Search results for: three dimensional primitive equations

Authors: Alireza Abbasi Moshaii, Mehdi Tale Masouleh, Esmail Zarezadeh, Kamran Farajzadeh

Abstract:

The main purpose of this study is static analysis of two three-degree of freedom parallel mechanisms: 3-RCC and 3- RRS. Geometry of these mechanisms is expressed and static equilibrium equations are derived for the whole chains. For these mechanisms due to the equal number of equations and unknowns, the solution is as same as 3-RCC mechanism. A mathematical software is used to solve the equations. In order to prove the results obtained from solving the equations of mechanisms, the CAD model of these robots has been simulated and their static is analysed in ADAMS software. Due to symmetrical geometry of the mechanisms, the force and external torque acting on the end-effecter have been considered asymmetric to prove the generality of the solution method. Finally, the results of both softwares, for both mechanisms are extracted and compared as graphs. The good achieved comparison between the results indicates the accuracy of the analysis.

Keywords: Robotic, Static analysis, 3-RCC, 3-RRS.

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Authors: Changjin Xu, Qianhong Zhang

Abstract:

In this paper, the existence of periodic solutions of a delayed competitive system with the effect of toxic substances is investigated by using the Gaines and Mawhin,s continuation theorem of coincidence degree theory on time scales. New sufficient conditions are obtained for the existence of periodic solutions. The approach is unified to provide the existence of the desired solutions for the continuous differential equations and discrete difference equations. Moreover, The approach has been widely applied to study existence of periodic solutions in differential equations and difference equations.

Keywords: Time scales, competitive system, periodic solution, coincidence degree, topological degree.

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Authors: Zarina Bibi, I., Khairil Iskandar, O.

Abstract:

In this paper, parallelism in the solution of Ordinary Differential Equations (ODEs) to increase the computational speed is studied. The focus is the development of parallel algorithm of the two point Block Backward Differentiation Formulas (PBBDF) that can take advantage of the parallel architecture in computer technology. Parallelism is obtained by using Message Passing Interface (MPI). Numerical results are given to validate the efficiency of the PBBDF implementation as compared to the sequential implementation.

Keywords: Ordinary differential equations, parallel.

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Authors: Javad Abdalkhani

Abstract:

Convergence of power series solutions for a class of non-linear Abel type equations, including an equation that arises in nonlinear cooling of semi-infinite rods, is very slow inside their small radius of convergence. Beyond that the corresponding power series are wildly divergent. Implementation of nonlinear sequence transformation allow effortless evaluation of these power series on very large intervals..

Keywords: Nonlinear transformation, Abel Volterra Equations, Mathematica

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Authors: Kohei Inoue, Kenji Hara, Kiichi Urahama

Abstract:

We describe a relationship between integral images and differential images. First, we derive a simple difference filter from conventional integral image. In the derivation, we show that an integral image and the corresponding differential image are related to each other by simultaneous linear equations, where the numbers of unknowns and equations are the same, and therefore, we can execute the integration and differentiation by solving the simultaneous equations. We applied the relationship to an image fusion problem, and experimentally verified the effectiveness of the proposed method.

Keywords: Integral images, differential images, differential filters, image fusion.

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Authors: D. C. Lo, S. S. Leu

Abstract:

In this paper, the differential quadrature method is applied to simulate natural convection in an inclined cubic cavity using velocity-vorticity formulation. The numerical capability of the present algorithm is demonstrated by application to natural convection in an inclined cubic cavity. The velocity Poisson equations, the vorticity transport equations and the energy equation are all solved as a coupled system of equations for the seven field variables consisting of three velocities, three vorticities and temperature. The coupled equations are simultaneously solved by imposing the vorticity definition at boundary without requiring the explicit specification of the vorticity boundary conditions. Test results obtained for an inclined cubic cavity with different angle of inclinations for Rayleigh number equal to 103, 104, 105 and 106 indicate that the present coupled solution algorithm could predict the benchmark results for temperature and flow fields. Thus, it is convinced that the present formulation is capable of solving coupled Navier-Stokes equations effectively and accurately.

Keywords: Natural convection, velocity-vorticity formulation, differential quadrature (DQ).

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Authors: Osama Yusuf Ababneh

Abstract:

For the last years, the variants of the Newton-s method with cubic convergence have become popular iterative methods to find approximate solutions to the roots of non-linear equations. These methods both enjoy cubic convergence at simple roots and do not require the evaluation of second order derivatives. In this paper, we present a new Newton-s method based on contra harmonic mean with cubically convergent. Numerical examples show that the new method can compete with the classical Newton's method.

Keywords: Third-order convergence, non-linear equations, root finding, iterative method.

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Authors: Mei-Hsiu Chi, Jyh-Yang Wu, Sheng-Gwo Chen

Abstract:

The diffusion-reaction equations are important Partial Differential Equations in mathematical biology, material science, physics, and so on. However, finding efficient numerical methods for diffusion-reaction systems on curved surfaces is still an important and difficult problem. The purpose of this paper is to present a convergent geometric method for solving the reaction-diffusion equations on closed surfaces by an O(r)-LTL configuration method. The O(r)-LTL configuration method combining the local tangential lifting technique and configuration equations is an effective method to estimate differential quantities on curved surfaces. Since estimating the Laplace-Beltrami operator is an important task for solving the reaction-diffusion equations on surfaces, we use the local tangential lifting method and a generalized finite difference method to approximate the Laplace-Beltrami operators and we solve this reaction-diffusion system on closed surfaces. Our method is not only conceptually simple, but also easy to implement.

Keywords: Close surfaces, high-order approach, numerical solutions, reaction-diffusion systems.

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Authors: Changqing Yang, Jianhua Hou

Abstract:

In this paper the Laplace Decomposition method is developed to solve linear and nonlinear fractional integro- differential equations of Volterra type.The fractional derivative is described in the Caputo sense.The Laplace decomposition method is found to be fast and accurate.Illustrative examples  are included to demonstrate the validity and applicability of presented technique and comparasion is made with exacting results.

Keywords: Integro-differential equations, Laplace transform, fractional derivative, adomian polynomials, pade appoximants.

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Authors: Rui Wu, Tapani Ristaniemi

Abstract:

In this paper, we propose a new algorithm for joint time-delay and direction-of-arrival (DOA) estimation, here called two-dimensional code acquisition, in an asynchronous directsequence code-division multiple-access (DS-CDMA) array system. This algorithm depends on eigenvector-eigenvalue decomposition of sample correlation matrix, and requires to know desired user-s training sequence. The performance of the algorithm is analyzed both analytically and numerically in uncorrelated and coherent multipath environment. Numerical examples show that the algorithm is robust with unknown number of coherent signals.

Keywords: Two-Dimensional Code Acquisition, EV-t, DSCDMA

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Authors: Arti Vaish, Harish Parthasarathy

Abstract:

The scalar wave equation for a potential in a curved space time, i.e., the Laplace-Beltrami equation has been studied in this work. An action principle is used to derive a finite element algorithm for determining the modes of propagation inside a waveguide of arbitrary shape. Generalizing this idea, the Maxwell theory in a curved space time determines a set of linear partial differential equations for the four electromagnetic potentials given by the metric of space-time. Similar to the Einstein-s formulation of the field equations of gravitation, these equations are also derived from an action principle. In this paper, the expressions for the action functional of the electromagnetic field have been derived in the presence of gravitational field.

Keywords: General theory of relativity, electromagnetism, metric tensor, Maxwells equations, test functions, finite element method.

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Authors: Janak Raj Sharma, Rajni Sharma

Abstract:

Based on Traub-s methods for solving nonlinear equation f(x) = 0, we develop two families of third-order methods for solving system of nonlinear equations F(x) = 0. The families include well-known existing methods as special cases. The stability is corroborated by numerical results. Comparison with well-known methods shows that the present methods are robust. These higher order methods may be very useful in the numerical applications requiring high precision in their computations because these methods yield a clear reduction in number of iterations.

Keywords: Nonlinear equations and systems, Newton's method, fixed point iteration, order of convergence.

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Authors: Sunita Jahirabadkar, Parag Kulkarni

Abstract:

Many real-world data sets consist of a very high dimensional feature space. Most clustering techniques use the distance or similarity between objects as a measure to build clusters. But in high dimensional spaces, distances between points become relatively uniform. In such cases, density based approaches may give better results. Subspace Clustering algorithms automatically identify lower dimensional subspaces of the higher dimensional feature space in which clusters exist. In this paper, we propose a new clustering algorithm, ISC – Intelligent Subspace Clustering, which tries to overcome three major limitations of the existing state-of-art techniques. ISC determines the input parameter such as є – distance at various levels of Subspace Clustering which helps in finding meaningful clusters. The uniform parameters approach is not suitable for different kind of databases. ISC implements dynamic and adaptive determination of Meaningful clustering parameters based on hierarchical filtering approach. Third and most important feature of ISC is the ability of incremental learning and dynamic inclusion and exclusions of subspaces which lead to better cluster formation.

Keywords: Density based clustering, high dimensional data, subspace clustering, dynamic parameter setting.

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Authors: N. M. Kamoh, M. C. Soomiyol

Abstract:

In this work, a five step continuous method for the solution of third order ordinary differential equations was developed in block form using collocation and interpolation techniques of the shifted Legendre polynomial basis function. The method was found to be zero-stable, consistent and convergent. The application of the method in solving third order initial value problem of ordinary differential equations revealed that the method compared favorably with existing methods.

Keywords: Shifted Legendre polynomials, third order block method, discrete method, convergent.

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Authors: T. G. Emam

Abstract:

The effect of variable chemical reaction on heat and mass transfer characteristics over unsteady stretching surface embedded in a porus medium is studied. The governing time dependent boundary layer equations are transformed into ordinary differential equations containing chemical reaction parameter, unsteadiness parameter, Prandtl number and Schmidt number. These equations have been transformed into a system of first order differential equations. MATHEMATICA has been used to solve this system after obtaining the missed initial conditions. The velocity gradient, temperature, and concentration profiles are computed and discussed in details for various values of the different parameters.

Keywords: Heat and mass transfer, stretching surface, chemical reaction, porus medium.

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Authors: Mao Wei

Abstract:

The main aim of this paper is to investigate the exponential stability of the Euler method for a stochastic age-dependent population equations with Poisson random measures. It is proved that the Euler scheme is exponentially stable in mean square sense. An example is given for illustration.

Keywords: Stochastic age-dependent population equations, poisson random measures, numerical solutions, exponential stability.

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Authors: M. M. Selim

Abstract:

The paper discuses the effect of initial stresses on the reflection coefficients of plane waves in a dissipative medium. Basic governing equations are formulated in context of Biot's incremental deformation theory. These governing equations are solved analytically to obtain the dimensional phase velocities of plane waves propagating in plane of symmetry. Closed-form expressions for the reflection coefficients of P and SV waves- incident at the free surface of an initially stressed dissipative medium are obtained. Numerical computations, using these expressions, are carried out for a particular model. Computations made with the results predicted in presence and absence of the initial stresses and the results have been shown graphically. The study shows that the presence of compressive initial stresses increases the velocity of longitudinal wave (P-wave) but diminishes that of transverse wave (SV-wave). Also the numerical results presented indicate that initial stresses and dissipation might affect the reflection coefficients significantly.

Keywords: Dissipation medium, initial stress, longitudinal waves, reflection coefficients, reflection of plane waves, transverse waves.

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Authors: Morten Willatzen, Mikhail Vladimirovich Deryabin

Abstract:

The governing two-dimensional equations of a heterogeneous material composed of a fluid (allowed to flow in the absence of acoustic excitations) and a crystalline piezoelectric cubic solid stacked one-dimensionally (along the z direction) are derived and special emphasis is given to the discussion of acoustic group velocity for the structure as a function of the wavenumber component perpendicular to the stacking direction (being the x axis). Variations in physical parameters with y are neglected assuming infinite material homogeneity along the y direction and the flow velocity is assumed to be directed along the x direction. In the first part of the paper, the governing set of differential equations are derived as well as the imposed boundary conditions. Solutions are provided using Hamilton-s equations for the wavenumber vs. frequency as a function of the number and thickness of solid layers and fluid layers in cases with and without flow (also the case of a position-dependent flow in the fluid layer is considered). In the first part of the paper, emphasis is given to the small-frequency case. Boundary conditions at the bottom and top parts of the full structure are left unspecified in the general solution but examples are provided for the case where these are subject to rigid-wall conditions (Neumann boundary conditions in the acoustic pressure). In the second part of the paper, emphasis is given to the general case of larger frequencies and wavenumber-frequency bandstructure formation. A wavenumber condition for an arbitrary set of consecutive solid and fluid layers, involving four propagating waves in each solid region, is obtained again using the monodromy matrix method. Case examples are finally discussed.

Keywords: Flow, acoustics, solid-fluid structures, periodicity.

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Authors: A. M. Sagir

Abstract:

In this paper, linear multistep technique using power series as the basis function is used to develop the block methods which are suitable for generating direct solution of the special second order ordinary differential equations with associated initial or boundary conditions. The continuous hybrid formulations enable us to differentiate and evaluate at some grids and off – grid points to obtain two different four discrete schemes, each of order (5,5,5,5)T, which were used in block form for parallel or sequential solutions of the problems. The computational burden and computer time wastage involved in the usual reduction of second order problem into system of first order equations are avoided by this approach. Furthermore, a stability analysis and efficiency of the block methods are tested on linear and non-linear ordinary differential equations and the results obtained compared favorably with the exact solution.

Keywords: Block Method, Hybrid, Linear Multistep Method, Self – starting, Special Second Order.

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Authors: Mohammad Taghi Darvishi, Mohammad Najafi

Abstract:

This paper considers the (2+1)-dimensional breaking soliton equation in its bilinear form. Some exact solutions to this equation are explicitly derived by the idea of three-wave solution method with the assistance of Maple. We can see that the new idea is very simple and straightforward.

Keywords: Soliton solution, computerized symbolic computation, painleve analysis, (2+1)-dimensional breaking soliton equation, Hirota's bilinear form.

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Authors: N. Fusun Oyman Serteller

Abstract:

In this paper, the techniques to solve time dependent electromagnetic wave propagation equations based on the Finite Difference Method (FDM) are proposed by comparing the results with Finite Element Method (FEM) in 2D while discussing some special simulation examples.  Here, 2D dynamical wave equations for lossy media, even with a constant source, are discussed for establishing symbolic manipulation of wave propagation problems. The main objective of this contribution is to introduce a comparative study of two suitable numerical methods and to show that both methods can be applied effectively and efficiently to all types of wave propagation problems, both linear and nonlinear cases, by using symbolic computation. However, the results show that the FDM is more appropriate for solving the nonlinear cases in the symbolic solution. Furthermore, some specific complex domain examples of the comparison of electromagnetic waves equations are considered. Calculations are performed through Mathematica software by making some useful contribution to the programme and leveraging symbolic evaluations of FEM and FDM.

Keywords: Finite difference method, finite element method, linear-nonlinear PDEs, symbolic computation, wave propagation equations.

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

Abstract:

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: M. Abdulkawi, Z. K. Eshkuvatov, N. M. A. Nik Long

Abstract:

This manuscript presents a method for the numerical solution of the Cauchy type singular integral equations of the first kind, over a finite segment which is bounded at the end points of the finite segment. The Chebyshev polynomials of the second kind with the corresponding weight function have been used to approximate the density function. The force function is approximated by using the Chebyshev polynomials of the first kind. It is shown that the numerical solution of characteristic singular integral equation is identical with the exact solution, when the force function is a cubic function. Moreover, it also shown that this numerical method gives exact solution for other singular integral equations with degenerate kernels.

Keywords: Singular integral equations, Cauchy kernel, Chebyshev polynomials, interpolation.

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Authors: A. Giniatoulline

Abstract:

A nonlinear model of the mathematical fluid dynamics which describes the motion of an incompressible viscous rotating fluid in a homogeneous gravitational field is considered. The model is a generalization of the known Navier-Stokes system with the addition of the Coriolis parameter and the equations for changeable density. An explicit algorithm for the solution is constructed, and the proof of the existence and uniqueness theorems for the strong solution of the nonlinear problem is given. For the linear case, the localization and the structure of the spectrum of inner waves are also investigated.

Keywords: Galerkin method, Navier-Stokes equations, nonlinear partial differential equations, Sobolev spaces, stratified fluid.

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Authors: N. Basanta Singh, Sanjoy Deb, G. P Mishra, Subir Kumar Sarkar

Abstract:

Carrier mobility has become the most important characteristic of high speed low dimensional devices. Due to development of very fast switching semiconductor devices, speed of computer and communication equipment has been increasing day by day and will continue to do so in future. As the response of any device depends on the carrier motion within the devices, extensive studies of carrier mobility in the devices has been established essential for the growth in the field of low dimensional devices. Small-signal ac transport of degenerate two-dimensional hot electrons in GaAs quantum wells is studied here incorporating deformation potential acoustic, polar optic and ionized impurity scattering in the framework of heated drifted Fermi-Dirac carrier distribution. Delta doping is considered in the calculations to investigate the effects of double delta doping on millimeter and submillimeter wave response of two dimensional hot electrons in GaAs nanostructures. The inclusion of delta doping is found to enhance considerably the two dimensional electron density which in turn improves the carrier mobility (both ac and dc) values in the GaAs quantum wells thereby providing scope of getting higher speed devices in future.

Keywords: Carrier mobility, Delta doping, Hot carriers, Quantum wells.

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Authors: R. B. Ogunrinde

Abstract:

This paper presents the development, analysis and implementation of an inverse polynomial numerical method which is well suitable for solving initial value problems in first order ordinary differential equations with applications to sample problems. We also present some basic concepts and fundamental theories which are vital to the analysis of the scheme. We analyzed the consistency, convergence, and stability properties of the scheme. Numerical experiments were carried out and the results compared with the theoretical or exact solution and the algorithm was later coded using MATLAB programming language.

Keywords: Differential equations, Numerical, Initial value problem, Polynomials.

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Authors: T. Li, J.Y. Zhang, W.H. Zhang, M.H. Zhu

Abstract:

A numerical simulation of vortex-induced vibration of a 2-dimensional elastic circular cylinder with two degree of freedom under the uniform flow is calculated when Reynolds is 200. 2-dimensional incompressible Navier-Stokes equations are solved with the space-time finite element method, the equation of the cylinder motion is solved with the new explicit integral method and the mesh renew is achieved by the spring moving mesh technology. Considering vortex-induced vibration with the low reduced damping parameter, the variety trends of the lift coefficient, the drag coefficient, the displacement of cylinder are analyzed under different oscillating frequencies of cylinder. The phenomena of locked-in, beat and phases-witch were captured successfully. The evolution of vortex shedding from the cylinder with time is discussed. There are very similar trends in characteristics between the results of the one degree of freedom cylinder model and that of the two degree of freedom cylinder model. The streamwise vibrations have a certain effect on the lateral vibrations and their characteristics.

Keywords: Fluid-structure interaction, Navier-Stokes equation, Space-time finite element method, vortex-induced vibration.

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Authors: Phool Singh, Ashok Jangid, N.S. Tomer, Deepa Sinha

Abstract:

The aim of this paper is to study the oblique stagnation point flow on vertical plate with uniform surface heat flux in presence of magnetic field. Using Stream function, partial differential equations corresponding to the momentum and energy equations are converted into non-linear ordinary differential equations. Numerical solutions of these equations are obtained using Runge-Kutta Fehlberg method with the help of shooting technique. In the present work the effects of striking angle, magnetic field parameter, Grashoff number, the Prandtl number on velocity and heat transfer characteristics have been discussed. Effect of above mentioned parameter on the position of stagnation point are also studied.

Keywords: Heat flux, Oblique stagnation point, Mixedconvection, Magneto hydrodynamics

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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: Devinder Singh, Arbind Kumar, Rajneesh Kumar

Abstract:

The general solution of the equations for a homogeneous isotropic microstretch thermo elastic medium with mass diffusion for two dimensional problems is obtained due to normal and tangential forces. The Integral transform technique is used to obtain the components of displacements, microrotation, stress and mass concentration, temperature change and mass concentration. A particular case of interest is deduced from the present investigation.

Keywords: Normal and tangential force, Microstretch, thermoelastic, The Integral transform technique.

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