Search results for: simplified conjugate-gradient method

Authors: M. Khouil, N. Saber, M. Mestari

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This study aimed to propose, a different architecture of a Path Planning using the NECMOP. where several nonlinear objective functions must be optimized in a conflicting situation. The ability to detect and avoid collision is very important for mobile intelligent machines. However, many artificial vision systems are not yet able to quickly and cheaply extract the wealth information. This network, which has been particularly reviewed, has enabled us to solve with a new approach the problem of collision detection between two convex polyhedra in a fixed time (O (1) time). We used two types of neurons linear and threshold logic, which simplified the actual implementation of all the networks proposed. This article represents a comprehensive algorithm that determine through the AMAXNET network a measure (a mini-maximum point) in a fixed time, which allows us to detect the presence of a potential collision.

Keywords: path planning, collision detection, convex polyhedron, neural network

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Authors: Olgha Giorgishvili

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The work is mainly concerned with the determination of modulus of deformation by laboratory method. It is known that a modulus of deformation is defining by laboratory and field methods. By laboratory method the modulus of deformation is defined in the compressive devices. Our goal is to conduct experiments by both methods and finally make to interpret the obtained results. In this article is considered the definition by new offered laboratory method of deformation modulus that is closer to the real deformation modulus. Finally, the obtained results gives the possibility to us to raise the issue of change the state norms for determining ground by laboratory method.

Keywords: building, soil mechanic, deformation moulus, compression methods

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Authors: Liqin Zhang, Liang Yan

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This paper addresses the speed synchronization control problem for a network-based multi-motor system from the perspective of cluster consensus theory. Each motor is considered as a single agent connected through fixed and undirected network. This paper presents an improved control protocol from three aspects. First, for the purpose of improving both tracking and synchronization performance, this paper presents a distributed leader-following method. The improved control protocol takes the importance of each motor’s speed into consideration, and all motors are divided into different groups according to speed weights. Specifically, by using control parameters optimization, the synchronization error and tracking error can be regulated and decoupled to some extent. The simulation results demonstrate the effectiveness and superiority of the proposed strategy. In practical engineering, the simplified models are unrealistic, such as single-integrator and double-integrator. And previous algorithms require the acceleration information of the leader available to all followers if the leader has a varying velocity, which is also difficult to realize. Therefore, the method focuses on an observer-based variable structure algorithm for consensus tracking, which gets rid of the leader acceleration. The presented scheme optimizes synchronization performance, as well as provides satisfactory robustness. What’s more, the existing algorithms can obtain a stable synchronous system; however, the obtained stable system may encounter some disturbances that may destroy the synchronization. Focus on this challenging technological problem, a state-dependent-switching approach is introduced. In the presence of unmeasured angular speed and unknown failures, this paper investigates a distributed fault-tolerant consensus tracking algorithm for a group non-identical motors. The failures are modeled by nonlinear functions, and the sliding mode observer is designed to estimate the angular speed and nonlinear failures. The convergence and stability of the given multi-motor system are proved. Simulation results have shown that all followers asymptotically converge to a consistent state when one follower fails to follow the virtual leader during a large enough disturbance, which illustrates the good performance of synchronization control accuracy.

Keywords: consensus control, distributed follow, fault-tolerant control, multi-motor system, speed synchronization

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

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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: aeroacoustics, fluid-structure coupling, inverse methods, naval, turbulent flow

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Authors: Hossain Samani, Mohammad Ehteram

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In this paper, we consider finite volume method (FVM) in water hammer. We will simulate these techniques on a looped network with complex boundary conditions. After comparing methods, we see the FVM method as the best method. We compare the results of FVM with experimental data. Finite volume using staggered grid is applied for solving water hammer equations.

Keywords: hydraulic transient, water hammer, interpolation, non-liner interpolation

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Authors: Mohamed Hafid, Marcel Lacroix

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This study presents a simple inverse heat transfer procedure for predicting the wall erosion and the time-varying thickness of the protective bank that covers the inside surface of the refractory brick wall of a melting furnace. The direct problem is solved by using the Finite-Volume model. The melting/solidification process is modeled using the enthalpy method. The inverse procedure rests on the Levenberg-Marquardt method combined with the Broyden method. The effect of the location of the temperature sensors and of the measurement noise on the inverse predictions is investigated. Recommendations are made concerning the location of the temperature sensor.

Keywords: melting furnace, inverse heat transfer, enthalpy method, levenberg–marquardt method

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Authors: Osama Terra, Hatem Hussein

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Calibration of Optical Time Domain Reflectometer (OTDR) is crucial for the accurate determination of loss budget for long optical fiber links. In this paper, the calibration of the attenuation scale of an OTDR using two different techniques is discussed and implemented. The first technique is the external modulation method (EM). A setup is proposed to calibrate an OTDR over a dynamic range of around 15 dB based on the EM method. Afterwards, the OTDR is calibrated using two standard reference fibers (SRF). Both SRF are calibrated using cut-back technique; one of them is calibrated at our home institute (the National Institute of Standards – NIS) while the other at the National Physical Laboratory (NPL) of the United Kingdom to confirm our results. In addition, the parameters contributing the calibration uncertainty are thoroughly investigated. Although the EM method has several advantages over the SRF method, the uncertainties in the SRF method is found to surpass that of the EM method.

Keywords: optical time domain reflectometer, fiber attenuation measurement, OTDR calibration, external source method

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Authors: Johannes J. Schneider, Mathias S. Weyland, Peter Eggenberger Hotz, William D. Jamieson, Oliver Castell, Alessia Faggian, Rudolf M. Füchslin

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Agglomerations of polydisperse systems of spherical particles are created in computer simulations using a simplified stochastic-hydrodynamic model: Particles sink to the bottom of the cylinder, taking into account gravity reduced by the buoyant force, the Stokes friction force, the added mass effect, and random velocity changes. Two types of particles are considered, with one of them being able to create connections to neighboring particles of the same type, thus forming a network within the agglomeration at the bottom of a cylinder. Decreasing the fraction of these particles, a percolation transition occurs. The critical regime is determined by investigating the maximum cluster size and the percolation susceptibility.

Keywords: binary system, maximum cluster size, percolation, polydisperse

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Authors: Seyed Amin Vakili, Sahar Sadat Vakili, Seyed Ehsan Vakili, Nader Abdoli Yazdi

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The main purpose of this paper is to present the Modified Newmark Method of buckling analysis frame considering the effect of the axial load. The discussion will be restricted to plane frameworks containing a constant cross-section for each element. In addition, it is assumed that the frames are prevented from out-of-plane deflection. In this method, stiffness matrix of the structure is considered to be constant. The most important advantage of such a method is that it obtains both upper and lower critical loads. The advanced of the present method is fast convergence, ability to use computer simulations, and ability to model structures with semi-rigid support conditions using linear and rotational spring.

Keywords: buckling, stability, frame, modified newmark method

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Authors: A. A. Soliman

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The Modified Regularized Long Wave (MRLW) equation is solved numerically by giving a new algorithm based on collocation method using quartic B-splines at the mid-knot points as element shape. Also, we use the fourth Runge-Kutta method for solving the system of first order ordinary differential equations instead of finite difference method. Our test problems, including the migration and interaction of solitary waves, are used to validate the algorithm which is found to be accurate and efficient. The three invariants of the motion are evaluated to determine the conservation properties of the algorithm. The temporal evaluation of a Maxwellian initial pulse is then studied.

Keywords: collocation method, MRLW equation, Quartic B-splines, solitons

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Authors: Nguyen Van Loi, Le Thanh Son, Tran Trung Kien

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The paper deals with the problem of the formation of range profiles (RPs) for an X-band coastal surveillance radar. Two popular methods, the difference operator method, and the window-based method, are reviewed and analyzed via two tests with different datasets. The test results show that although the original window-based method achieves a better performance than the difference operator method, it has three main drawbacks that are the use of 3 or 4 peaks of an RP for creating the windows, the extension of the window size using the power sum of three adjacent cells in the left and the right sides of the windows and the same threshold applied for all types of vessels to finish the formation process of RPs. These drawbacks lead to inaccurate RPs due to the low signal-to-clutter ratio. Therefore, some suggestions are proposed to improve the original window-based method.

Keywords: range profile, difference operator method, window-based method, automatic target recognition

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Authors: Chien-Kuo Chiu

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In the displacement-based seismic design and evaluation, equivalent linearization method is one of the approximation methods to estimate the maximum inelastic displacement response of a system. In this study, the accuracy of two equivalent linearization methods are investigated. The investigation consists of three soil condition in Taiwan (Taipei Basin 1, 2, and 3) and five different heights of building (H_r= 10, 20, 30, 40, and 50 m). The first method is the Taiwan equivalent linearization method (TELM) which was proposed based on Japanese equivalent linear method considering the modification factor, α_T= 0.85. On the basis of Lin and Miranda study, the second method is proposed with some modification considering Taiwan soil conditions. From this study, it is shown that Taiwanese equivalent linearization method gives better estimation compared to the modified Lin and Miranda method (MLM). The error index for the Taiwanese equivalent linearization method are 16%, 13%, and 12% for Taipei Basin 1, 2, and 3, respectively. Furthermore, a ductility demand spectrum of single-degree-of-freedom (SDOF) system is presented in this study as a guide for engineers to estimate the ductility demand of a structure.

Keywords: displacement-based design, ductility demand spectrum, equivalent linearization method, RC buildings, single-degree-of-freedom

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Authors: Beldjilali Bilal, Benadda Belkacem, Kahlouche Salem

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Due to the Doppler effect caused by the high velocity of satellite and in some case receivers, the frequency of the Global Positioning System (GPS) signals are transformed into a new ones. Several acquisition algorithms frequency of the Global Positioning System (GPS) signals are transformed can be used to estimate the new frequency and phase shifts values. Numerous algorithms are based on the frequencies domain calculation. Our developed algorithm is a new approach dedicated to the Global Positioning System signal acquisition based on the fast Fourier transform. Our proposed new algorithm is easier to implement and has fast execution time compared with elder ones.

Keywords: global positioning system, acquisition, FFT, GPS/L1, software receiver, weak signal

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Authors: Adil Hassabo

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In this paper, a horizontal circular curve computations calculator is developed in Microsoft Windows. The developed calculator can be used for determining the necessary information required for setting out horizontal curves. Three methods are applied in the developed program namely: incremental chord method, total chord method, and the coordinates method. Computations of horizontal curves by the developed calculator is faster, easier, accurate, and less subject to errors comparable to the traditional method of calculations. Finally, the results obtained by the traditional method and by the developed calculator are presented for checking the behavior of the developed calculator.

Keywords: calculator, circular, computations, curve

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Authors: Dong Wook Lee, Adrian Mistreanu

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The authors have studied a method for analyzing containment and penetration using an explicit nonlinear Finite Element Analysis. This method may be used in the stage of concept design for the protection of external configurations or components of aircraft engines and nuclear power plant structures. This paper consists of the modeling method, the results obtained from the method and the comparison of the results with those calculated from simple analytical method. It shows that the containment capability obtained by proposed method matches well with analytically calculated containment capability.

Keywords: computer aided engineering, containment analysis, finite element analysis, impact analysis, penetration analysis

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Authors: Auwal Nata'ala

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The Information and Communication Technology (ICT) has had impacts in almost every area human endeavor. From business, industries, banks to none profit organizations. ICT has simplified business process such as sorting, summarizing, coding, updating and generating a report in a real-time processing mode. However, the use of these ICT facilities such as computer and internet has also brought unintended consequences of criminal activities such as spamming, credit card frauds, ATM frauds, phishing, identity theft, denial of services and other related cyber crimes. This study sought to examined cyber-crime and its impact on the banking institution in Nigeria. It also examined the existing policy framework and assessed the success of the institutional countermeasures in combating cyber crime in the banking industry. This paper X-ray’s cyber crimes, policies issues and provides insight from a Nigeria perspective.

Keywords: cyber crimes, e-banking, policies, ICT

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Authors: Reza Mohammadi

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Using quartic spline, we develop a method for numerical solution of singularly perturbed two-point boundary-value problems. The purposed method is fourth-order accurate and applicable to problems both in singular and non-singular cases. The convergence analysis of the method is given. The resulting linear system of equations has been solved by using a tri-diagonal solver. We applied the presented method to test problems which have been solved by other existing methods in references, for comparison of presented method with the existing methods. Numerical results are given to illustrate the efficiency of our methods.

Keywords: second-order ordinary differential equation, singularly-perturbed, quartic spline, convergence analysis

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Authors: Ali Khwaldeh, Nimer Adwan

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In this paper, a method for constructing a controlled balanced Boolean function satisfying the criterion of a Strictly Avalanche Criteria (SAC) effect is proposed. The proposed method is based on the use of three orthogonal nonlinear components which is unlike the high-order SAC functions. So, the generator synthesized by the proposed method has separate sets of control and information inputs. The proposed method proves its simplicity and the implementation ability. The proposed method allows synthesizing a SAC function generator with fixed control and information inputs. This ensures greater efficiency of the built-in oscillator compared to high-order SAC functions that can be used as a generator. Accordingly, the method is completely formalized and implemented as a software product.

Keywords: boolean function, controlled balanced boolean function, strictly avalanche criteria, orthogonal nonlinear

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Authors: Abdul Hakim Chikho

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A simple method of calculating satisfactory of the effect of instability on the distribution of in-plane bending moments in unbraced semi-rigidly multistory steel framed structures is presented in this paper. This method, which is a modified form of the current amplified sway method of BS5950: part1:2000, uses an approximate load factor at elastic instability in each storey of a frame which in turn dependent up on the axial loads acting in the columns. The calculated factors are then used to represent the geometrical deformations due to the presence of axial loads, acting in that storey. Only a first order elastic analysis is required to accomplish the calculation. Comparison of the prediction of the proposed method and the current BS5950 amplified sway method with an accurate second order elastic computation shows that the proposed method leads to predictions which are markedly more accurate than the current approach of BS5950.

Keywords: improved amplified sway method, steel frames, semi-rigid connections, secondary effects

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Authors: Azza Habibullah

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The principal objective of this paper is to show the use of participatory culture in the parliamentarian campaign. The use of this method has always been non-popular amongst the parliamentarian candidates due to the amount of times and energy that they need to spent with the constituents. However, due to many parliamentarian corruption cases in the last five years period, some political party have been losing peoples trust. That political party trust lost had also affecting the parliamentarian candidates electability, so they invent some creative campaign method that involving their constituent with more intimates and friendly environment. In this paper, an observation is done to a parliamentarian candidate from Partai Keadilan Sejahtera (Prosperous Justice Party) in Bandung and Cimahi City area, West Java. This Parliamentraian candidate is known for her personal-approach campaign method such as a puppet show, hanging out with group of ex-bike gang leaders, and going fishing with the constituent. This paper will compare her method with other parliamentarian candidates from the same party as her that mostly use mainstream campaign method such as open speech, print media, an other one way campaign method. While the other parliamentarian candidates failed to reach the parliamentarian threshold, the participatory method had proven as an effective method.

Keywords: participatory culture, Indonesian parliamentary election, Prosperous Justice Party, electability

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Authors: Jinho Hur, Minjung Shin, Heekyu Kim

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In many places, new railway constructions in the city are being used to build a viaduct station to take advantage of the space below the line, for difficulty of securing railway site and disconnections of areas. The space under the viaduct has limited to use by noise and vibration. In order to use it for various purposes, reducing noise and vibration is required. The vibration reduction method for new structures is recently developed enough to use as accommodation, but the reduction method for existing structures is still far-off. In this study, it suggests vibration reduction method by filling vibration reduction material to column members which is path of structure-bone-noise from trains run. Because most of railroad stations are reinforced concrete structures. It compares vibration reduction of station applied the method and original station by FEM analysis. As a result, reduction of vibration acceleration level in bandwidth 15~30Hz can be reduced. Therefore, using this method for viaduct railroad station, vibration of station is expected to be reduced.

Keywords: structure borne noise, TPU, viaduct rail station, vibration reduction method

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Authors: Kharisma Utomo Mulyodinoto, Suwarno, A. Abu-Siada

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Dissolved Gas Analysis is one of impressive technique to detect and predict internal fault of transformers by using gas generated by transformer oil sample. A number of methods are used to interpret the dissolved gas from transformer oil sample: Doernenberg Ratio Method, IEC (International Electrotechnical Commission) Ratio Method, and Duval Triangle Method. While the assessment of dissolved gas within transformer oil samples has been standardized over the past two decades, analysis of the results is not always straight forward as it depends on personnel expertise more than mathematical formulas. To get over this limitation, this paper is aimed at improving the interpretation of Doernenberg Ratio Method, IEC Ratio Method, and Duval Triangle Method using Two Stages Adaptive Neuro-Fuzzy Inference System (ANFIS). Dissolved gas analysis data from 520 faulty transformers was analyzed to establish the proposed ANFIS model. Results show that the developed ANFIS model is accurate and can standardize the dissolved gas interpretation process with accuracy higher than 90%.

Keywords: ANFIS, dissolved gas analysis, Doernenberg ratio method, Duval triangular method, IEC ratio method, transformer

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Authors: Maryam Mosleh, Mahmood Otadi

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The hybrid differential equations have a wide range of applications in science and engineering. In this paper, the homotopy analysis method (HAM) is applied to obtain the series solution of the hybrid differential equations. Using the homotopy analysis method, it is possible to find the exact solution or an approximate solution of the problem. Comparisons are made between improved predictor-corrector method, homotopy analysis method and the exact solution. Finally, we illustrate our approach by some numerical example.

Keywords: Fuzzy number, parametric form of a fuzzy number, fuzzy integrodifferential equation, homotopy analysis method

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Authors: Tomoko Fukuyama, Osamu Senbu

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Prestressed concrete is used a lot in infrastructures such as roads or bridges. However, poor grout filling and PC steel corrosion are currently major issues of prestressed concrete structures. One of the problems with nondestructive corrosion detection of PC steel is a plastic pipe which covers PC steel. The insulative property of pipe makes a nondestructive diagnosis difficult; therefore a practical technology to detect these defects is necessary for the maintenance of infrastructures. The goal of the research is a development of an electrochemical technique which enables to detect internal defects from the surface of prestressed concrete nondestructively. Ideally, the measurements should be conducted from the surface of structural members to diagnose non-destructively. In the present experiment, a prestressed concrete member is simplified as a layered specimen to simulate a current path between an input and an output electrode on a member surface. The specimens which are layered by mortar and the prestressed concrete constitution materials (steel, polyethylene, stainless steel, or galvanized steel plates) were provided to the alternating current impedance measurement. The magnitude of an applied electric field was 0.01-volt or 1-volt, and the frequency range was from 106 Hz to 10-2 Hz. The frequency spectrums of impedance, which relate to charge reactions activated by an electric field, were measured to clarify the effects of the material configurations or the properties. In the civil engineering field, the Nyquist diagram is popular to analyze impedance and it is a good way to grasp electric relaxation using a shape of the plot. However, it is slightly not suitable to figure out an influence of a measurement frequency which is reciprocal of reaction time. Hence, Bode diagram is also applied to describe charge reactions in the present paper. From the experiment results, the alternating current impedance method looks to be applicable to the insulative material measurement and eventually prestressed concrete diagnosis. At the same time, the frequency spectrums of impedance show the difference of the material configuration. This is because the charge mobility reflects the variety of substances and also the measuring frequency of the electric field determines migration length of charges which are under the influence of the electric field. However, it could not distinguish the differences of the material thickness and is inferred the difficulties of prestressed concrete diagnosis to identify the amount of an air void or a layer of corrosion product by the technique.

Keywords: capacitance, conductance, prestressed concrete, susceptance

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Authors: Imen Debbabi, Hédi BelHadjSalah

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The Improved Element Free Galerkin (IEFG) method is presented to treat the steady states and the transient heat transfer problems. As a result of a combination between the Improved Moving Least Square (IMLS) approximation and the Element Free Galerkin (EFG) method, the IEFG's shape functions don't have the Kronecker delta property and the penalty method is used to impose the Dirichlet boundary conditions. In this paper, two heat transfer problems, transient and steady states, are studied to improve the efficiency of this meshfree method for 2D heat transfer problems. The performance of the IEFG method is shown using the comparison between numerical and analytic results.

Keywords: meshfree methods, the Improved Moving Least Square approximation (IMLS), the Improved Element Free Galerkin method (IEFG), heat transfer problems

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Authors: Hamdy M. Youssef, Eman A. Al-Lehaibi

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This paper presents an iteration method for the numerical solutions of a one-dimensional problem of generalized thermoelasticity with one relaxation time under given initial and boundary conditions. The thermoelastic material with variable properties as a power functional graded has been considered. Adomian’s decomposition techniques have been applied to the governing equations. The numerical results have been calculated by using the iterations method with a certain algorithm. The numerical results have been represented in figures, and the figures affirm that Adomian’s decomposition method is a successful method for modeling thermoelastic problems. Moreover, the empirical parameter of the functional graded, and the lattice design parameter have significant effects on the temperature increment, the strain, the stress, the displacement.

Keywords: Adomian, decomposition method, generalized thermoelasticity, algorithm

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Authors: Khairil I. Othman, Mahfuzah Mahayaddin, Zarina Bibi Ibrahim

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We develop and demonstrate a computationally efficient numerical technique to solve first order stiff differential equations. This technique is based on block method whereby three approximate points are calculated. The Cholistani of varied step sizes are presented in divided difference form. Stability regions of the formulae are briefly discussed in this paper. Numerical results show that this block method perform very well compared to existing methods.

Keywords: block method, divided difference, stiff, computational

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Authors: H. Majour, L. Djabri

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Many methods in the groundwater vulnerability have been developed in the world (methods like PRAST, DRIST, APRON/ARAA, PRASTCHIM, GOD). In this study, our choice dealt with two recent complementary methods using category mapping of index with weighting criteria (Point County Systems Model MSCP) namely the standard DRASTIC method and SI (Susceptibility Index). At present, these two methods are the most used for the mapping of the intrinsic vulnerability of groundwater. Two classes of groundwater vulnerability in the Biskra sandy aquifer were identified by the DRASTIC method (average and high) and the SI method (very high and high). Integrated analysis has revealed that the high class is predominant for the DRASTIC method whereas for that of SI the preponderance is for the very high class. Furthermore, we notice that the method SI estimates better the vulnerability for the pollution in nitrates, with a rate of 85 % between the concentrations in nitrates of groundwater and the various established classes of vulnerability, against 75 % for the DRASTIC method. By including the land use parameter, the SI method produced more realistic results.

Keywords: DRASTIC, SI, GIS, Biskra sandy aquifer, Algeria

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Authors: Rubin Dan, Xingcai Wang, Ziyang Chen

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A chaotic time series noise reduction method based on the fusion of the local projection method, wavelet transform, and particle swarm algorithm (referred to as the LW-PSO method) is proposed to address the problem of false recognition due to noise in the recognition process of chaotic time series containing noise. The method first uses phase space reconstruction to recover the original dynamical system characteristics and removes the noise subspace by selecting the neighborhood radius; then it uses wavelet transform to remove D1-D3 high-frequency components to maximize the retention of signal information while least-squares optimization is performed by the particle swarm algorithm. The Lorenz system containing 30% Gaussian white noise is simulated and verified, and the phase space, SNR value, RMSE value, and K value of the 0-1 test method before and after noise reduction of the Schreiber method, local projection method, wavelet transform method, and LW-PSO method are compared and analyzed, which proves that the LW-PSO method has a better noise reduction effect compared with the other three common methods. The method is also applied to the classical system to evaluate the noise reduction effect of the four methods and the original system identification effect, which further verifies the superiority of the LW-PSO method. Finally, it is applied to the Chengdu rainfall chaotic sequence for research, and the results prove that the LW-PSO method can effectively reduce the noise and improve the chaos recognition rate.

Keywords: Schreiber noise reduction, wavelet transform, particle swarm optimization, 0-1 test method, chaotic sequence denoising

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Authors: Archit Yajnik, Rustam Ali

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In this paper, numerical method based on discrete GHM multiwavelets is presented for solving the Fredholm integral equations of second kind. There is hardly any article available in the literature in which the integral equations are numerically solved using discrete GHM multiwavelet. A number of examples are demonstrated to justify the applicability of the method. In GHM multiwavelets, the values of scaling and wavelet functions are calculated only at t = 0, 0.5 and 1. The numerical solution obtained by the present approach is compared with the traditional Quadrature method. It is observed that the present approach is more accurate and computationally efficient as compared to quadrature method.

Keywords: GHM multiwavelet, fredholm integral equations, quadrature method, function approximation

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