensional Function Approximation

Authors: Diogo Silva, Fadul Rodor, Carlos Moraes

Abstract:

This work compares the results of multidimensional function approximation using two algorithms: the classical Particle Swarm Optimization (PSO) and the Quantum Particle Swarm Optimization (QPSO). These algorithms were both tested on three functions - The Rosenbrock, the Rastrigin, and the sphere functions - with different characteristics by increasing their number of dimensions. As a result, this study shows that the higher the function space, i.e. the larger the function dimension, the more evident the advantages of using the QPSO method compared to the PSO method in terms of performance and number of necessary iterations to reach the stop criterion.

Keywords: PSO, QPSO, function approximation, AI, optimization, multidimensional functions.

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2585 Analytical Solution for Free Vibration of Rectangular Kirchhoff Plate from Wave Approach

Authors: Mansour Nikkhah-Bahrami, Masih Loghmani, Mostafa Pooyanfar

Abstract:

In this paper, an analytical approach for free vibration analysis of four edges simply supported rectangular Kirchhoff plates is presented. The method is based on wave approach. From wave standpoint vibration propagate, reflect and transmit in a structure. Firstly, the propagation and reflection matrices for plate with simply supported boundary condition are derived. Then, these matrices are combined to provide a concise and systematic approach to free vibration analysis of a simply supported rectangular Kirchhoff plate. Subsequently, the eigenvalue problem for free vibration of plates is formulated and the equation of plate natural frequencies is constructed. Finally, the effectiveness of the approach is shown by comparison of the results with existing classical solution.

Keywords: Kirchhoff plate, propagation matrix, reflection matrix, vibration analysis.

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2584 Statistical Approach to Basis Function Truncation in Digital Interpolation Filters

Authors: F. Castillo, J. Arellano, S. Sánchez

Abstract:

In this paper an alternative analysis in the time domain is described and the results of the interpolation process are presented by means of functions that are based on the rule of conditional mathematical expectation and the covariance function. A comparison between the interpolation error caused by low order filters and the classic sinc(t) truncated function is also presented. When fewer samples are used, low-order filters have less error. If the number of samples increases, the sinc(t) type functions are a better alternative. Generally speaking there is an optimal filter for each input signal which depends on the filter length and covariance function of the signal. A novel scheme of work for adaptive interpolation filters is also presented.

Keywords: Interpolation, basis function, over-sampling.

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2583 Polarization Modulation by free-Standing Asymmetric Hole Arrays

Authors: Hong-Wen Hsieh, Shun-Tung Yen

Abstract:

We theoretically demonstrate modulation of light polarization by a crossed rectangular hole array with asymmetric arm lengths. There are two waveguide modes that can modulate the x- and y- polarized incident waves independently. A specific structure is proposed to convert a left-hand incident wave to a right-hand outgoing wave by transmission.

Keywords: Crossed rectangular hole array, extraordinary optical transmission, polarization modulation.

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2582 Dynamic Interaction between Two Neighboring Tunnels in a Layered Half-Space

Authors: Chao He, Shunhua Zhou, Peijun Guo

Abstract:

The vast majority of existing underground railway lines consist of twin tunnels. In this paper, the dynamic interaction between two neighboring tunnels in a layered half-space is investigated by an analytical model. The two tunnels are modelled as cylindrical thin shells, while the soil in the form of a layered half-space with two cylindrical cavities is simulated by the elastic continuum theory. The transfer matrix method is first used to derive the relationship between the plane wave vectors in arbitrary layers and the source layer. Thereafter, the wave translation and transformation are introduced to determine the plane and cylindrical wave vectors in the source layer. The solution for the dynamic interaction between twin tunnels in a layered half-space is obtained by means of the compatibility of displacements and equilibrium of stresses on the two tunnel–soil interfaces. By coupling the proposed model with a fully track model, the train-induced vibrations from twin tunnels in a multi-layered half-space are investigated. The numerical results demonstrate that the existence of a neighboring tunnel has a significant effect on ground vibrations.

Keywords: Underground railway, twin tunnels, wave translation and transformation, transfer matrix method.

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2581 A Case Study to Assess the Validity of Function Points

Authors: Neelam Bawane nee' Singhal, C. V. Srikrishna

Abstract:

Many metrics were proposed to evaluate the characteristics of the analysis and design model of a given product which in turn help to assess the quality of the product. Function point metric is a measure of the 'functionality' delivery by the software. This paper presents an analysis of a set of programs of a project developed in Cµ through Function Points metric. Function points are measured for a Data Flow Diagram (DFD) of the case developed at initial stage. Lines of Codes (LOCs) and possible errors are calculated with the help of measured Function Points (FPs). The calculations are performed using suitable established functions. Calculated LOCs and errors are compared with actual LOCs and errors found at the time of analysis & design review, implementation and testing. It has been observed that actual found errors are more than calculated errors. On the basis of analysis and observations, authors conclude that function point provides useful insight and helps to analyze the drawbacks in the development process.

Keywords: Function Points, Data Flow Diagram, Lines ofCodes.

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2580 Two-Dimensional Solitary Wave Solution to the Quadratic Nonlinear Schrdinger Equation

Authors: Sarun Phibanchon

Abstract:

The solitary wave solution of the quadratic nonlinear Schrdinger equation is determined by the iterative method called Petviashvili method. This solution is also used for the initial condition for the time evolution to study the stability analysis. The spectral method is applied for the time evolution.

Keywords: soliton, iterative method, spectral method, plasma

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2579 Characteristic Function in Estimation of Probability Distribution Moments

Authors: Vladimir S. Timofeev

Abstract:

In this article the problem of distributional moments estimation is considered. The new approach of moments estimation based on usage of the characteristic function is proposed. By statistical simulation technique author shows that new approach has some robust properties. For calculation of the derivatives of characteristic function there is used numerical differentiation. Obtained results confirmed that author’s idea has a certain working efficiency and it can be recommended for any statistical applications.

Keywords: Characteristic function, distributional moments, robustness, outlier, statistical estimation problem, statistical simulation.

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2578 Surge Protection of Power Supply used for Automation Devices in Power Distribution System

Authors: Liheng Ying, Guangjiong Sun

Abstract:

The intent of this essay is to evaluate the effectiveness of surge suppressor aimed at power supply used for automation devices in power distribution system which is consist of MOV and T type low-pass filter. Books, journal articles and e-sources related to surge protection of power supply used for automation devices in power distribution system were consulted, and the useful information was organized, analyzed and developed into five parts: characteristics of surge wave, protection against surge wave, impedance characteristics of target, using Matlab to simulate circuit response after 5kV,1.2/50s surge wave and suggestions for surge protection. The results indicate that various types of load situation have great impact on the effectiveness of surge protective device. Therefore, type and parameters of surge protective device need to be carefully selected, and load matching is also vital to be concerned.

Keywords: automation devices in power distribution system, MOV, surge, T type low-pass filter.

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2577 Analysing and Classifying VLF Transients

Authors: Ernst D. Schmitter

Abstract:

Monitoring lightning electromagnetic pulses (sferics) and other terrestrial as well as extraterrestrial transient radiation signals is of considerable interest for practical and theoretical purposes in astro- and geophysics as well as meteorology. Managing a continuous flow of data, automation of the analysis and classification process is important. Features based on a combination of wavelet and statistical methods proved efficient for this task and serve as input into a radial basis function network that is trained to discriminate transient shapes from pulse like to wave like. We concentrate on signals in the Very Low Frequency (VLF, 3 -30 kHz) range in this paper, but the developed methods are independent of this specific choice.

Keywords: Transient signals, statistics, wavelets, neural networks

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2576 Numerical Investigation of Nozzle Shape Effect on Shock Wave in Natural Gas Processing

Authors: Esam I. Jassim, Mohamed M. Awad

Abstract:

Natural gas flow contains undesirable solid particles, liquid condensation, and/or oil droplets and requires reliable removing equipment to perform filtration. Recent natural gas processing applications are demanded compactness and reliability of process equipment. Since conventional means are sophisticated in design, poor in efficiency, and continue lacking robust, a supersonic nozzle has been introduced as an alternative means to meet such demands. A 3-D Convergent-Divergent Nozzle is simulated using commercial Code for pressure ratio (NPR) varies from 1.2 to 2. Six different shapes of nozzle are numerically examined to illustrate the position of shock-wave as such spot could be considered as a benchmark of particle separation. Rectangle, triangle, circular, elliptical, pentagon, and hexagon nozzles are simulated using Fluent Code with all have same cross-sectional area. The simple one-dimensional inviscid theory does not describe the actual features of fluid flow precisely as it ignores the impact of nozzle configuration on the flow properties. CFD Simulation results, however, show that nozzle geometry influences the flow structures including location of shock wave. The CFD analysis predicts shock appearance when p01/pa>1.2 for almost all geometry and locates at the lower area ratio (Ae/At). Simulation results showed that shock wave in Elliptical nozzle has the farthest distance from the throat among the others at relatively small NPR. As NPR increases, hexagon would be the farthest. The numerical result is compared with available experimental data and has shown good agreement in terms of shock location and flow structure.

Keywords: CFD, Particle Separation, Shock wave, Supersonic Nozzle.

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2575 Image Analysis of Fine Structures of Supercavitation in the Symmetric Wake of a Cylinder

Authors: Y. Obikane , M.Kaneko, K.Kakioka, K.Ogura

Abstract:

The fine structure of supercavitation in the wake of a symmetrical cylinder is studied with high-speed video cameras. The flow is observed in a cavitation tunnel at the speed of 8m/sec when the sidewall and the wake are partially filled with the massive cavitation bubbles. The present experiment observed that a two-dimensional ripple wave with a wave length of 0.3mm is propagated in a downstream direction, and then abruptly increases to a thicker three-dimensional layer. IR-photography recorded that the wakes originated from the horseshoe vortexes alongside the cylinder. The wake was developed to inside the dead water zone, which absorbed the bubbly wake propelled from the separated vortices at the center of the cylinder. A remote sensing classification technique (maximum most likelihood) determined that the surface porosity was 0.2, and the mean speed in the mixed wake was 7m/sec. To confirm the existence of two-dimensional wave motions in the interface, the experiments were conducted at a very low frequency, and showed similar gravity waves in both the upper and lower interfaces.

Keywords: Supercavitation, density gradient correlation

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2574 Simulation and Measurement the Radiation of an Antenna inside a Metallic Case using FDTD

Authors: Shabnam Ladan, M. S. Abrishamian

Abstract:

In this paper we have developed a FDTD simulation code which can treat wave propagation of a monopole antenna in a metallic case which covers with PML, and performed a series of three dimensional FDTD simulations of electromagnetic wave propagation in this space .We also provide a measurement set up in antenna lab and fortunately the simulations and measurements show good agreement. According to simulation and measurement results, we confirmed that the computer program which had been written in FORTRAN, works correctly.

Keywords: FDTD, EMC, monopole antenna.

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2573 Subclasses of Bi-Univalent Functions Associated with Hohlov Operator

Authors: Rashidah Omar, Suzeini Abdul Halim, Aini Janteng

Abstract:

The coefficients estimate problem for Taylor-Maclaurin series is still an open problem especially for a function in the subclass of bi-univalent functions. A function f ϵ A is said to be bi-univalent in the open unit disk D if both f and f-1 are univalent in D. The symbol A denotes the class of all analytic functions f in D and it is normalized by the conditions f(0) = f’(0) – 1=0. The class of bi-univalent is denoted by  The subordination concept is used in determining second and third Taylor-Maclaurin coefficients. The upper bound for second and third coefficients is estimated for functions in the subclasses of bi-univalent functions which are subordinated to the function φ. An analytic function f is subordinate to an analytic function g if there is an analytic function w defined on D with w(0) = 0 and |w(z)| < 1 satisfying f(z) = g[w(z)]. In this paper, two subclasses of bi-univalent functions associated with Hohlov operator are introduced. The bound for second and third coefficients of functions in these subclasses is determined using subordination. The findings would generalize the previous related works of several earlier authors.

Keywords: Analytic functions, bi-univalent functions, Hohlov operator, subordination.

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2572 Application of Strong Optical Feedback to Enhance the Modulation Bandwidth of Semiconductor Lasers to the Millimeter-Wave Band

Authors: Moustafa Ahmed, Ahmed Bakry, Fumio Koyama

Abstract:

We report on the use of strong external optical feedback to enhance the modulation response of semiconductor lasers over a frequency passband around modulation frequencies higher than 60 GHz. We show that this modulation enhancement is a type of photon-photon resonance (PPR) of oscillating modes in the external cavity formed between the laser and the external reflector. The study is based on a time-delay rate equation model that takes into account both the strong feedback and multiple reflections in the external cavity. We examine the harmonic and intermodulation distortions associated with single and two-tone modulations in the mm-wave band of the resonant modulation. We show that compared with solitary lasers modulated around the carrier-photon resonance frequency, the present mm-wave modulated signal has lower distortions.

Keywords: Distortion, intensity modulation, optical feedback, semiconductor laser.

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2571 Investigation on a Wave-Powered Electrical Generator Consisted of a Geared Motor-Generator Housed by a Double-Cone Rolling on Concentric Circular Rails

Authors: Barenten Suciu

Abstract:

An electrical generator able to harness energy from the water waves and designed as a double-cone geared motor-generator (DCGMG), is proposed and theoretically investigated. Similar to a differential gear mechanism, used in the transmission system of the auto vehicle wheels, an angular speed differential is created between the cones rolling on two concentric circular rails. Water wave acting on the floating DCGMG produces and a gear-box amplifies the speed differential to gain sufficient torque for power generation. A model that allows computation of the speed differential, torque, and power of the DCGMG is suggested. Influence of various parameters, regarding the construction of the DCGMG, as well as the contact between the double-cone and rails, on the electro-mechanical output, is emphasized. Results obtained indicate that the generated electrical power can be increased by augmenting the mass of the double-cone, the span of the rails, the apex angle of the cones, the friction between cones and rails, the amplification factor of the gear-box, and the efficiency of the motor-generator. Such findings are useful to formulate a design methodology for the proposed wave-powered generator.

Keywords: Wave-powered electrical generator, double-cone, circular concentric rails, amplification of angular speed differential.

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2570 Buckling of Plates on Foundation with Different Types of Sides Support

Authors: Ali N. Suri, Ahmad A. Al-Makhlufi

Abstract:

In this paper the problem of buckling of plates on foundation of finite length and with different side support is studied.

The Finite Strip Method is used as tool for the analysis. This method uses finite strip elastic, foundation, and geometric matrices to build the assembly matrices for the whole structure, then after introducing boundary conditions at supports, the resulting reduced matrices is transformed into a standard Eigenvalue-Eigenvector problem. The solution of this problem will enable the determination of the buckling load, the associated buckling modes and the buckling wave length.

To carry out the buckling analysis starting from the elastic, foundation, and geometric stiffness matrices for each strip a computer program FORTRAN list is developed.

Since stiffness matrices are function of wave length of buckling, the computer program used an iteration procedure to find the critical buckling stress for each value of foundation modulus and for each boundary condition.

The results showed the use of elastic medium to support plates subject to axial load increase a great deal the buckling load, the results found are very close with those obtained by other analytical methods and experimental work.

The results also showed that foundation compensates the effect of the weakness of some types of constraint of side support and maximum benefit found for plate with one side simply supported the other free.

Keywords: Buckling, Finite Strip, Different Sides Support, Plates on Foundation.

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2569 Explicit Chain Homotopic Function to Compute Hochschild Homology of the Polynomial Algebra

Authors: Z. Altawallbeh

Abstract:

In this paper, an explicit homotopic function is constructed to compute the Hochschild homology of a finite dimensional free k-module V. Because the polynomial algebra is of course fundamental in the computation of the Hochschild homology HH and the cyclic homology CH of commutative algebras, we concentrate our work to compute HH of the polynomial algebra, by providing certain homotopic function.

Keywords: Exterior algebra, free resolution, free and projective modules, Hochschild homology, homotopic function, symmetric algebra.

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2568 High Order Accurate Runge Kutta Nodal Discontinuous Galerkin Method for Numerical Solution of Linear Convection Equation

Authors: Faheem Ahmed, Fareed Ahmed, Yongheng Guo, Yong Yang

Abstract:

This paper deals with a high-order accurate Runge Kutta Discontinuous Galerkin (RKDG) method for the numerical solution of the wave equation, which is one of the simple case of a linear hyperbolic partial differential equation. Nodal DG method is used for a finite element space discretization in 'x' by discontinuous approximations. This method combines mainly two key ideas which are based on the finite volume and finite element methods. The physics of wave propagation being accounted for by means of Riemann problems and accuracy is obtained by means of high-order polynomial approximations within the elements. High order accurate Low Storage Explicit Runge Kutta (LSERK) method is used for temporal discretization in 't' that allows the method to be nonlinearly stable regardless of its accuracy. The resulting RKDG methods are stable and high-order accurate. The L1 ,L2 and L∞ error norm analysis shows that the scheme is highly accurate and effective. Hence, the method is well suited to achieve high order accurate solution for the scalar wave equation and other hyperbolic equations.

Keywords: Nodal Discontinuous Galerkin Method, RKDG, Scalar Wave Equation, LSERK

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