Search results for: system of equations

Authors: R. Mahjoub, K. Maghsoudi Mehraban

Abstract:

In recent years, solid oxide fuel cells have been used as one of the main technologies for the production of electrical energy with high-efficiency ratio, which is used hydrogen and other hydrocarbons as fuels. The fuel cell technology can be used either alone or in hybrid gas turbines systems. In this study, thermodynamics analysis for GT-SOFC hybrid system is developed, and then mass balance and exergy equations have been applied not only on the process but also on the individual components of the hybrid system, which enable us to estimate the thermal efficiency of the hybrid systems. Furthermore, various sources of irreversibility in the solid oxide fuel cell system are discussed, and modeling and parametric analyses like heat and pressure are carried out. This study enables us to consider the irreversible effects of solid oxide fuel cells, and also it leads to the specification of efficiency of the system accurately. Next in the study, both methane and hydrogen as a fuel for SOFC are used and implemented, and finally, our results are compared with other references.

Keywords: hybrid system, gas turbine, entropy and exergy analysis, irreversibility analysis

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Authors: Serifenur Cebesoy, Yelda Aygar, Elgiz Bairamov

Abstract:

In this study, we examine some spectral properties of non-selfadjoint matrix-valued difference equations consisting of a polynomial-type Jost solution. The aim of this study is to investigate the eigenvalues and spectral singularities of the difference operator L which is expressed by the above-mentioned difference equation. Firstly, thanks to the representation of polynomial type Jost solution of this equation, we obtain asymptotics and some analytical properties. Then, using the uniqueness theorems of analytic functions, we guarantee that the operator L has a finite number of eigenvalues and spectral singularities.

Keywords: Difference Equations, Jost Functions, Asymptotics, Eigenvalues, Continuous Spectrum, Spectral Singularities.

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Authors: Ameleh Aghajanloo, Moharam Dolatshahi Pirouz, Masoud Montazeri Namin

Abstract:

In this paper, a two-dimensional (2D) numerical model for the tidal currents simulation in Persian Gulf is presented. The model is based on the depth averaged equations of shallow water which consider hydrostatic pressure distribution. The continuity equation and two momentum equations including the effects of bed friction, the Coriolis effects and wind stress have been solved. To integrate the 2D equations, the Alternative Direction Implicit (ADI) technique has been used. The base of equations discritization was finite volume method applied on rectangular mesh. To evaluate the model validation, a dam break case study including analytical solution is selected and the comparison is done. After that, the capability of the model in simulation of tidal current in a real field is represented by modeling the current behavior in Persian Gulf. The tidal fluctuations in Hormuz Strait have caused the tidal currents in the area of study. Therefore, the water surface oscillations data at Hengam Island on Hormoz Strait are used as the model input data. The check point of the model is measured water surface elevations at Assaluye port. The comparison between the results and the acceptable agreement of them showed the model ability for modeling marine hydrodynamic.

Keywords: Persian Gulf, Tidal Currents, Shallow Water Equations, Finite Volumes

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Authors: Hnin Hnin Kyi, Khaing Khaing Aye

Abstract:

Acoustic function plays an important role in aerodynamic mechanical engineering. It can classify the kind of air-vehicle such as subsonic or supersonic. Acoustic velocity relates with velocity and Mach number. Mach number relates again acoustic stability or instability condition. Mach number plays an important role in growth or decay in energy system. Acoustic is a function of temperature and temperature is directly proportional to pressure. If we control the pressure, we can control acoustic function. To get pressure stability condition, we apply Navier-Stokes equations.

Keywords: Acoustic velocity, Irrotational, Mach number, Rotational.

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Authors: T. H. Young, S. J. Huang, Y. S. Chiu

Abstract:

This paper investigates the parametric stability of an axially moving web subjected to non-uniform in-plane edge excitations on two opposite, simply-supported edges. The web is modeled as a viscoelastic plate whose constitutive relation obeys the Kelvin-Voigt model, and the in-plane edge excitations are expressed as the sum of a static tension and a periodical perturbation. Due to the in-plane edge excitations, the moving plate may bring about parametric instability under certain situations. First, the in-plane stresses of the plate due to the non-uniform edge excitations are determined by solving the in-plane forced vibration problem. Then, the dependence on the spatial coordinates in the equation of transverse motion is eliminated by the generalized Galerkin method, which results in a set of discretized system equations in time. Finally, the method of multiple scales is utilized to solve the set of system equations analytically if the periodical perturbation of the in-plane edge excitations is much smaller as compared with the static tension of the plate, from which the stability boundaries of the moving plate are obtained. Numerical results reveal that only combination resonances of the summed-type appear under the in-plane edge excitations considered in this work.

Keywords: Axially moving viscoelastic plate, in-plane periodic excitation, non-uniformly distributed edge tension, dynamic stability.

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Authors: J. Geiser, R. Röhle

Abstract:

In this paper we present discretization and decomposition methods for a multi-component transport model of a chemical vapor deposition (CVD) process. CVD processes are used to manufacture deposition layers or bulk materials. In our transport model we simulate the deposition of thin layers. The microscopic model is based on the heavy particles, which are derived by approximately solving a linearized multicomponent Boltzmann equation. For the drift-process of the particles we propose diffusionreaction equations as well as for the effects of heat conduction. We concentrate on solving the diffusion-reaction equation with analytical and numerical methods. For the chemical processes, modelled with reaction equations, we propose decomposition methods and decouple the multi-component models to simpler systems of differential equations. In the numerical experiments we present the computational results of our proposed models.

Keywords: Chemical reactions, chemical vapor deposition, convection-diffusion-reaction equations, decomposition methods, multi-component transport.

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Authors: Fadi Awawdeh, O. Alsayyed

Abstract:

New exact three-wave solutions including periodic two-solitary solutions and doubly periodic solitary solutions for the (2+1)-dimensional asymmetric Nizhnik-Novikov- Veselov (ANNV) system are obtained using Hirota's bilinear form and generalized three-wave type of ansatz approach. It is shown that the generalized three-wave method, with the help of symbolic computation, provides an e¤ective and powerful mathematical tool for solving high dimensional nonlinear evolution equations in mathematical physics.

Keywords: Soliton Solution, Hirota Bilinear Method, ANNV System.

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Authors: Rampal Singh, S. Balasundaram

Abstract:

In this paper, we study the application of Extreme Learning Machine (ELM) algorithm for single layered feedforward neural networks to non-linear chaotic time series problems. In this algorithm the input weights and the hidden layer bias are randomly chosen. The ELM formulation leads to solving a system of linear equations in terms of the unknown weights connecting the hidden layer to the output layer. The solution of this general system of linear equations will be obtained using Moore-Penrose generalized pseudo inverse. For the study of the application of the method we consider the time series generated by the Mackey Glass delay differential equation with different time delays, Santa Fe A and UCR heart beat rate ECG time series. For the choice of sigmoid, sin and hardlim activation functions the optimal values for the memory order and the number of hidden neurons which give the best prediction performance in terms of root mean square error are determined. It is observed that the results obtained are in close agreement with the exact solution of the problems considered which clearly shows that ELM is a very promising alternative method for time series prediction.

Keywords: Chaotic time series, Extreme learning machine, Generalization performance.

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Authors: Z. N. Haji, S. O. Oyadiji, H. Samami, O. Farrell

Abstract:

The prediction of the vibration response of rubber products by analytical or numerical method depends mainly on the predefined intrinsic material properties such as Young’s modulus, damping factor and Poisson’s ratio. Such intrinsic properties are determined experimentally by subjecting a bonded rubber sample to compression tests. The compression tests on such a sample yield an apparent Young’s modulus which is greater in magnitude than the intrinsic Young’s modulus of the rubber. As a result, many analytical equations have been developed to determine Young’s modulus from an apparent Young’s modulus of bonded rubber materials. In this work, the applicability of some of these analytical equations is assessed via experimental testing. The assessment is based on testing of vulcanized nitrile butadiene rubber (NBR70) samples using tensile test and compression test methods. The analytical equations are used to determine the intrinsic Young’s modulus from the apparent modulus that is derived from the compression test data of the bonded rubber samples. Then, these Young’s moduli are compared with the actual Young’s modulus that is derived from the tensile test data. The results show significant discrepancy between the Young’s modulus derived using the analytical equations and the actual Young’s modulus.

Keywords: Bonded rubber, quasi-static test, shape factor, apparent Young’s modulus.

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Authors: H.R.Goshayeshi, M.Fahim inia, M.M.Naserian

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In this research, the laminar heat transfer of natural convection on vertical surfaces has been investigated. Most of the studies on natural convection have been considered constantly whereas velocity and temperature domain, do not change with time, transient one are used a lot. Governing equations are solved using a finite volume approach. The convective terms are discretized using the power-law scheme, whereas for diffusive terms the central difference is employed. Coupling between the velocity and pressure is made with SIMPLE algorithm. The resultant system of discretized linear algebraic equations is solved with an alternating direction implicit scheme. Then a configuration of rectangular fins is put in different ways on the surface and heat transfer of natural convection on these surfaces without sliding is studied and finally optimization is done.

Keywords: Natural convection, vertical surfaces, SIMPLE algorithm, Rectangular fins.

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Authors: Rudolf Csikja, Janos Toth

Abstract:

Methods to detect and localize time singularities of polynomial and quasi-polynomial ordinary differential equations are systematically presented and developed. They are applied to examples taken form different fields of applications and they are also compared to better known methods such as those based on the existence of linear first integrals or Lyapunov functions.

Keywords: blow up, finite escape time, polynomial ODE, singularity, Lotka–Volterra equation, Painleve analysis, Ψ-series, global existence

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Authors: O. Miraliyari

Abstract:

This article attempts to analyze functionally graded beam thermal buckling along with piezoelectric layers applying based on the third order shearing deformation theory considering various boundary conditions. The beam properties are assumed to vary continuously from the lower surface to the upper surface of the beam. The equilibrium equations are derived using the total potential energy equations, Euler equations, piezoelectric material constitutive equations and third order shear deformation theory assumptions. In order to fulfill such an aim, at first functionally graded beam with piezoelectric layers applying the third order shearing deformation theory along with clamped -clamped boundary conditions are thoroughly analyzed, and then following making sure of the correctness of all the equations, the very same beam is analyzed with piezoelectric layers through simply-simply and simply-clamped boundary conditions. In this article buckling critical temperature for functionally graded beam is derived in two different ways, without piezoelectric layer and with piezoelectric layer and the results are compared together. Finally, all the conclusions obtained will be compared and contrasted with the same samples in the same and distinguished conditions through tables and charts. It would be noteworthy that in this article, the software MAPLE has been applied in order to do the numeral calculations.

Keywords: Thermal buckling, functionally graded beam, piezoelectric layer, various boundary conditions.

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Authors: M. Ashaque Meah, M. Shah Noor, M Asif Arefin, Md. Fazlul Karim

Abstract:

A numerical technique in a boundary-fitted curvilinear grid model is developed to simulate the extent of inland inundation along the coastal belts of Peninsular Malaysia and Southern Thailand due to 2004 Indian ocean tsunami. Tsunami propagation and run-up are also studied in this paper. The vertically integrated shallow water equations are solved by using the method of lines (MOL). For this purpose the boundary-fitted grids are generated along the coastal and island boundaries and the other open boundaries of the model domain. A transformation is used to the governing equations so that the transformed physical domain is converted into a rectangular one. The MOL technique is applied to the transformed shallow water equations and the boundary conditions so that the equations are converted into ordinary differential equations initial value problem. Finally the 4^th order Runge-Kutta method is used to solve these ordinary differential equations. The moving boundary technique is applied instead of fixed sea side wall or fixed coastal boundary to ensure the movement of the coastal boundary. The extent of intrusion of water and associated tsunami propagation are simulated for the 2004 Indian Ocean tsunami along the west coast of Peninsular Malaysia and southern Thailand. The simulated results are compared with the results obtained from a finite difference model and the data available in the USGS website. All simulations show better approximation than earlier research and also show excellent agreement with the observed data.

Keywords: Open boundary condition, moving boundary condition, boundary-fitted curvilinear grids, far field tsunami, Shallow Water Equations, tsunami source, Indonesian tsunami of 2004.

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Authors: Simon Brown

Abstract:

Glomerular filtration rate (GFR) is a measure of kidney function. It is usually estimated from serum concentrations of cystatin C or creatinine although there has been considerable debate in the literature about (i) the best equation to use and (ii) the variability in the correlation between the concentrations of creatinine and cystatin C. The equations for GFR can be written in a general form and from these I calculate the error of the GFR estimates associated with analyte measurement error. These show that the error of the GFR estimates is such that it is not possible to distinguish between the equations over much of the concentration range of either analyte. The general forms of the equations are also used to derive an expression for the concentration of cystatin C as a function of the concentration of creatinine. This equation shows that these analyte concentrations are not linearly related. Clinical reports of cystatin C and creatinine concentration are consistent with the expression derived.

Keywords: creatinine, cystatin C, error analysis, glomerularfiltration rate, measurement error.

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Authors: Noureddine Seddari, Mohamed Belaoued, Salah Bougueroua

Abstract:

The modeling of complex systems is generally based on the decomposition of their components into sub-systems easier to handle. This division has to be made in a methodical way. In this paper, we introduce an industrial control system modeling and simulation based on the Multi-Agent System (MAS) methodology AALAADIN and more particularly the underlying conceptual model Agent/Group/Role (AGR). Indeed, in this division using AGR model, the overall system is decomposed into sub-systems in order to improve the understanding of regulation and control systems, and to simplify the implementation of the obtained agents and their groups, which are implemented using the Multi-Agents Development KIT (MAD-KIT) platform. This approach appears to us to be the most appropriate for modeling of this type of systems because, due to the use of MAS, it is possible to model real systems in which very complex behaviors emerge from relatively simple and local interactions between many different individuals, therefore a MAS is well adapted to describe a system from the standpoint of the activity of its components, that is to say when the behavior of the individuals is complex (difficult to describe with equations). The main aim of this approach is the take advantage of the performance, the scalability and the robustness that are intuitively provided by MAS.

Keywords: Complex systems, modeling and simulation, industrial control system, MAS, AALAADIN, AGR, MAD-KIT.

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Authors: Fuziyah Ishak, Mohamed B. Suleiman, Zanariah A. Majid, Khairil I. Othman

Abstract:

This paper considers the development of a two-point predictor-corrector block method for solving delay differential equations. The formulae are represented in divided difference form and the algorithm is implemented in variable stepsize variable order technique. The block method produces two new values at a single integration step. Numerical results are compared with existing methods and it is evident that the block method performs very well. Stability regions of the block method are also investigated.

Keywords: block method, delay differential equations, predictor-corrector, stability region, variable stepsize variable order.

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Authors: Felicia Magpantay, Kenzu Abdella

Abstract:

A model of a system concerning one species of demersal (inshore) fish and one of pelagic (offshore) fish undergoing fishing restricted by marine protected areas is proposed in this paper. This setup was based on the FISH-BE model applied to the Tabina fishery in Zamboanga del Sur, Philippines. The components of the model equations have been adapted from widely-accepted mechanisms in population dynamics. The model employs Gompertz-s law of growth and interaction on each type of protected and unprotected subpopulation. Exchange coefficients between protected and unprotected areas were assumed to be proportional to the relative area of the entry region. Fishing harvests were assumed to be proportional to both the number of fishers and the number of unprotected fish. An extra term was included for the pelagic population to allow for the exchange between the unprotected area and the outside environment. The systems were found to be bounded for all parameter values. The equations for the steady state were unsolvable analytically but the existence and uniqueness of non-zero steady states can be proven. Plots also show that an MPA size yielding the maximum steady state of the unprotected population can be found. All steady states were found to be globally asymptotically stable for the entire range of parameter values.

Keywords: fisheries modelling, marine protected areas, sustainablefisheries, Gompertz Law

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Authors: Xin Luo, Jin Huang, Chuan-Long Wang

Abstract:

The mechanical quadrature methods for solving the boundary integral equations of the anisotropic Darcy-s equations with Dirichlet conditions in smooth domains are presented. By applying the collectively compact theory, we prove the convergence and stability of approximate solutions. The asymptotic expansions for the error show that the methods converge with the order O (h3), where h is the mesh size. Based on these analysis, extrapolation methods can be introduced to achieve a higher convergence rate O (h5). An a posterior asymptotic error representation is derived in order to construct self-adaptive algorithms. Finally, the numerical experiments show the efficiency of our methods.

Keywords: Darcy's equation, anisotropic, mechanical quadrature methods, extrapolation methods, a posteriori error estimate.

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Authors: Naveed Ahmed, Gunar Matthies

Abstract:

We deal with the numerical solution of time-dependent convection-diffusion-reaction equations. We combine the local projection stabilization method for the space discretization with two different time discretization schemes: the continuous Galerkin-Petrov (cGP) method and the discontinuous Galerkin (dG) method of polynomial of degree k. We establish the optimal error estimates and present numerical results which shows that the cGP(k) and dG(k)- methods are accurate of order k +1, respectively, in the whole time interval. Moreover, the cGP(k)-method is superconvergent of order 2k and dG(k)-method is of order 2k +1 at the discrete time points. Furthermore, the dependence of the results on the choice of the stabilization parameter are discussed and compared.

Keywords: Convection-diffusion-reaction equations, stabilized finite elements, discontinuous Galerkin, continuous Galerkin-Petrov.

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Authors: Wisuwat Plodpradista

Abstract:

Tubular linear induction motor (TLIM) can be used as a capsule pump in a large pneumatic capsule pipeline (PCP) system. Parametric performance evaluation of the designed 1-meter diameter PCP-TLIM system yields encouraging results for practical implementation. The capsule thrust and speed inside the TLIM pump can be calculated from the combination of the PCP fluid mechanics and the TLIM equations. The TLIM equivalent circuits derived from those of the conventional three-phase induction motor are used as a model to predict the static test results of a small-scale PCP-TLIM system. In this paper, additional dynamic tests are performed on the same small-scale PCP-TLIM system with two capsules of different diameters. The behaviors of the capsule inside the pump are observed and analyzed. The dynamic performances from the dynamic tests are compared with the theoretical predictions based on the TLIM equivalent circuit model.

Keywords: Pneumatic capsule pipeline, Tubular linear induction motor

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Authors: M. Behbahani-Nejad, Y. Shekari

Abstract:

A reduced order modeling approach for natural gas transient flow in pipelines is presented. The Euler equations are considered as the governing equations and solved numerically using the implicit Steger-Warming flux vector splitting method. Next, the linearized form of the equations is derived and the corresponding eigensystem is obtained. Then, a few dominant flow eigenmodes are used to construct an efficient reduced-order model. A well-known test case is presented to demonstrate the accuracy and the computational efficiency of the proposed method. The results obtained are in good agreement with those of the direct numerical method and field data. Moreover, it is shown that the present reduced-order model is more efficient than the conventional numerical techniques for transient flow analysis of natural gas in pipelines.

Keywords: Eigenmode, Natural Gas, Reduced Order Modeling, Transient Flow.

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Authors: Zanariah Abdul Majid, Mohamed Suleiman

Abstract:

The aim of this paper is to investigate the performance of the developed two point block method designed for two processors for solving directly non stiff large systems of higher order ordinary differential equations (ODEs). The method calculates the numerical solution at two points simultaneously and produces two new equally spaced solution values within a block and it is possible to assign the computational tasks at each time step to a single processor. The algorithm of the method was developed in C language and the parallel computation was done on a parallel shared memory environment. Numerical results are given to compare the efficiency of the developed method to the sequential timing. For large problems, the parallel implementation produced 1.95 speed-up and 98% efficiency for the two processors.

Keywords: Numerical methods, parallel method, block method, higher order ODEs.

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Authors: Reza Abazari, Rasool Abazari

Abstract:

In this paper, the two-dimension differential transformation method (DTM) is employed to obtain the closed form solutions of the three famous coupled partial differential equation with physical interest namely, the coupled Korteweg-de Vries(KdV) equations, the coupled Burgers equations and coupled nonlinear Schrödinger equation. We begin by showing that how the differential transformation method applies to a linear and non-linear part of any PDEs and apply on these coupled PDEs to illustrate the sufficiency of the method for this kind of nonlinear differential equations. The results obtained are in good agreement with the exact solution. These results show that the technique introduced here is accurate and easy to apply.

Keywords: Coupled Korteweg-de Vries(KdV) equation, Coupled Burgers equation, Coupled Schrödinger equation, differential transformation method.

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Authors: N. A. Samat, D. F. Percy

Abstract:

The main aim of this study is to describe and introduce a method of numerical analysis in obtaining approximate solutions for the SIR-SI differential equations (susceptible-infectiverecovered for human populations; susceptible-infective for vector populations) that represent a model for dengue disease transmission. Firstly, we describe the ordinary differential equations for the SIR-SI disease transmission models. Then, we introduce the numerical analysis of solutions of this continuous time, discrete space SIR-SI model by simplifying the continuous time scale to a densely populated, discrete time scale. This is followed by the application of this numerical analysis of solutions of the SIR-SI differential equations to the estimation of relative risk using continuous time, discrete space dengue data of Kuala Lumpur, Malaysia. Finally, we present the results of the analysis, comparing and displaying the results in graphs, table and maps. Results of the numerical analysis of solutions that we implemented offers a useful and potentially superior model for estimating relative risks based on continuous time, discrete space data for vector borne infectious diseases specifically for dengue disease. 

Keywords: Dengue disease, disease mapping, numerical analysis, SIR-SI differential equations.

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Authors: S. Arun Prakash, V. Malathi, M. S. Mani Rajan

Abstract:

The analytical bright two soliton solution of the 3- coupled nonlinear Schrödinger equations with variable coefficients in birefringent optical fiber is obtained by Darboux transformation method. To the design of ultra-speed optical devices, Soliton interaction and control in birefringence fiber is investigated. Lax pair is constructed for N coupled NLS system through AKNS method. Using two-soliton solution, we demonstrate different interaction behaviors of solitons in birefringent fiber depending on the choice of control parameters. Our results shows that interactions of optical solitons have some specific applications such as construction of logic gates, optical computing, soliton switching, and soliton amplification in wavelength division multiplexing (WDM) system.

Keywords: Optical soliton, soliton interaction, soliton switching, WDM.

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Authors: Jessada Tariboon

Abstract:

In this article, using distribution kernel, we study the nonlinear equations with n-dimensional telegraph operator iterated k-times.

Keywords: Telegraph operator, Elementary solution, Distribution kernel.

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Authors: Lianglin Xiong, Yun Zhao, Tao Jiang

Abstract:

In this paper, we study the stability of n-dimensional linear fractional neutral differential equation with time delays. By using the Laplace transform, we introduce a characteristic equation for the above system with multiple time delays. We discover that if all roots of the characteristic equation have negative parts, then the equilibrium of the above linear system with fractional order is Lyapunov globally asymptotical stable if the equilibrium exist that is almost the same as that of classical differential equations. An example is provided to show the effectiveness of the approach presented in this paper.

Keywords: Fractional neutral differential equation, Laplace transform, characteristic equation.

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Authors: Dylan M. Copeland

Abstract:

We present new finite element methods for Helmholtz and Maxwell equations on general three-dimensional polyhedral meshes, based on domain decomposition with boundary elements on the surfaces of the polyhedral volume elements. The methods use the lowest-order polynomial spaces and produce sparse, symmetric linear systems despite the use of boundary elements. Moreover, piecewise constant coefficients are admissible. The resulting approximation on the element surfaces can be extended throughout the domain via representation formulas. Numerical experiments confirm that the convergence behavior on tetrahedral meshes is comparable to that of standard finite element methods, and equally good performance is attained on more general meshes.

Keywords: Boundary elements, finite elements, Helmholtz equation, Maxwell equations.

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Authors: Li Xiguang

Abstract:

In this paper, by constructing a special set and utilizing fixed point index theory, we study the existence of solution for the boundary value problem of second-order singular differential equations in Banach space, which improved and generalize the result of related paper.

Keywords: Banach space, cone, fixed point index, singular equation.

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Authors: I. Abuiziah, A. Oulhaj, K. Sebari, D. Ouazar

Abstract:

The primary objectives of transient analysis are to determine the values of transient pressures that can result from flow control operations and to establish the design criteria for system equipment and devices (such as control devices and pipe wall thickness) so as to provide an acceptable level of protection against system failure due to pipe collapse or bursting. Because of the complexity of the equations needed to describe transients, numerical computer models are used to analyze transient flow hydraulics. An effective numerical model allows the hydraulic engineer to analyze potential transient events and to identify and evaluate alternative solutions for controlling hydraulic transients, thereby protecting the integrity of the hydraulic system. This paper presents the influence of using the protection devices to control the adverse effects due to excessive and low pressure occurs in the transient.

Keywords: Flow Transient, Water hammer, Pipeline System, Surge Tank, Simulation Model, Protection Devices.

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