Search results for: random dither method.
Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 8502

Search results for: random dither method.

8142 Material Parameter Identification of Modified AbdelKarim-Ohno Model

Authors: M. Cermak, T. Karasek, J. Rojicek

Abstract:

The key role in phenomenological modelling of cyclic plasticity is good understanding of stress-strain behaviour of given material. There are many models describing behaviour of materials using numerous parameters and constants. Combination of individual parameters in those material models significantly determines whether observed and predicted results are in compliance. Parameter identification techniques such as random gradient, genetic algorithm and sensitivity analysis are used for identification of parameters using numerical modelling and simulation. In this paper genetic algorithm and sensitivity analysis are used to study effect of 4 parameters of modified AbdelKarim-Ohno cyclic plasticity model. Results predicted by Finite Element (FE) simulation are compared with experimental data from biaxial ratcheting test with semi-elliptical loading path.

Keywords: Genetic algorithm, sensitivity analysis, inverse approach, finite element method, cyclic plasticity, ratcheting.

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8141 Optimal Control of Volterra Integro-Differential Systems Based On Legendre Wavelets and Collocation Method

Authors: Khosrow Maleknejad, Asyieh Ebrahimzadeh

Abstract:

In this paper, the numerical solution of optimal control problem (OCP) for systems governed by Volterra integro-differential (VID) equation is considered. The method is developed by means of the Legendre wavelet approximation and collocation method. The properties of Legendre wavelet together with Gaussian integration method are utilized to reduce the problem to the solution of nonlinear programming one. Some numerical examples are given to confirm the accuracy and ease of implementation of the method.

Keywords: Collocation method, Legendre wavelet, optimal control, Volterra integro-differential equation.

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8140 The Perception of Omani E-consumers on the Importance and Performance of Dubai SMHs' Website Dimensions and Attributes

Authors: Mohammed G. Montasser, Rehab Y. Zoweil

Abstract:

There is no doubt that Internet technology is widely used by hotels and its demand is constantly booming. Hotels have largely adopted website information services through using different interactive tools, dimensions and attributes to achieve excellence in functionality and usability but these do not necessary equate with website effectiveness. One way to investigate the effectiveness of hotel website is from the perspective ofe-consumers. This exploratory research is to investigate the perceived importance of websites effectiveness of some selected independent small and medium-sized hotels (SMHs) located in Dubai, United Arab Emirates, from the perspective of Omanie-consumers by using non-random sampling method. From 400 questionnaire addressed to respondents in 27 organizations in Muscat the capital city of Oman, 173 are valid. Findings of this study assist SMHs management in Dubai with the reallocation of their resources and efforts in order to supportebusiness development and to sustain a competitive advantage.

Keywords: Dubai's SMHs, Hotel websites, Omani e-consumer perception, weight and performance evaluation.

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8139 Comparison of Three Versions of Conjugate Gradient Method in Predicting an Unknown Irregular Boundary Profile

Authors: V. Ghadamyari, F. Samadi, F. Kowsary

Abstract:

An inverse geometry problem is solved to predict an unknown irregular boundary profile. The aim is to minimize the objective function, which is the difference between real and computed temperatures, using three different versions of Conjugate Gradient Method. The gradient of the objective function, considered necessary in this method, obtained as a result of solving the adjoint equation. The abilities of three versions of Conjugate Gradient Method in predicting the boundary profile are compared using a numerical algorithm based on the method. The predicted shapes show that due to its convergence rate and accuracy of predicted values, the Powell-Beale version of the method is more effective than the Fletcher-Reeves and Polak –Ribiere versions.

Keywords: Boundary elements, Conjugate Gradient Method, Inverse Geometry Problem, Sensitivity equation.

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8138 Effect of Processing Methods on Texture Evolution in AZ31 Mg Alloy Sheet

Authors: Jung-Ho Moon, Tae Kwon Ha

Abstract:

Textures of AZ31 Mg alloy sheets were evaluated by using neutron diffraction method in this study. The AZ31 sheets were fabricated either by conventional casting and subsequent hot rolling or strip casting. The effect of warm rolling was investigated using the AZ31 Mg alloy sheet produced by conventional casting. Warm rolling of 30% thickness reduction per pass was possible without any side-crack at temperatures as low as 200oC under the roll speed of 30 m/min. The initial microstructure of conventionally cast specimen was found to be partially recrystallized structures. Grain refinement was found to occur actively during the warm rolling. The (0002),(10-10) (10-11),and (10-12) complete pole figures were measured using the HANARO FCD (Neutron Four Circle Diffractometer) and ODF were calculated. The major texture of all specimens can be expressed by ND//(0001) fiber texture. Texture of hot rolled specimen showed the strongest fiber component, while that of strip cast sheet seemed to be similar to random distribution.

Keywords: Mg alloy, texture, pole figure, ODF, neutron diffraction, warm rolling.

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8137 Discovery of Sequential Patterns Based On Constraint Patterns

Authors: Shigeaki Sakurai, Youichi Kitahata, Ryohei Orihara

Abstract:

This paper proposes a method that discovers sequential patterns corresponding to user-s interests from sequential data. This method expresses the interests as constraint patterns. The constraint patterns can define relationships among attributes of the items composing the data. The method recursively decomposes the constraint patterns into constraint subpatterns. The method evaluates the constraint subpatterns in order to efficiently discover sequential patterns satisfying the constraint patterns. Also, this paper applies the method to the sequential data composed of stock price indexes and verifies its effectiveness through comparing it with a method without using the constraint patterns.

Keywords: Sequential pattern mining, Constraint pattern, Attribute constraint, Stock price indexes

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8136 A Machine Learning Approach for Earthquake Prediction in Various Zones Based on Solar Activity

Authors: Viacheslav Shkuratskyy, Aminu Bello Usman, Michael O’Dea, Mujeeb Ur Rehman, Saifur Rahman Sabuj

Abstract:

This paper examines relationships between solar activity and earthquakes, it applied machine learning techniques: K-nearest neighbour, support vector regression, random forest regression, and long short-term memory network. Data from the SILSO World Data Center, the NOAA National Center, the GOES satellite, NASA OMNIWeb, and the United States Geological Survey were used for the experiment. The 23rd and 24th solar cycles, daily sunspot number, solar wind velocity, proton density, and proton temperature were all included in the dataset. The study also examined sunspots, solar wind, and solar flares, which all reflect solar activity, and earthquake frequency distribution by magnitude and depth. The findings showed that the long short-term memory network model predicts earthquakes more correctly than the other models applied in the study, and solar activity is more likely to effect earthquakes of lower magnitude and shallow depth than earthquakes of magnitude 5.5 or larger with intermediate depth and deep depth

.

Keywords: K-Nearest Neighbour, Support Vector Regression, Random Forest Regression, Long Short-Term Memory Network, earthquakes, solar activity, sunspot number, solar wind, solar flares.

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8135 Large Deviations for Lacunary Systems

Authors: Bainian Li, Kongsheng Zhang

Abstract:

Let Xi be a Lacunary System, we established large deviations inequality for Lacunary System. Furthermore, we gained Marcinkiewicz Larger Number Law with dependent random variables sequences.

Keywords: Lacunary system, larger deviations, Locally GeneralizedGaussian, Strong law of large numbers.

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8134 A Methodology for the Synthesis of Multi-Processors

Authors: Hamid Yasinian

Abstract:

Random epistemologies and hash tables have garnered minimal interest from both security experts and experts in the last several years. In fact, few information theorists would disagree with the evaluation of expert systems. In our research, we discover how flip-flop gates can be applied to the study of superpages. Though such a hypothesis at first glance seems perverse, it is derived from known results.

Keywords: Synthesis, Multi-Processors, Interactive Model, Moor’s Law.

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8133 Implementation of the SIP Express Router with Mediaproxy Method on VoIP

Authors: Heru Nurwarsito, R. Arief Setyawan, Rakhmadhany Primananda

Abstract:

Voice Over IP (VoIP) is a technology that could pass the voice traffic and data packet form over an IP network. Network can be used for intranet or Internet. Phone calls using VoIP has advantages in terms of cheaper cost of PSTN phone to more than half, because the cost is calculated by the cost of the global nature of the Internet. Session Initiation Protocol (SIP) is a signaling protocol at the application layer which serves to establish, modify, and terminate a multimedia session involving one or more users. This SIP signaling has SIP message in text form that is used for session management by the SIP components, such as User Agent, Registrar, Redirect Server, and Proxy Server. To build a SIP communication is required SIP Express Router (SER) to be able to receive SIP messages, for handling the basic functions of SIP messages. Problems occur when the NAT through which affects the voice communication will be blocked starting from the sound that is not sent or one side of the sound are sent (half duplex). How that could be used to penetrate NAT is to use a given mediaproxy random RTP port to penetrate NAT.

Keywords: VoIP, SIP, SIP Express Router, NAT, Mediaproxy.

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8132 Efficient Detection Using Sequential Probability Ratio Test in Mobile Cognitive Radio Systems

Authors: Yeon-Jea Cho, Sang-Uk Park, Won-Chul Choi, Dong-Jo Park

Abstract:

This paper proposes a smart design strategy for a sequential detector to reliably detect the primary user-s signal, especially in fast fading environments. We study the computation of the log-likelihood ratio for coping with a fast changing received signal and noise sample variances, which are considered random variables. First, we analyze the detectability of the conventional generalized log-likelihood ratio (GLLR) scheme when considering fast changing statistics of unknown parameters caused by fast fading effects. Secondly, we propose an efficient sensing algorithm for performing the sequential probability ratio test in a robust and efficient manner when the channel statistics are unknown. Finally, the proposed scheme is compared to the conventional method with simulation results with respect to the average number of samples required to reach a detection decision.

Keywords: Cognitive radio, fast fading, sequential detection, spectrum sensing.

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8131 A Force-directed Graph Drawing based on the Hierarchical Individual Timestep Method

Authors: T. Matsubayashi, T. Yamada

Abstract:

In this paper, we propose a fast and efficient method for drawing very large-scale graph data. The conventional force-directed method proposed by Fruchterman and Rheingold (FR method) is well-known. It defines repulsive forces between every pair of nodes and attractive forces between connected nodes on a edge and calculates corresponding potential energy. An optimal layout is obtained by iteratively updating node positions to minimize the potential energy. Here, the positions of the nodes are updated every global timestep at the same time. In the proposed method, each node has its own individual time and time step, and nodes are updated at different frequencies depending on the local situation. The proposed method is inspired by the hierarchical individual time step method used for the high accuracy calculations for dense particle fields such as star clusters in astrophysical dynamics. Experiments show that the proposed method outperforms the original FR method in both speed and accuracy. We implement the proposed method on the MDGRAPE-3 PCI-X special purpose parallel computer and realize a speed enhancement of several hundred times.

Keywords: visualization, graph drawing, Internet Map

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8130 Iris Localization using Circle and Fuzzy Circle Detection Method

Authors: Marzieh. Savoj, S. Amirhassan. Monadjemi

Abstract:

Iris localization is a very important approach in biometric identification systems. Identification process usually is implemented in three levels: iris localization, feature extraction, and pattern matching finally. Accuracy of iris localization as the first step affects all other levels and this shows the importance of iris localization in an iris based biometric system. In this paper, we consider Daugman iris localization method as a standard method, propose a new method in this field and then analyze and compare the results of them on a standard set of iris images. The proposed method is based on the detection of circular edge of iris, and improved by fuzzy circles and surface energy difference contexts. Implementation of this method is so easy and compared to the other methods, have a rather high accuracy and speed. Test results show that the accuracy of our proposed method is about Daugman method and computation speed of it is 10 times faster.

Keywords: Convolution, Edge detector filter, Fuzzy circle, Identification

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8129 A Review on Higher Order Spline Techniques for Solving Burgers Equation Using B-Spline Methods and Variation of B-Spline Techniques

Authors: Maryam Khazaei Pool, Lori Lewis

Abstract:

This is a summary of articles based on higher order B-splines methods and the variation of B-spline methods such as Quadratic B-spline Finite Elements Method, Exponential Cubic B-Spline Method Septic B-spline Technique, Quintic B-spline Galerkin Method, and B-spline Galerkin Method based on the Quadratic B-spline Galerkin method (QBGM) and Cubic B-spline Galerkin method (CBGM). In this paper we study the B-spline methods and variations of B-spline techniques to find a numerical solution to the Burgers’ equation. A set of fundamental definitions including Burgers equation, spline functions, and B-spline functions are provided. For each method, the main technique is discussed as well as the discretization and stability analysis. A summary of the numerical results is provided and the efficiency of each method presented is discussed. A general conclusion is provided where we look at a comparison between the computational results of all the presented schemes. We describe the effectiveness and advantages of these methods.

Keywords: Burgers’ Equation, Septic B-spline, Modified Cubic B-Spline Differential Quadrature Method, Exponential Cubic B-Spline Technique, B-Spline Galerkin Method, and Quintic B-Spline Galerkin Method.

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8128 Inhibition Kinetic Determination of Trace Amounts of Ruthenium(III) by the Spectrophotometric method with Rhodamine B in Micellar Medium

Authors: Mohsen Keyvanfard

Abstract:

A new, simple and highly sensitive kinetic spectrophotometric method was developed for the determination of trace amounts of Ru(III) in the range of 0.06-20 ng/ml .The method is based on the inhibitory effect of ruthenium(III) on the oxidation of Rhodamine B by bromate in acidic and micellar medium. The reaction was monitored spectrophotometrically by measuring the decreasing in absorbance of Rhodamine B at 554 nm with a fixedtime method..The limit of detection is 0.04 ng/ml Ru(III).The relative standard deviation of 5 and 10 ng/ml Ru(III) was 2.3 and 2.7 %, respectively. The method was applied to the determination of ruthenium in real water samples

Keywords: Ruthenium ;Inhibitory; Rhodamine B; bromate

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8127 Estimation of Train Operation Using an Exponential Smoothing Method

Authors: Taiyo Matsumura, Kuninori Takahashi, Takashi Ono

Abstract:

The purpose of this research is to improve the convenience of waiting for trains at level crossings and stations and to prevent accidents resulting from forcible entry into level crossings, by providing level crossing users and passengers with information that tells them when the next train will pass through or arrive. For this paper, we proposed methods for estimating operation by means of an average value method, variable response smoothing method, and exponential smoothing method, on the basis of open data, which has low accuracy, but for which performance schedules are distributed in real time. We then examined the accuracy of the estimations. The results showed that the application of an exponential smoothing method is valid.

Keywords: Exponential smoothing method, open data, operation estimation, train schedule.

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8126 Power Flow Analysis for Radial Distribution System Using Backward/Forward Sweep Method

Authors: J. A. Michline Rupa, S. Ganesh

Abstract:

This paper proposes a backward/forward sweep method to analyze the power flow in radial distribution systems. The distribution system has radial structure and high R/X ratios. So the newton-raphson and fast decoupled methods are failed with distribution system. The proposed method presents a load flow study using backward/forward sweep method, which is one of the most effective methods for the load-flow analysis of the radial distribution system. By using this method, power losses for each bus branch and voltage magnitudes for each bus node are determined. This method has been tested on IEEE 33-bus radial distribution system and effective results are obtained using MATLAB.

Keywords: Backward/Forward sweep method, Distribution system, Load flow analysis.

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8125 The Impact of Government Expenditure on Economic Growth: A Study of Asian Countries

Authors: K. P. K. S. Lahirushan, W. G. V. Gunasekara

Abstract:

Main purpose of this study is to identify the impact of government expenditure on economic growth in Asian Countries. Consequently, main objective is to analyze whether government expenditure causes economic growth in Asian countries vice versa and then scrutinizing long-run equilibrium relationship exists between them. The study completely based on secondary data. The methodology being quantitative that includes econometrical techniques of cointegration, panel fixed effects model and granger causality in the context of panel data of Asian countries; Singapore, Malaysia, Thailand, South Korea, Japan, China, Sri Lanka, India and Bhutan with 44 observations in each country, totaling to 396 observations from 1970 to 2013. The model used is the random effects panel OLS model. As with the above methodology, the study found the fascinating outcome. At first, empirical findings exhibit a momentous positive impact of government expenditure on Gross Domestic Production in Asian region. Secondly, government expenditure and economic growth indicate a long-run relationship in Asian countries. In conclusion, there is a unidirectional causality from economic growth to government expenditure and government expenditure to economic growth in Asian countries. Hence the study is validated that it is in line with the Keynesian theory and Wagner’s law as well. Consequently, it can be concluded that role of government would play a vital role in economic growth of Asian Countries. However; if government expenditure did not figure out with the economy’s needs it might be considerably inspiration the economy in a negative way so that society bears the costs.

Keywords: Asian Countries, Government Expenditure, Keynesian theory, Wagner’s theory, Random effects panel OLS model.

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8124 An Expansion Method for Schrödinger Equation of Quantum Billiards with Arbitrary Shapes

Authors: İnci M. Erhan

Abstract:

A numerical method for solving the time-independent Schrödinger equation of a particle moving freely in a three-dimensional axisymmetric region is developed. The boundary of the region is defined by an arbitrary analytic function. The method uses a coordinate transformation and an expansion in eigenfunctions. The effectiveness is checked and confirmed by applying the method to a particular example, which is a prolate spheroid.

Keywords: Bessel functions, Eigenfunction expansion, Quantum billiard, Schrödinger equation, Spherical harmonics

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8123 An Analytical Method to Analysis of Foam Drainage Problem

Authors: A. Nikkar, M. Mighani

Abstract:

In this study, a new reliable technique use to handle the foam drainage equation. This new method is resulted from VIM by a simple modification that is Reconstruction of Variational Iteration Method (RVIM). The drainage of liquid foams involves the interplay of gravity, surface tension, and viscous forces. Foaming occurs in many distillation and absorption processes. Results are compared with those of Adomian’s decomposition method (ADM).The comparisons show that the Reconstruction of Variational Iteration Method is very effective and overcome the difficulty of traditional methods and quite accurate to systems of non-linear partial differential equations.

Keywords: Reconstruction of Variational Iteration Method (RVIM), Foam drainage, nonlinear partial differential equation.

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8122 Preconditioned Mixed-Type Splitting Iterative Method For Z-Matrices

Authors: Li Jiang, Baoguang Tian

Abstract:

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

Keywords: Z-matrix, mixed-type splitting iterative method, precondition, comparison theorem, linear system.

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8121 Alternating Implicit Block FDTD Method For Scalar Wave Equation

Authors: N. M. Nusi, M. Othman, M. Suleiman, F. Ismail, N. Alias

Abstract:

In this paper, an alternating implicit block method for solving two dimensional scalar wave equation is presented. The new method consist of two stages for each time step implemented in alternating directions which are very simple in computation. To increase the speed of computation, a group of adjacent points is computed simultaneously. It is shown that the presented method increase the maximum time step size and more accurate than the conventional finite difference time domain (FDTD) method and other existing method of natural ordering.

Keywords: FDTD, Scalar wave equation, alternating direction implicit (ADI), alternating group explicit (AGE), asymmetric approximation.

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8120 An Improved Greedy Routing Algorithm for Grid using Pheromone-Based Landmarks

Authors: Lada-On Lertsuwanakul, Herwig Unger

Abstract:

This paper objects to extend Jon Kleinberg-s research. He introduced the structure of small-world in a grid and shows with a greedy algorithm using only local information able to find route between source and target in delivery time O(log2n). His fundamental model for distributed system uses a two-dimensional grid with longrange random links added between any two node u and v with a probability proportional to distance d(u,v)-2. We propose with an additional information of the long link nearby, we can find the shorter path. We apply the ant colony system as a messenger distributed their pheromone, the long-link details, in surrounding area. The subsequence forwarding decision has more option to move to, select among local neighbors or send to node has long link closer to its target. Our experiment results sustain our approach, the average routing time by Color Pheromone faster than greedy method.

Keywords: Routing algorithm, Small-World network, Ant Colony Optimization, and Peer-to-peer System.

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8119 A Calibration Device for Force-Torque Sensors

Authors: Nicolay Zarutskiy, Roman Bulkin

Abstract:

The paper deals with the existing methods of force-torque sensor calibration with a number of components from one to six, analyzed their advantages and disadvantages, the necessity of introduction of a calibration method. Calibration method and its constructive realization are also described here. A calibration method allows performing automated force-torque sensor calibration both with selected components of the main vector of forces and moments and with complex loading. Thus, two main advantages of the proposed calibration method are achieved: the automation of the calibration process and universality.

Keywords: Automation, calibration, calibration device, calibration method, force-torque sensors.

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8118 Coupled Galerkin-DQ Approach for the Transient Analysis of Dam-Reservoir Interaction

Authors: S. A. Eftekhari

Abstract:

In this paper, a numerical algorithm using a coupled Galerkin-Differential Quadrature (DQ) method is proposed for the solution of dam-reservoir interaction problem. The governing differential equation of motion of the dam structure is discretized by the Galerkin method and the DQM is used to discretize the fluid domain. The resulting systems of ordinary differential equations are then solved by the Newmark time integration scheme. The mixed scheme combines the simplicity of the Galerkin method and high accuracy and efficiency of the DQ method. Its accuracy and efficiency are demonstrated by comparing the calculated results with those of the existing literature. It is shown that highly accurate results can be obtained using a small number of Galerkin terms and DQM sampling points. The technique presented in this investigation is general and can be used to solve various fluid-structure interaction problems.

Keywords: Dam-reservoir system, Differential quadrature method, Fluid-structure interaction, Galerkin method, Integral quadrature method.

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8117 Discontinuous Galerkin Method for Total Variation Minimization on Inpainting Problem

Authors: Xijian Wang

Abstract:

This paper is concerned with the numerical minimization of energy functionals in BV ( ) (the space of bounded variation functions) involving total variation for gray-scale 1-dimensional inpainting problem. Applications are shown by finite element method and discontinuous Galerkin method for total variation minimization. We include the numerical examples which show the different recovery image by these two methods.

Keywords: finite element method, discontinuous Galerkin method, total variation minimization, inpainting

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8116 Numerical Solution of Second-Order Ordinary Differential Equations by Improved Runge-Kutta Nystrom Method

Authors: Faranak Rabiei, Fudziah Ismail, S. Norazak, Saeid Emadi

Abstract:

In this paper we developed the Improved Runge-Kutta Nystrom (IRKN) method for solving second order ordinary differential equations. The methods are two step in nature and require lower number of function evaluations per step compared with the existing Runge-Kutta Nystrom (RKN) methods. Therefore, the methods are computationally more efficient at achieving the higher order of local accuracy. Algebraic order conditions of the method are obtained and the third and fourth order method are derived with two and three stages respectively. The numerical results are given to illustrate the efficiency of the proposed method compared to the existing RKN methods.

Keywords: Improved Runge-Kutta Nystrom method, Two step method, Second-order ordinary differential equations, Order conditions

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8115 On-line and Off-line POD Assisted Projective Integral for Non-linear Problems: A Case Study with Burgers-Equation

Authors: Montri Maleewong, Sirod Sirisup

Abstract:

The POD-assisted projective integration method based on the equation-free framework is presented in this paper. The method is essentially based on the slow manifold governing of given system. We have applied two variants which are the “on-line" and “off-line" methods for solving the one-dimensional viscous Bergers- equation. For the on-line method, we have computed the slow manifold by extracting the POD modes and used them on-the-fly along the projective integration process without assuming knowledge of the underlying slow manifold. In contrast, the underlying slow manifold must be computed prior to the projective integration process for the off-line method. The projective step is performed by the forward Euler method. Numerical experiments show that for the case of nonperiodic system, the on-line method is more efficient than the off-line method. Besides, the online approach is more realistic when apply the POD-assisted projective integration method to solve any systems. The critical value of the projective time step which directly limits the efficiency of both methods is also shown.

Keywords: Projective integration, POD method, equation-free.

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8114 Introduction of the Fluid-Structure Coupling into the Force Analysis Technique

Authors: Océane Grosset, Charles Pézerat, Jean-Hugh Thomas, Frédéric Ablitzer

Abstract:

This paper presents a method to take into account the fluid-structure coupling into an inverse method, the Force Analysis Technique (FAT). The FAT method, also called RIFF method (Filtered Windowed Inverse Resolution), allows to identify the force distribution from local vibration field. In order to only identify the external force applied on a structure, it is necessary to quantify the fluid-structure coupling, especially in naval application, where the fluid is heavy. This method can be decomposed in two parts, the first one consists in identifying the fluid-structure coupling and the second one to introduced it in the FAT method to reconstruct the external force. Results of simulations on a plate coupled with a cavity filled with water are presented.

Keywords: Fluid-structure coupling, inverse methods, naval, vibrations.

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8113 Accelerating Quantum Chemistry Calculations: Machine Learning for Efficient Evaluation of Electron-Repulsion Integrals

Authors: Nishant Rodrigues, Nicole Spanedda, Chilukuri K. Mohan, Arindam Chakraborty

Abstract:

A crucial objective in quantum chemistry is the computation of the energy levels of chemical systems. This task requires electron-repulsion integrals as inputs and the steep computational cost of evaluating these integrals poses a major numerical challenge in efficient implementation of quantum chemical software. This work presents a moment-based machine learning approach for the efficient evaluation of electron-repulsion integrals. These integrals were approximated using linear combinations of a small number of moments. Machine learning algorithms were applied to estimate the coefficients in the linear combination. A random forest approach was used to identify promising features using a recursive feature elimination approach, which performed best for learning the sign of each coefficient, but not the magnitude. A neural network with two hidden layers was then used to learn the coefficient magnitudes, along with an iterative feature masking approach to perform input vector compression, identifying a small subset of orbitals whose coefficients are sufficient for the quantum state energy computation. Finally, a small ensemble of neural networks (with a median rule for decision fusion) was shown to improve results when compared to a single network.

Keywords: Quantum energy calculations, atomic orbitals, electron-repulsion integrals, ensemble machine learning, random forests, neural networks, feature extraction.

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