Search results for: finite difference method

Authors: Mostafa Jafarian Abyaneh, Khashayar Jafari, Vahab Toufigh

Abstract:

The cost of experiments on different types of concrete has raised the demand for prediction of their behavior with numerical analysis. In this research, an advanced numerical model has been presented to predict the complete elastic-plastic behavior of polymer concrete (PC), high-strength concrete (HSC), high performance concrete (HPC) along with different steel fiber contents under uniaxial compression. The accuracy of the numerical response was satisfactory as compared to other conventional simple models such as Mohr-Coulomb and Drucker-Prager. In order to predict the complete elastic-plastic behavior of specimens including softening behavior, disturbed state concept (DSC) was implemented by nonlinear finite element analysis (NFEA) and hierarchical single surface (HISS) failure criterion, which is a failure surface without any singularity.

Keywords: Disturbed state concept, hierarchical single surface, failure criterion, high performance concrete, high-strength concrete, nonlinear finite element analysis, polymer concrete, steel fibers, uniaxial compression test.

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Authors: Mogeeb A. El-Sheikh

Abstract:

The study has developed the previous design of an artificial anthropomorphic humanoid hand and accustomed it as a prosthetic hand. The main specifications of this design are determined. The development of our previous design involves the main artificial hand’s parts and subassemblies, palm, fingers, and thumb. In addition, the study presents an adaptable socket design for a transradial amputee. This hand has 3 fingers and thumb. It is more reliable, cosmetics, modularity, and ease of assembly. Its size and weight are almost as a natural hand. The socket cavity has the capability for different sizes of a transradial amputee. The study implements the developed design by using rapid prototype and specifies its main specifications by using a data glove and finite element method.

Keywords: Adaptable socket, prosthetic hand, transradial amputee.

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Authors: Wael I. Alnahhal

Abstract:

It is a major challenge to build a bridge superstructure that has long-term durability and low maintenance requirements. A solution to this challenge may be to use new materials or to implement new structural systems. Fiber Reinforced Polymer (FRP) composites have continued to play an important role in solving some of persistent problems in infrastructure applications because of its high specific strength, light weight, and durability. In this study, the concept of the hybrid FRP-concrete structural systems is applied to a bridge superstructure. The hybrid FRP-concrete bridge superstructure is intended to have durable, structurally sound, and cost effective hybrid system that will take full advantage of the inherent properties of both FRP materials and concrete. In this study, two hybrid FRP-concrete bridge systems were investigated. The first system consists of trapezoidal cell units forming a bridge superstructure. The second one is formed by arch cells. The two systems rely on using cellular components to form the core of the bridge superstructure, and an outer shell to warp around those cells to form the integral unit of the bridge. Both systems were investigated analytically by using finite element (FE) analysis. From the rigorous FE studies, it was concluded that first system is more efficient than the second.

Keywords: Bridge superstructure, hybrid system, fiber reinforced polymer, finite element analysis.

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Authors: Mark Kaahwa, Chang Zhu, Moses Muhumuza

Abstract:

This study investigates the satisfaction of distance education university students (DEUS) with the use of audio media as a medium of instruction. Studying students’ satisfaction is vital because it shows whether learners are comfortable with a certain instructional strategy or not. Although previous studies have investigated the use of audio media, the satisfaction of students with an instructional strategy that combines radio teaching and podcasts as an independent teaching strategy has not been fully investigated. In this study, all lectures were delivered through the radio and students had no direct contact with their instructors. No modules or any other material in form of text were given to the students. They instead, revised the taught content by listening to podcasts saved on their mobile electronic gadgets. Prior to data collection, DEUS received orientation through workshops on how to use audio media in distance education. To achieve objectives of the study, a survey, naturalistic observations and face-to-face interviews were used to collect data from a sample of 211 undergraduate and graduate students. Findings indicate that there was no statistically significant difference in the levels of satisfaction between male and female students. The results from post hoc analysis show that there is a statistically significant difference in the levels of satisfaction regarding the use of audio media between diploma and graduate students. Diploma students are more satisfied compared to their graduate counterparts. T-test results reveal that there was no statistically significant difference in the general satisfaction with audio media between rural and urban-based students. And ANOVA results indicate that there is no statistically significant difference in the levels of satisfaction with the use of audio media across age groups. Furthermore, results from observations and interviews reveal that DEUS found learning using audio media a pleasurable medium of instruction. This is an indication that audio media can be considered as an instructional strategy on its own merit.

Keywords: Audio media, distance education, distance education university students, medium of instruction, satisfaction.

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Authors: M. Saeki

Abstract:

This paper presents the results of an experimental study on the performance of a triboelectric separator of plastic mixtures used for recycling. The separator consists of four cylindrical electrodes. The principle behind the separation technique is based on the difference in the Coulomb force acting on the plastic particles after triboelectric charging. The separation of mixtures of acrylonitrile butadiene styrene (ABS) and polystyrene (PS) using this method was studied. The effects of the triboelectric charging time and applied voltage on the separation efficiency were investigated. The experimental results confirm that it is possible to obtain a high purity and recovery rate for the initial compositions considered in this study.

Keywords: Coulomb force, recycling, triboelectric separator, waste plastics.

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Authors: Nicolò Vaiana, Filip C. Filippou, Giorgio Serino

Abstract:

The solution of the nonlinear dynamic equilibrium equations of base-isolated structures adopting a conventional monolithic solution approach, i.e. an implicit single-step time integration method employed with an iteration procedure, and the use of existing nonlinear analytical models, such as differential equation models, to simulate the dynamic behavior of seismic isolators can require a significant computational effort. In order to reduce numerical computations, a partitioned solution method and a one dimensional nonlinear analytical model are presented in this paper. A partitioned solution approach can be easily applied to base-isolated structures in which the base isolation system is much more flexible than the superstructure. Thus, in this work, the explicit conditionally stable central difference method is used to evaluate the base isolation system nonlinear response and the implicit unconditionally stable Newmark’s constant average acceleration method is adopted to predict the superstructure linear response with the benefit in avoiding iterations in each time step of a nonlinear dynamic analysis. The proposed mathematical model is able to simulate the dynamic behavior of seismic isolators without requiring the solution of a nonlinear differential equation, as in the case of widely used differential equation model. The proposed mixed explicit-implicit time integration method and nonlinear exponential model are adopted to analyze a three dimensional seismically isolated structure with a lead rubber bearing system subjected to earthquake excitation. The numerical results show the good accuracy and the significant computational efficiency of the proposed solution approach and analytical model compared to the conventional solution method and mathematical model adopted in this work. Furthermore, the low stiffness value of the base isolation system with lead rubber bearings allows to have a critical time step considerably larger than the imposed ground acceleration time step, thus avoiding stability problems in the proposed mixed method.

Keywords: Base-isolated structures, earthquake engineering, mixed time integration, nonlinear exponential model.

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Authors: P. Karimi, A. H. Khedmati Bazkiaei

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The main goal of this study is to test differential neural network as a controller of smart structure and is to enumerate its advantages and disadvantages in comparison with other controllers. In this study, the smart structure has been considered as a Euler Bernoulli cantilever beam and it has been tried that it be under control with the use of vibration neural network resulting from movement. Also, a linear observer has been considered as a reference controller and has been compared its results. The considered vibration charts and the controlled state have been recounted in the final part of this text. The obtained result show that neural observer has better performance in comparison to the implemented linear observer.

Keywords: Smart material, on-line differential artificial neural network, active control, finite element method.

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Authors: G.Hariharan, K.Kannan

Abstract:

In this paper, we develop an accurate and efficient Haar wavelet method for well-known FitzHugh-Nagumo equation. The proposed scheme can be used to a wide class of nonlinear reaction-diffusion equations. The power of this manageable method is confirmed. Moreover the use of Haar wavelets is found to be accurate, simple, fast, flexible, convenient, small computation costs and computationally attractive.

Keywords: FitzHugh-Nagumo equation, Haar wavelet method, adomain decomposition method, computationally attractive.

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Authors: H. Ozbasaran

Abstract:

IPN and IPE sections, which are commonly used European I shapes, are widely used in steel structures as cantilever beams to support overhangs. A considerable number of studies exist on calculating lateral torsional buckling load of I sections. However, most of them provide series solutions or complex closed-form equations. In this paper, a simple equation is presented to calculate lateral torsional buckling load of IPN and IPE section cantilever beams. First, differential equation of lateral torsional buckling is solved numerically for various loading cases. Then a parametric study is conducted on results to present an equation for lateral torsional buckling load of European IPN and IPE beams. Finally, results obtained by presented equation are compared to differential equation solutions and finite element model results. ABAQUS software is utilized to generate finite element models of beams. It is seen that the results obtained from presented equation coincide with differential equation solutions and ABAQUS software results. It can be suggested that presented formula can be safely used to calculate critical lateral torsional buckling load of European IPN and IPE section cantilevers.

Keywords: Cantilever, IPN, IPE, lateral torsional buckling

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Authors: Indunil Jayatilake, Warna Karunasena

Abstract:

Fiber Reinforced Polymer (FRP) composites enjoy an array of applications ranging from aerospace, marine and military to automobile, recreational and civil industry due to their outstanding properties. A structural glass fiber reinforced polymer (GFRP) composite sandwich panel made from E-glass fiber skin and a modified phenolic core has been manufactured in Australia for civil engineering applications. One of the major mechanisms of damage in FRP composites is skin-core debonding. The presence of debonding is of great concern not only because it severely affects the strength but also it modifies the dynamic characteristics of the structure, including natural frequency and vibration modes. This paper deals with the investigation of the dynamic characteristics of a GFRP beam with single and multiple debonding by finite element based numerical simulations and analyses using the STRAND7 finite element (FE) software package. Three-dimensional computer models have been developed and numerical simulations were done to assess the dynamic behavior. The FE model developed has been validated with published experimental, analytical and numerical results for fully bonded as well as debonded beams. A comparative analysis is carried out based on a comprehensive parametric investigation. It is observed that the reduction in natural frequency is more affected by single debonding than the equally sized multiple debonding regions located symmetrically to the single debonding position. Thus it is revealed that a large single debonding area leads to more damage in terms of natural frequency reduction than isolated small debonding zones of equivalent area, appearing in the GFRP beam. Furthermore, the extents of natural frequency shifts seem mode-dependent and do not seem to have a monotonous trend of increasing with the mode numbers.

Keywords: Debonding, dynamic response, finite element modelling, FRP beams.

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Authors: Ali Raad Hassan

Abstract:

In this paper, an (irregular) case relating to base circle, root circle, and pressure angle has been discussed and a computer programme has been developed to simulate and plot spur gear tooth profile, including involute and trochoid curves based on the formulation of rack cutter using different values of pressure angle and profile shift factor and it gave the values of all important geometric parameters. The results showed the flexibility of this approach and versatility of the programme to draw many different cases of spur gear teeth of any module, pressure angle, profile shift factor, number of teeth and rack cutter tip radius. The procedure developed can be extended to produce finite element models of heretofore intractable geometrical forms, to exploring fabrication of nonstandard tooth forms also. Finite elements model of these irregular cases have been built using above programme, and modal analysis has been done using ANSYS software, and natural frequencies of these selected cases have been obtained and discussed.

Keywords: involute, trochoid, pressure angle, profile shift factor, natural frequency

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Authors: John N. Ellinas

Abstract:

In this paper, a new reversible watermarking method is presented that reduces the size of a stereoscopic image sequence while keeping its content visible. The proposed technique embeds the residuals of the right frames to the corresponding frames of the left sequence, halving the total capacity. The residual frames may result in after a disparity compensated procedure between the two video streams or by a joint motion and disparity compensation. The residuals are usually lossy compressed before embedding because of the limited embedding capacity of the left frames. The watermarked frames are visible at a high quality and at any instant the stereoscopic video may be recovered by an inverse process. In fact, the left frames may be exactly recovered whereas the right ones are slightly distorted as the residuals are not embedded intact. The employed embedding method reorders the left frame into an array of consecutive pixel pairs and embeds a number of bits according to their intensity difference. In this way, it hides a number of bits in intensity smooth areas and most of the data in textured areas where resulting distortions are less visible. The experimental evaluation demonstrates that the proposed scheme is quite effective.

Keywords: Stereoscopic video, Reversible watermarking, Disparity compensation, Joint compensation

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Authors: Neslihan Genckal, Reha Gursoy, Vedat Z. Dogan

Abstract:

In this study, dynamic responses of composite plates on elastic foundations subjected to impact and moving loads are investigated. The first order shear deformation (FSDT) theory is used for moderately thick plates. Pasternak-type (two-parameter) elastic foundation is assumed. Elastic foundation effects are integrated into the governing equations. It is assumed that plate is first hit by a mass as an impact type loading then the mass continues to move on the composite plate as a distributed moving loading, which resembles the aircraft landing on airport pavements. Impact and moving loadings are modeled by a mass-spring-damper system with a wheel. The wheel is assumed to be continuously in contact with the plate after impact. The governing partial differential equations of motion for displacements are converted into the ordinary differential equations in the time domain by using Galerkin’s method. Then, these sets of equations are solved by using the Runge-Kutta method. Several parameters such as vertical and horizontal velocities of the aircraft, volume fractions of the steel rebar in the reinforced concrete layer, and the different touchdown locations of the aircraft tire on the runway are considered in the numerical simulation. The results are compared with those of the ABAQUS, which is a commercial finite element code.

Keywords: Elastic foundation, impact, moving load, thick plate.

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Authors: Chang, Chun-Lang, Liu, Chun-Kai

Abstract:

This study, for its research subjects, uses patients who had undergone total knee replacement surgery from the database of the National Health Insurance Administration. Through the review of literatures and the interviews with physicians, important factors are selected after careful screening. Then using Cross Entropy Method, Genetic Algorithm Logistic Regression, and Particle Swarm Optimization, the weight of each factor is calculated and obtained. In the meantime, Excel VBA and Case Based Reasoning are combined and adopted to evaluate the system. Results show no significant difference found through Genetic Algorithm Logistic Regression and Particle Swarm Optimization with over 97% accuracy in both methods. Both ROC areas are above 0.87. This study can provide critical reference to medical personnel as clinical assessment to effectively enhance medical care quality and efficiency, prevent unnecessary waste, and provide practical advantages to resource allocation to medical institutes.

Keywords: Total knee replacement, Case Based Reasoning, Cross Entropy Method, Genetic Algorithm Logistic Regression, Particle Swarm Optimization.

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Authors: Ali Raad Hassan

Abstract:

Natural frequencies and dynamic response of a spur gear sector are investigated using a two dimensional finite element model that offers significant advantages for dynamic gear analyses. The gear teeth are analyzed for different operating speeds. A primary feature of this modeling is determination of mesh forces using a detailed contact analysis for each time step as the gears roll through the mesh. ANSYS software has been used on the proposed model to find the natural frequencies by Block Lanczos technique and displacements and dynamic stresses by transient mode super position method. The effect of rotational speed of the gear on the dynamic response of gear tooth has been studied and design limits have been discussed.

Keywords: Spur gear, Natural frequency, transient analysis, Mode super position technique.

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Authors: Dhiraj Dolai, Rupayan Bhattacharya

Abstract:

In this study, a comparison of Range Of Motion (ROM) of middle and long-distance runners and swimmers has been made. The mobility of the various joints is essential for the quick movement of any sportsman. Knowledge of a ROM helps in preventing injuries, in repeating the movement, and in generating speed and power. ROM varies among individuals, and it is influenced by factors such as gender, age, and whether the motion is performed actively or passively. ROM for running and swimming, both performed with due consideration on speed, plays an important role. The time of generation of speed and mobility of the particular joints are very important for both kinds of athletes. The difficulties that happen during running and swimming in the direction of motion is changed. In this study, data were collected for a total of 102 subjects divided into three groups: control group (22), middle and long-distance runners (40), and swimmers (40), and their ages are between 12 to 18 years. The swimmers have higher ROM in shoulder joint flexion, extension, abduction, and adduction movement. Middle and long-distance runners have significantly greater ROM from Control Group in the left shoulder joint flexion with a 5.82 mean difference. Swimmers have significantly higher ROM from the Control Group in the left shoulder joint flexion with 24.84 mean difference and swimmers have significantly higher ROM from the Middle and Long distance runners in left shoulder flexion with 19.02 mean difference. The picture will be clear after a more detailed investigation.

Keywords: Range of motion, runners, swimmers, significance.

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Authors: L. Fridrichova, R. Knížek, V. Bajzík

Abstract:

Drape is one of the important visual characteristics of the fabric. This paper is introducing an innovative method of measurement and evaluation of the drape shape of the fabric. The measuring principle is based on the possibility of multiple vertical strain of the fabric. This method more accurately simulates the real behavior of the fabric in the process of draping. The method is fully automated, so the sample can be measured by using any number of cycles in any time horizon. Using the present method of measurement, we are able to describe the viscoelastic behavior of the fabric.

Keywords: Drape, drape shape, automated drape meter.

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Authors: Atul K. Desai, Hemal J. Shah

Abstract:

The tall windmill towers are designed as monopole tower or lattice tower. In the present research, a 125-meter high hybrid tower which is a combination of lattice and monopole type is proposed. The response of hybrid tower is compared with conventional monopole tower. The towers were analyzed in finite element method software considering nonlinear seismic time history load. The synthetic seismic time history for different soil is derived using the SeismoARTIF software. From the present research, it is concluded that, in the hybrid tower, we are not getting resonance condition. The base shear is less in hybrid tower compared to monopole tower for different soil conditions.

Keywords: Dynamic analysis, hybrid wind mill tower, resonance condition, synthetic time history.

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Authors: Liudmyla Koliechkina, Olena Dvirna

Abstract:

The statement of the multi-objective optimization problem on combinatorial configurations is formulated, and the approach to its solution is proposed. The problem is of interest as a combinatorial optimization one with many criteria, which is a model of many applied tasks. The approach to solving the multi-objective optimization problem on combinatorial configurations consists of two stages; the first is the reduction of the multi-objective problem to the single criterion based on existing multi-objective optimization methods, the second stage solves the directly replaced single criterion combinatorial optimization problem by the horizontal combinatorial method. This approach provides the optimal solution to the multi-objective optimization problem on combinatorial configurations, taking into account additional restrictions for a finite number of steps.

Keywords: Discrete set, linear combinatorial optimization, multi-objective optimization, multipermutation, Pareto solutions, partial permutation set, permutation, structural graph.

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Authors: Mohammed Salem Alzahrani

Abstract:

In this paper, student admission process is studied to optimize the assignment of vacant seats with three main objectives. Utilizing all vacant seats, satisfying all programs of study admission requirements and maintaining fairness among all candidates are the three main objectives of the optimization model. Seat Assignment Method (SAM) is used to build the model and solve the optimization problem with help of Northwest Coroner Method and Least Cost Method. A closed formula is derived for applying the priority of assigning seat to candidate based on SAM.

Keywords: Admission Process Model, Assignment Problem, Hungarian Method, Least Cost Method, Northwest Corner Method, Seat Assignment Method (SAM).

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Authors: M. Ali, K. Alam, E. Ohioma

Abstract:

This paper presents a numerical investigation on the behavior of fiber reinforced polymer composite tubes (FRP) under thermomechanical coupled loading using finite element software ABAQUS and a special add-on subroutine, CZone. Three cases were explored; pure mechanical loading, pure thermal loading, and coupled thermomechanical loading. The failure index (Tsai-Wu) under all three loading cases was assessed for all plies in the tube walls. The simulation results under pure mechanical loading showed that composite tube failed at a tensile load of 3.1 kN. However, with the superposition of thermal load on mechanical load on the composite tube, the failure index of the previously failed plies in tube walls reduced significantly causing the tube to fail at 6 kN. This showed 93% improvement in the load carrying capacity of the composite tube in present study. The increase in load carrying capacity was attributed to the stress effects of the coefficients of thermal expansion (CTE) on the laminate as well as the inter-lamina stresses induced due to the composite stack layup.

Keywords: Thermal, mechanical, composites, square tubes.

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Authors: Belkacem Brahmi, Mohand Ouamer Bibi

Abstract:

In this paper, we present a new method for solving quadratic programming problems, not strictly convex. Constraints of the problem are linear equalities and inequalities, with bounded variables. The suggested method combines the active-set strategies and support methods. The algorithm of the method and numerical experiments are presented, while comparing our approach with the active set method on randomly generated problems.

Keywords: Convex quadratic programming, dual support methods, active set methods.

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Authors: H. Katkhuda

Abstract:

A time domain approach is used in this paper to identify unknown dynamic forces applied on two dimensional frames using the measured dynamic structural responses for a sub-structure in the two dimensional frame. In this paper a sub-structure finite element model with short length of measurement from only three or four accelerometers is required, and an iterative least-square algorithm is used to identify the unknown dynamic force applied on the structure. Validity of the method is demonstrated with numerical examples using noise-free and noise-contaminated structural responses. Both harmonic and impulsive forces are studied. The results show that the proposed approach can identify unknown dynamic forces within very limited iterations with high accuracy and shows its robustness even noise- polluted dynamic response measurements are utilized.

Keywords: Dynamic Force Identification, Dynamic Responses, Sub-structure and Time Domain.

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Authors: N. Senu, I. A. Kasim, F. Ismail, N. Bachok

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In this paper zero-dissipative explicit Runge-Kutta method is derived for solving second-order ordinary differential equations with periodical solutions. The phase-lag and dissipation properties for Runge-Kutta (RK) method are also discussed. The new method has algebraic order three with dissipation of order infinity. The numerical results for the new method are compared with existing method when solving the second-order differential equations with periodic solutions using constant step size.

Keywords: Dissipation, Oscillatory solutions, Phase-lag, Runge- Kutta methods.

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Authors: Sarra Ben Hariz, Zied Elouedi, Khaled Mellouli

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The belief K-modes method (BKM) approach is a new clustering technique handling uncertainty in the attribute values of objects in both the cluster construction task and the classification one. Like the standard version of this method, the BKM results depend on the chosen initial modes. So, one selection method of initial modes is developed, in this paper, aiming at improving the performances of the BKM approach. Experiments with several sets of real data show that by considered the developed selection initial modes method, the clustering algorithm produces more accurate results.

Keywords: Clustering, Uncertainty, Belief function theory, Belief K-modes Method, Initial modes selection.

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Authors: Sara Barati, Karim Ivaz

Abstract:

In this paper, using a model transformation approach a system of linear delay differential equations (DDEs) with multiple delays is converted to a non-delayed initial value problem. The variational iteration method (VIM) is then applied to obtain the approximate analytical solutions. Numerical results are given for several examples involving scalar and second order systems. Comparisons with the classical fourth-order Runge-Kutta method (RK4) verify that this method is very effective and convenient.

Keywords: Variational iteration method, delay differential equations, multiple delays, Runge-Kutta method.

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Authors: Ammar Anwar Khan, Nissar R. Wani, Nazar Malik, Abdulrehman Al-Arainy, and Saad Alghuwainem

Abstract:

Power cables are vulnerable to failure due to aging or defects that occur with the passage of time under continuous operation and loading stresses. PD detection and characterization provide information on the location, nature, form and extent of the degradation. As a result, PD monitoring has become an important part of condition based maintenance (CBM) program among power utilities. Online partial discharge (PD) localization of defect sources in power cable system is possible using the time of flight method. The information regarding the time difference between the main and reflected pulses and cable length can help in locating the partial discharge source along the cable length. However, if the length of the cable is not known and the defect source is located at the extreme ends of the cable or in the middle of the cable, then double ended measurement is required to indicate the location of PD source. Use of multiple sensors can also help in discriminating the cable PD or local/ external PD. This paper presents the experience and results from online partial discharge measurements conducted in the laboratory and the challenges in partial discharge source localization.

Keywords: Power cables, partial discharge localization, HFCT, condition based monitoring.

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Authors: M. Saravi, F. Ashrafi, S.R. Mirrajei

Abstract:

As we know, most differential equations concerning physical phenomenon could not be solved by analytical method. Even if we use Series Method, some times we need an appropriate change of variable, and even when we can, their closed form solution may be so complicated that using it to obtain an image or to examine the structure of the system is impossible. For example, if we consider Schrodinger equation, i.e., We come to a three-term recursion relations, which work with it takes, at least, a little bit time to get a series solution[6]. For this reason we use a change of variable such as or when we consider the orbital angular momentum[1], it will be necessary to solve. As we can observe, working with this equation is tedious. In this paper, after introducing Clenshaw method, which is a kind of Spectral method, we try to solve some of such equations.

Keywords: Chebyshev polynomials, Clenshaw method, ODEs, Spectral methods

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Authors: A.Memari

Abstract:

In this article, a simulation method called the Homotopy Perturbation Method (HPM) is employed in the steady flow of a Walter's B' fluid in a vertical channel with porous wall. We employed Homotopy Perturbation Method to derive solution of a nonlinear form of equation obtained from exerting similarity transforming to the ordinary differential equation gained from continuity and momentum equations of this kind of flow. The results obtained from the Homotopy Perturbation Method are then compared with those from the Runge–Kutta method in order to verify the accuracy of the proposed method. The results show that the Homotopy Perturbation Method can achieve good results in predicting the solution of such problems. Ultimately we use this solution to obtain the other terms of velocities and physical discussion about it.

Keywords: Steady flow; Walter's B' Fluid;, vertical channel;porous media, Homotopy Perturbation Method (HPM), Numerical Solution (NS).

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Authors: Vladimir Korovkin, Albert Park, Evgeny Kaganer

Abstract:

Digital divide, the gap in the access to the world of digital technologies and the socio-economic opportunities that they create is an important phenomenon of the XXI century. This gap may exist between countries, regions within a country or socio-demographic groups, creating the classes of “digital have and have nots”. While the 1st-level divide (the difference in opportunities to access the digital networks) was demonstrated to diminish with time, the issues of 2nd level divide (the difference in skills and usage of digital systems) and 3rd level divide (the difference in effects obtained from digital technology) may grow. The paper offers a systemic review of literature on the measurement of the digital divide, noting the certain conceptual stagnation due to the lack of effective instruments that would capture the complex nature of the phenomenon. As a result, many important concepts do not receive the empiric exploration they deserve. As a solution the paper suggests a composite Digital Life Index, that studies separately the digital supply and demand across seven independent dimensions providing for 14 subindices. The Index is based on Internet-borne data, a distinction from traditional research approaches that rely on official statistics or surveys. The application of the model to the study of the digital divide between Russian regions and between cities in China have brought promising results. The paper advances the existing methodological literature on the 2nd level digital divide and can also inform practical decision-making regarding the strategies of national and regional digital development.

Keywords: Digital transformation, second-level digital divide, composite index, digital policy.

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