Search results for: dynamic equations

Authors: Leili Nosrati, Alireza Nemaney Pour

Abstract:

Although e-mail is the most efficient and popular communication method, unwanted and mass unsolicited e-mails, also called spam mail, endanger the existence of the mail system. This paper proposes a new algorithm called Dynamic Weighted Majority Concept Drift Detection (DWM-CDD) for content-based filtering. The design purposes of DWM-CDD are first to accurate the performance of the previously proposed algorithms, and second to speed up the time to construct the model. The results show that DWM-CDD can detect both sudden and gradual changes quickly and accurately. Moreover, the time needed for model construction is less than previously proposed algorithms.

Keywords: Concept drift, Content-based filtering, E-mail, Spammail.

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Authors: R. Haoui

Abstract:

The purpose of this work is to simulate the flow at the exit of Vulcan 1 engine of European launcher Ariane 5. The geometry of the propellant nozzle is already determined using the characteristics method. The pressure in the outlet section of the nozzle is less than atmospheric pressure on the ground, causing the existence of oblique and normal shock waves at the exit. During the rise of the launcher, the atmospheric pressure decreases and the shock wave disappears. The code allows the capture of shock wave at exit of nozzle. The numerical technique uses the Flux Vector Splitting method of Van Leer to ensure convergence and avoid the calculation instabilities. The Courant, Friedrichs and Lewy coefficient (CFL) and mesh size level are selected to ensure the numerical convergence. The nonlinear partial derivative equations system which governs this flow is solved by an explicit unsteady numerical scheme by the finite volume method. The accuracy of the solution depends on the size of the mesh and also the step of time used in the discretized equations. We have chosen in this study the mesh that gives us a stationary solution with good accuracy.

Keywords: Launchers, supersonic flow, finite volume, nozzles, shock wave.

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Authors: O. Rahli, N. Mimouni, R. Bennacer, K. Bouhadef

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This numerical study investigates the travelling wave’s appearance and the behavior of Poiseuille-Rayleigh-Benard (PRB) flow induced in 3D thermosolutale mixed convection (TSMC) in horizontal rectangular channels. The governing equations are discretized by using a control volume method with third order Quick scheme in approximating the advection terms. Simpler algorithm is used to handle coupling between the momentum and continuity equations. To avoid the excessively high computer time, full approximation storage (FAS) with full multigrid (FMG) method is used to solve the problem. For a broad range of dimensionless controlling parameters, the contribution of this work is to analyzing the flow regimes of the steady longitudinal thermoconvective rolls (noted R//) for both thermal and mass transfer (TSMC). The transition from the opposed volume forces to cooperating ones, considerably affects the birth and the development of the longitudinal rolls. The heat and mass transfers distribution are also examined.

Keywords: Heat and mass transfer, mixed convection, Poiseuille-Rayleigh-Benard flow, rectangular duct.

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Authors: D.K. Rao, M.G.M. Khan, K.G. Reddy

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The focus of this paper is to develop a technique of solving a combined problem of determining Optimum Strata Boundaries(OSB) and Optimum Sample Size (OSS) of each stratum, when the population understudy isskewed and the study variable has a Pareto frequency distribution. The problem of determining the OSB isformulated as a Mathematical Programming Problem (MPP) which is then solved by dynamic programming technique. A numerical example is presented to illustrate the computational details of the proposed method. The proposed technique is useful to obtain OSB and OSS for a Pareto type skewed population, which minimizes the variance of the estimate of population mean.

Keywords: Stratified sampling, Optimum strata boundaries, Optimum sample size, Pareto distribution, Mathematical programming problem, Dynamic programming technique.

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Authors: Ho Yuan-Hong, Hunag Chiung-Ju

Abstract:

This study conducts simulation analyses to find the optimal debt ceiling of Taiwan, while factoring in welfare maximization under a dynamic stochastic general equilibrium framework. The simulation is based on Taiwan's 2001 to 2011 economic data and shows that welfare is maximized at a debt/GDP ratio of 0.2, increases in the debt/GDP ratio leads to increases in both tax and interest rates and decreases in the consumption ratio and working hours. The study results indicate that the optimal debt ceiling of Taiwan is 20% of GDP, where if the debt/GDP ratio is greater than 40%, the welfare will be negative and result in welfare loss.

Keywords: Debt sustainability, optimal debt ceiling, dynamic stochastic general equilibrium, welfare maximization.

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Authors: Mouna Hamed, Ammar B. Brahim

Abstract:

The objective of this work was to develop a theoretical model to study the dynamic thermal behavior of a flat plate solar collector integrated with a phase change material (PCM). The PCM acted as a heat source for the solar system during low intensity solar radiation and night. The energy balance equations for the various components of the collector as well as for the PCM were formulated and numerically solved using Matlab computational program. The effect of natural convection on heat during the melting process was taken into account by using an effective thermal conductivity. The model was used to investigate the effect of inlet water temperature, water mass flow rate, and PCM thickness on the outlet water temperature and the melt fraction during charging and discharging modes. A comparison with a collector without PCM was made. Results showed that charging and discharging processes of PCM have six stages. The adding of PCM caused a decrease in temperature during charge and an increase during discharge. The rise was most enhanced for higher inlet water temperature, PCM thickness and for lower mass flow rate. Analysis indicated that the complete melting time was shorter than the solidification time due to the high heat transfer coefficient during melting. The increases in PCM height and mass flow rate were not linear with the melting and solidification times.

Keywords: Thermal energy storage, phase change material, melting, solidification.

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Authors: Mouna Hamed, Ammar B. Brahim

Abstract:

The objective of this work was to develop a theoretical model to study the dynamic thermal behavior of a flat plate solar collector integrated with a phase change material (PCM). The PCM acted as a heat source for the solar system during low intensity solar radiation and night. The energy balance equations for the various components of the collector as well as for the PCM were formulated and numerically solved using MATLAB computational program. The effect of natural convection on heat during the melting process was taken into account by using an effective thermal conductivity. The model was used to investigate the effect of inlet water temperature, water mass flow rate, and PCM thickness on the outlet water temperature and the melt fraction during charging and discharging modes. A comparison with a collector without PCM was made. Results showed that charging and discharging processes of PCM have six stages. The adding of PCM caused a decrease in temperature during charge and an increase during discharge. The rise was most enhanced for higher inlet water temperature, PCM thickness and for lower mass flow rate. Analysis indicated that the complete melting time was shorter than the solidification time due to the high heat transfer coefficient during melting. The increases in PCM height and mass flow rate were not linear with the melting and solidification times.

Keywords: Thermal energy storage, phase change material, melting, solidification.

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Authors: Patrick Maier, Marcus Tönnis, Gudrun Klinker

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Spatial understanding and the understanding of dynamic change in the spatial structure of molecules during a reaction is essential for designing new molecules. Knowing the physical processes in the reactions helps to speed up the designing process. To support the designer with the correct representation of the designed molecule as well as showing the dynamic behavior of the whole reacting system is the goal of our application. Our system shows the spatial deformation of the molecules at every time interval by minimizing the energy level of the molecules. The position and orientation of the molecules can be intuitively controlled by manipulating objects of the real world using Augmented Reality techniques. Our approach has the potential to speed up the design of new molecules and help students to understand the chemical processes better.

Keywords: Augmented Augmented Chemical Reactions, Augmented Reality, chemistry, education.

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Authors: Worachat Wannawong, Usa W. Humphries, Prungchan Wongwises, Suphat Vongvisessomjai, Wiriya Lueangaram

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A numerical analysis of wave and hydrodynamic models is used to investigate the influence of WAve and Storm Surge (WASS) in the regional and coastal zones. The numerical analyzed system consists of the WAve Model Cycle 4 (WAMC4) and the Princeton Ocean Model (POM) which used to solve the energy balance and primitive equations respectively. The results of both models presented the incorporated surface wave in the regional zone affected the coastal storm surge zone. Specifically, the results indicated that the WASS generally under the approximation is not only the peak surge but also the coastal water level drop which can also cause substantial impact on the coastal environment. The wave–induced surface stress affected the storm surge can significantly improve storm surge prediction. Finally, the calibration of wave module according to the minimum error of the significant wave height (Hs) is not necessarily result in the optimum wave module in the WASS analyzed system for the WASS prediction.

Keywords: energy balance equation, numerical analysis, primitiveequation, storm surge, wave.

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Authors: M. Bobojanov, D. Rismukhamedov, F. Tuychiev, Kh. Shamsutdinov

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The article presents the results of experimental study of a two-speed asynchronous motor 4A80B6/4U3 with pole-changing winding on a fan drive VSUN 160x74-0.55-4 in static and dynamic modes. A prototype of a pole-changing Motor was made based on the results of the calculation and the performance and mechanical characteristics of the Motor were removed at the experimental stand, and useful capacities and other parameters from both poles were determined. In dynamic mode, the curves of changes of torque and current of the stator were removed by direct start, constant speed operation, by switching of speeds and stopping.

Keywords: Pole-changing winding, two speed asynchronous machine, basic scheme, winding factor, differential leakage factor.

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Authors: Bandaris Shankar, Yohannes Yirga

Abstract:

In this paper, the problem of heat and mass transfer in unsteady MHD boundary-layer flow of nanofluids over stretching sheet with a non uniform heat source/sink is considered. The unsteadiness in the flow and temperature is caused by the time-dependent stretching velocity and surface temperature. The unsteady boundary layer equations are transformed to a system of non-linear ordinary differential equations and solved numerically using Keller box method. The velocity, temperature, and concentration profiles were obtained and utilized to compute the skin-friction coefficient, local Nusselt number, and local Sherwood number for different values of the governing parameters viz. solid volume fraction parameter, unsteadiness parameter, magnetic field parameter, Schmidt number, space-dependent and temperature-dependent parameters for heat source/sink. A comparison of the numerical results of the present study with previously published data revealed an excellent agreement.

Keywords: Manetohydrodynamics, nanofluid, non-uniform heat source/sink, unsteady.

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Authors: Mostafa.A. Fellani, Daw .E. Abaid

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This paper deals with stability analysis for synchronous reluctance motors drive. Special attention is paid to the transient performance with variations in motor's parameters such as Ld and Rs. A study of the dynamic control using d-q model is presented first in order to clarify the stability of the motor drive system. Based on the experimental parameters of the synchronous reluctance motor, this paper gives some simulation results using MATLAB/SIMULINK software packages. It is concluded that the motor parameters, especially Ld, affect the estimator stability and hence the whole drive system.

Keywords: Dynamic Simulation, MATLAB, PWM-inverter, Reluctance Machine, Sensorless Control

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Authors: Qian Liu, Steve Furber

Abstract:

To explore how the brain may recognise objects in its general,accurate and energy-efficient manner, this paper proposes the use of a neuromorphic hardware system formed from a Dynamic Video Sensor (DVS) silicon retina in concert with the SpiNNaker real-time Spiking Neural Network (SNN) simulator. As a first step in the exploration on this platform a recognition system for dynamic hand postures is developed, enabling the study of the methods used in the visual pathways of the brain. Inspired by the behaviours of the primary visual cortex, Convolutional Neural Networks (CNNs) are modelled using both linear perceptrons and spiking Leaky Integrate-and-Fire (LIF) neurons. In this study’s largest configuration using these approaches, a network of 74,210 neurons and 15,216,512 synapses is created and operated in real-time using 290 SpiNNaker processor cores in parallel and with 93.0% accuracy. A smaller network using only 1/10th of the resources is also created, again operating in real-time, and it is able to recognise the postures with an accuracy of around 86.4% - only 6.6% lower than the much larger system. The recognition rate of the smaller network developed on this neuromorphic system is sufficient for a successful hand posture recognition system, and demonstrates a much improved cost to performance trade-off in its approach.

Keywords: Spiking neural network (SNN), convolutional neural network (CNN), posture recognition, neuromorphic system.

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Authors: Hisashi Kojima, Masatora Daito

Abstract:

We investigate an asymmetric connections model with a dynamic network formation process, using an agent based simulation. We permit heterogeneity of agents- value. Valuable persons seem to have many links on real social networks. We focus on this point of view, and examine whether valuable agents change the structures of the terminal networks. Simulation reveals that valuable agents diversify the terminal networks. We can not find evidence that valuable agents increase the possibility that star networks survive the dynamic process. We find that valuable agents disperse the degrees of agents in each terminal network on an average.

Keywords: network formation, agent based simulation, connections model.

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Authors: A. M. Wahab, E. Rustighi

Abstract:

Elastomeric dielectric material has recently become a new alternative for actuator technology. The characteristics of dielectric elastomers placed between two electrodes to withstand large strain when electrodes are charged has attracted the attention of many researcher to study this material for actuator technology. Thus, in the past few years Danfoss Ventures A/S has established their own dielectric electro-active polymer (DEAP), which was called PolyPower. The main objective of this work was to investigate the dynamic characteristics for vibration control of a PolyPower actuator folded in ‘pull’ configuration. A range of experiments was carried out on the folded actuator including passive (without electrical load) and active (with electrical load) testing. For both categories static and dynamic testing have been done to determine the behavior of folded DEAP actuator. Voltage-Strain experiments show that the DEAP folded actuator is a non-linear system. It is also shown that the voltage supplied has no effect on the natural frequency. Finally, varying AC voltage with different amplitude and frequency shows the parameters that influence the performance of DEAP folded actuator. As a result, the actuator performance dominated by the frequency dependence of the elastic response and was less influenced by dielectric properties.

Keywords: Dielectric Electro-active Polymer, Pull Actuator, Static, Dynamic, Electromechanical.

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Authors: Li Zong-Cheng

Abstract:

It is by reason of the unified measure of varieties of resources and the unified processing of the disposal of varieties of resources, that these closely related three of new basic models called the resources assembled node and the disposition integrated node as well as the intelligent organizing node are put forth in this paper; the three closely related quantities of integrative analytical mechanics including the disposal intensity and disposal- weighted intensity as well as the charge of resource charge are set; and then the resources assembled space and the disposition integrated space as well as the intelligent organizing space are put forth. The system of fundamental equations and model of complete factor synergetics is preliminarily approached for the general situation in this paper, to form the analytical base of complete factor synergetics. By the essential variables constituting this system of equations we should set twenty variables respectively with relation to the essential dynamical effect, external synergetic action and internal synergetic action of the system.

Keywords: complex system, disposal of resources, completefactor synergetics, fundamental equation.

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Authors: Nina Øystad-Larsen, Miran Cemalovic, Amir M. Kaynia

Abstract:

The nonlinear static and dynamic analysis procedures presented in EN 1998-1 for the structural response of a RC wall-frame building are assessed. The structure is designed according to the guidelines for high ductility (DCH) in 1998-1. The finite element packages SeismoStruct and OpenSees are utilized and evaluated. The structural response remains nearly in the elastic range even though the building was designed for high ductility. The overstrength is a result of oversized and heavily reinforced members, with emphasis on the lower storey walls. Nonlinear response history analysis in the software packages give virtually identical results for displacements.

Keywords: Behaviour factor, Dual system, OpenSEES, Overstrength, SeismoStruct.

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Authors: M. M. Rahman

Abstract:

The present contribution deals with the thermophoretic deposition of nanoparticles over a rapidly rotating permeable disk in the presence of partial slip, magnetic field, thermal radiation, thermal-diffusion, and diffusion-thermo effects. The governing nonlinear partial differential equations such as continuity, momentum, energy and concentration are transformed into nonlinear ordinary differential equations using similarity analysis, and the solutions are obtained through the very efficient computer algebra software MATLAB. Graphical results for non-dimensional concentration and temperature profiles including thermophoretic deposition velocity and Stanton number (thermophoretic deposition flux) in tabular forms are presented for a range of values of the parameters characterizing the flow field. It is observed that slip mechanism, thermal-diffusion, diffusion-thermo, magnetic field and radiation significantly control the thermophoretic particles deposition rate. The obtained results may be useful to many industrial and engineering applications.

Keywords: Boundary layer flows, convection, diffusion-thermo, rotating disk, thermal-diffusion, thermophoresis.

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Authors: Oladeinde Mobolaji Humphrey, Akpobi John

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A mathematical model for the hydrodynamic lubrication of parabolic slider bearings with couple stress lubricants is presented. A numerical solution for the mathematical model using finite element scheme is obtained using three nodes isoparametric quadratic elements. Stiffness integrals obtained from the weak form of the governing equations were solved using Gauss Quadrature to obtain a finite number of stiffness matrices. The global system of equations was obtained for the bearing and solved using Gauss Seidel iterative scheme. The converged pressure solution was used to obtain the load capacity of the bearing. Parametric studies were carried out and it was shown that the effect of couple stresses and profile parameter are to increase the load carrying capacity of the parabolic slider bearing. Numerical experiments reveal that the magnitude of the profile parameter at which maximum load is obtained increases with decrease in couple stress parameter. The results are presented in graphical form.

Keywords: Finite element, numerical, parabolic slider.

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Authors: M. Wasy Akhtar

Abstract:

Multi-modal film boiling simulations are carried out on adaptive octree grids. The liquid-vapor interface is captured using the volume-of-fluid framework adjusted to account for exchanges of mass, momentum, and energy across the interface. Surface tension effects are included using a volumetric source term in the momentum equations. The phase change calculations are conducted based on the exact location and orientation of the interface; however, the source terms are calculated using the mixture variables to be consistent with the one field formulation used to represent the entire fluid domain. The numerical model on octree representation of the computational grid is first verified using test cases including advection tests in severely deforming velocity fields, gravity-based instabilities and bubble growth in uniformly superheated liquid under zero gravity. The model is then used to simulate both single and multi-modal film boiling simulations. The octree grid is dynamically adapted in order to maintain the highest grid resolution on the instability fronts using markers of interface location, volume fraction, and thermal gradients. The method thus provides an efficient platform to simulate fluid instabilities with or without phase change in the presence of body forces like gravity or shear layer instabilities.

Keywords: Boiling flows, dynamic octree grids, heat transfer, interface capturing, phase change.

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Authors: Abolfazl Mohammadijoo

Abstract:

In this paper, we are investigating sliding mode control approach for trajectory tracking of a two-link-manipulator with wheeled mobile robot in its base. The main challenge of this work is dynamic interaction between mobile base and manipulator which makes trajectory tracking more difficult than n-link manipulators with fixed base. Another challenging part of this work is to avoid chattering phenomenon of sliding mode control that makes lots of damages for actuators in real industrial cases. The results show the effectiveness of sliding mode control approach for desired trajectory.

Keywords: Mobile manipulator, sliding mode control, dynamic interaction, mobile robotics.

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Authors: M. G. Murtaza, E. E. Tzirtzilakis, M. Ferdows

Abstract:

Biomagnetic fluid dynamics is an interdisciplinary field comprising engineering, medicine, and biology. Bio fluid dynamics is directed towards finding and developing the solutions to some of the human body related diseases and disorders. This article describes the flow and heat transfer of two dimensional, steady, laminar, viscous and incompressible biomagnetic fluid over a non-linear stretching sheet in the presence of magnetic dipole. Our model is consistent with blood fluid namely biomagnetic fluid dynamics (BFD). This model based on the principles of ferrohydrodynamic (FHD). The temperature at the stretching surface is assumed to follow a power law variation, and stretching velocity is assumed to have a nonlinear form with signum function or sign function. The governing boundary layer equations with boundary conditions are simplified to couple higher order equations using usual transformations. Numerical solutions for the governing momentum and energy equations are obtained by efficient numerical techniques based on the common finite difference method with central differencing, on a tridiagonal matrix manipulation and on an iterative procedure. Computations are performed for a wide range of the governing parameters such as magnetic field parameter, power law exponent temperature parameter, and other involved parameters and the effect of these parameters on the velocity and temperature field is presented. It is observed that for different values of the magnetic parameter, the velocity distribution decreases while temperature distribution increases. Besides, the finite difference solutions results for skin-friction coefficient and rate of heat transfer are discussed. This study will have an important bearing on a high targeting efficiency, a high magnetic field is required in the targeted body compartment.

Keywords: Biomagnetic fluid, FHD, nonlinear stretching sheet, slip parameter.

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Authors: Naren Bag, S. Bhattacharyya, Partha P. Gopmandal

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In this study, we have analyzed the transport of analytes under a two dimensional steady incompressible flow of power-law fluids through rectangular nanochannel. A mathematical model based on the Cauchy momentum-Nernst-Planck-Poisson equations is considered to study the combined effect of mixed electroosmotic (EO) and pressure driven (PD) flow. The coupled governing equations are solved numerically by finite volume method. We have studied extensively the effect of key parameters, e.g., flow behavior index, concentration of the electrolyte, surface potential, imposed pressure gradient and imposed electric field strength on the net average flow across the channel. In addition to study the effect of mixed EOF and PD on the analyte distribution across the channel, we consider a nonlinear model based on general convective-diffusion-electromigration equation. We have also presented the retention factor for various values of electrolyte concentration and flow behavior index.

Keywords: Electric double layer, finite volume method, flow behavior index, mixed electroosmotic/pressure driven flow, Non-Newtonian power-law fluids, numerical simulation.

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Authors: Giuliano Raimondo, Jörg Wangemann, Peer Drechsel

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In systems development involving Fuel Cells generators, it is important to have from an early stage of the project a dynamic model for the electrical behavior of the stack to be shared between involved development parties. It allows independent and early design and tests of fuel cell related power electronic. This paper presents an empirical Fuel Cell system model derived from characterization tests on a real system. Moreover, it is illustrated how the obtained model is used to build and validate a real-time Fuel Cell system emulator which is used for aerospace electrical integration testing activities.

Keywords: Fuel cell dynamics, real time simulation, fuel cell, modelling, testing.

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Authors: Mohd Agos Salim Nasir, Ros Fadilah Deraman, Siti Salmah Yasiran

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The Goursat partial differential equation arises in linear and non linear partial differential equations with mixed derivatives. This equation is a second order hyperbolic partial differential equation which occurs in various fields of study such as in engineering, physics, and applied mathematics. There are many approaches that have been suggested to approximate the solution of the Goursat partial differential equation. However, all of the suggested methods traditionally focused on numerical differentiation approaches including forward and central differences in deriving the scheme. An innovation has been done in deriving the Goursat partial differential equation scheme which involves numerical integration techniques. In this paper we have developed a new scheme to solve the Goursat partial differential equation based on the Adomian decomposition (ADM) and associated with Boole-s integration rule to approximate the integration terms. The new scheme can easily be applied to many linear and non linear Goursat partial differential equations and is capable to reduce the size of computational work. The accuracy of the results reveals the advantage of this new scheme over existing numerical method.

Keywords: Goursat problem, partial differential equation, Adomian decomposition method, Boole's integration rule.

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Authors: Jihyung Kim, Taejin Kim, Sungho Park, Jun-Dong Cho

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In this paper, the problem of reducing switching activity in on-chip buses at the stage of high-level synthesis is considered, and a high-level low power bus binding based on dynamic bit reordering is proposed. Whereas conventional methods use a fixed bit ordering between variables within a bus, the proposed method switches a bit ordering dynamically to obtain a switching activity reduction. As a result, the proposed method finds a binding solution with a smaller value of total switching activity (TSA). Experimental result shows that the proposed method obtains a binding solution having 12.0-34.9% smaller TSA compared with the conventional methods.

Keywords: bit reordering, bus binding, low power, switching activity matrix

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Authors: F. Gurkalo, K. Poutos

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Earthquakes produce some of the most violent loading situations that a structure can be subjected to and if a structure fails under these loads then inevitably human life is put at risk. One of the most common methods by which a structure fails under seismic loading is at the connection of structural elements. The research presented in this paper investigates the interlock systems as a novel method for building structures. The main objective of this experimental study wasto determine the dynamic characteristics and the seismic behaviour of the proposed structures compared to conventional structural systemsduring seismic motions. Results of this study indicate that the interlock mechanism of the panels influences the behaviour of lateral load-resisting systems of the structures during earthquakes, contributing to better structural flexibility and easier maintenance.

Keywords: Watertower, earthquake, seismic, interlocked panels

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Authors: Ferhat Kadioglu, Ahmet Reha Gunay

Abstract:

Correct measurement of a structural damping value is an important issue for the reliable design of the components exposed to vibratory and noise conditions. As far as a vibrating beam technique is concerned, the specimens under the test somehow are interacted with measuring and exciting devices and also with boundary conditions of the test set-up. The aim of this study is to propose a vibrating beam method that offers a non-contact dynamic measurement of solid beam specimens. To evaluate possible effects of the clamped portion of the specimens with clamped-free ends on the dynamic values (damping and the elastic modulus), the same measuring devices were used, and the results were compared to those with the free-free ends. To get clear idea about the sensitivity of the boundary conditions to the damping values at low, medium and high levels, representative materials were subjected to the tests. The results show that the specimens with low damping values are especially sensitive to the boundary conditions and the most reliable structural damping values are obtained for the specimens with free-free ends. For the damping values at the low levels, a deviation of about 368% was obtained between the specimens with free-free and clamped-free ends, yet, for those having high inherent damping values, comparable results were obtained.

Keywords: Vibrating beam technique, dynamic values, damping, boundary conditions, non-contact measuring systems.

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Authors: Halil Snopce, Ilir Spahiu, Lavdrim Elmazi

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A lot of Scientific and Engineering problems require the solution of large systems of linear equations of the form bAx in an effective manner. LU-Decomposition offers good choices for solving this problem. Our approach is to find the lower bound of processing elements needed for this purpose. Here is used the so called Omega calculus, as a computational method for solving problems via their corresponding Diophantine relation. From the corresponding algorithm is formed a system of linear diophantine equalities using the domain of computation which is given by the set of lattice points inside the polyhedron. Then is run the Mathematica program DiophantineGF.m. This program calculates the generating function from which is possible to find the number of solutions to the system of Diophantine equalities, which in fact gives the lower bound for the number of processors needed for the corresponding algorithm. There is given a mathematical explanation of the problem as well. Keywordsgenerating function, lattice points in polyhedron, lower bound of processor elements, system of Diophantine equationsand : calculus.

Keywords: generating function, lattice points in polyhedron, lower bound of processor elements, system of Diophantine equations and calculus.

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Authors: Khalil Ur Rehman, M. Y. Malik, Usman Ali

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In this paper, the problem proposed by Von Karman is treated in the attendance of additional flow field effects when the liquid is spaced above the rotating rigid disk. To be more specific, a purely viscous fluid flow yield by rotating rigid disk with Navier’s condition is considered in both magnetohydrodynamic and hydrodynamic frames. The rotating flow regime is manifested with heat source/sink and chemically reactive species. Moreover, the features of thermophoresis and Brownian motion are reported by considering nanofluid model. The flow field formulation is obtained mathematically in terms of high order differential equations. The reduced system of equations is solved numerically through self-coded computational algorithm. The pertinent outcomes are discussed systematically and provided through graphical and tabular practices. A simultaneous way of study makes this attempt attractive in this sense that the article contains dual framework and validation of results with existing work confirms the execution of self-coded algorithm for fluid flow regime over a rotating rigid disk.

Keywords: Nanoparticles, Newtonian fluid model, chemical reaction, heat source/sink.

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