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Effect of Gravitational Acceleration on Unsteady Biomagnetic Fluid Flow
Nor Amirah Idris,
Norsarahaida Amin,
Hamisan Rahmat
Issue:
Volume 3, Issue 6, December 2014
Pages:
285-294
Received:
4 November 2014
Accepted:
19 November 2014
Published:
24 November 2014
Abstract: This paper investigates the effect of gravitational acceleration on unsteady biomagnetic fluid flow in a channel under the influence of a spatially varying magnetic field. The study on biomagnetic fluid under the action of an applied magnetic field is important in the development of Biomagnetic Fluid Dynamics (BFD). Most existing studies analyze flows in steady state conditions and the effect of gravitational acceleration has not been addressed. For the mathematical model, the Navier-Stokes equations, energy equation and an additional term that describes the magnetic force and gravitational effect which is consistent with the principles of ferrohydrodynamics (FHD) are employed. The nonlinear governing differential equations are non-dimensionalized and then discretized based on a finite difference technique on a staggered grid system. The solution of these problems is obtained numerically using pressure correction method with SIMPLE algorithm. For a range of governing parameters such as the magnetic number MnF and Richardson number Ri, the numerical results show that the gravitational acceleration has a profound effect on both velocity and temperature profiles. The streamlines plotted also show that vortices appear near the lower plate where the magnetic source is located.
Abstract: This paper investigates the effect of gravitational acceleration on unsteady biomagnetic fluid flow in a channel under the influence of a spatially varying magnetic field. The study on biomagnetic fluid under the action of an applied magnetic field is important in the development of Biomagnetic Fluid Dynamics (BFD). Most existing studies analyze fl...
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Multisorted Tree Algebra
Erick Patrick Zobo,
Marcel Fouda Ndjodo
Issue:
Volume 3, Issue 6, December 2014
Pages:
295-302
Received:
24 November 2014
Accepted:
5 December 2014
Published:
16 December 2014
Abstract: This paper introduces basic concepts describing a hierarchical algebraic structure called multisorted tree algebra. This structure is constructed by placing multisorted algebra at the bottom of a hierarchy and placing at other intermediate nodes the aggregation of algebras placed at their immediate subordinate nodes. These constructions are different from the one of subalgebras, homomorphic images and product algebras used to characterize varieties in universal algebra theory. The resulting hierarchical algebraic structures cannot be easily classified in common universal algebra varieties. The aggregation method and the fundamental properties of the aggregated algebras have been presented with an illustrative example. Multisorted tree algebras spans multisorted algebra concepts and can be used as modelling framework for building hierarchical abstract data types for information processing in organizations.
Abstract: This paper introduces basic concepts describing a hierarchical algebraic structure called multisorted tree algebra. This structure is constructed by placing multisorted algebra at the bottom of a hierarchy and placing at other intermediate nodes the aggregation of algebras placed at their immediate subordinate nodes. These constructions are differe...
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(α, β)- Infimum and Supremum of Q- Fuzzy Subgroups over Implication Operator of M* ([0,1])
R. Nagarajan,
K. Balamurugan
Issue:
Volume 3, Issue 6, December 2014
Pages:
303-306
Received:
25 August 2014
Accepted:
18 December 2014
Published:
23 December 2014
Abstract: In this paper, the concept of (α,β)- inf-sup Q-fuzzy set is generalized and there after we defined (α,β)- inf-sup Q-fuzzy group and a few of its properties are discussed. On the other hand we give the definition of the upper normal Q- fuzzy subgroups, and study the main theorem for this. We also give new results on this subject. Characterization of inf-sup normal Q-fuzzy subgroups also investigated.
Abstract: In this paper, the concept of (α,β)- inf-sup Q-fuzzy set is generalized and there after we defined (α,β)- inf-sup Q-fuzzy group and a few of its properties are discussed. On the other hand we give the definition of the upper normal Q- fuzzy subgroups, and study the main theorem for this. We also give new results on this subject. Characterization of...
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Evaluation of Holomorphic Ackermanns
Issue:
Volume 3, Issue 6, December 2014
Pages:
307-314
Received:
21 November 2014
Accepted:
17 December 2014
Published:
27 December 2014
Abstract: Holomorphic extension of the Ackermann function is suggested. Algorithms of evaluation of tetration and pentation are discussed and illustrated with explicit plots and complex maps.
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An Approximate Analytical Solution of Higher-Order Linear Differential Equations with Variable Coefficients Using Improved Rational Chebyshev Collocation Method
Mohamed A. Ramadan,
Kamal R. Raslan,
Mahmoud A. Nassar
Issue:
Volume 3, Issue 6, December 2014
Pages:
315-322
Received:
5 December 2014
Accepted:
18 December 2014
Published:
27 December 2014
Abstract: The purpose of this paper is to investigate the use of rational Chebyshev (RC) collocation method for solving high-order linear ordinary differential equations with variable coefficients. Using the rational Chebyshev collocation points, this method transforms the high-order linear ordinary differential equations and the given conditions to matrix equations with unknown rational Chebyshev coefficients. These matrices together with the collocation method are utilized to reduce the solution of higher-order ordinary differential equations to the solution of a system of algebraic equations. The solution is obtained in terms of RC functions. Numerical examples are given to demonstrate the validity and applicability of the method. The obtained numerical results are compared with others existing methods and the exact solution where it shown to be very attractive and maintains better accuracy.
Abstract: The purpose of this paper is to investigate the use of rational Chebyshev (RC) collocation method for solving high-order linear ordinary differential equations with variable coefficients. Using the rational Chebyshev collocation points, this method transforms the high-order linear ordinary differential equations and the given conditions to matrix e...
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An Analytical Treatment to Fractional Gas Dynamics Equation
Mohamed S. Al-luhaibi,
Nahed A. Saker
Issue:
Volume 3, Issue 6, December 2014
Pages:
323-329
Received:
24 October 2014
Accepted:
9 December 2014
Published:
29 December 2014
Abstract: In this paper, the new iterative method (NIM) is applied to solve nonlinear fractional gas dynamics equation. Further, a coupling of the Sumudu transform and Adomian decomposion (STADM) is used to get an approximate solution of the same problem. The results obtained by the two methods are found to be in agreement. Therefore, the NIM may be considered efficient method for finding approximate solutions of both linear and nonlinear fractional differential equations.
Abstract: In this paper, the new iterative method (NIM) is applied to solve nonlinear fractional gas dynamics equation. Further, a coupling of the Sumudu transform and Adomian decomposion (STADM) is used to get an approximate solution of the same problem. The results obtained by the two methods are found to be in agreement. Therefore, the NIM may be consid...
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The Line Method Combined with Spectral Chebyshev for Space-Time Fractional Diffusion Equation
I. K. Youssef,
A. M. Shukur
Issue:
Volume 3, Issue 6, December 2014
Pages:
330-336
Received:
13 November 2014
Accepted:
27 November 2014
Published:
31 December 2014
Abstract: The Method of Lines Combined with Chebyshev Spectral Method respect to weighted residual (Collocation Points) for Space-Time fractional diffusion equation is considered, the direct way will be used for approximating Time fractional and the expiation of shifted first kind of Chebyshev polynomial will be used to approximate unknown functions, the structure of the systems and the matrices will be fund, the algorithm steps is illustrated, The tables and figures of the results of the implementation by using this method at different values of fractional order will be shown, with the helping of programs of matlab.
Abstract: The Method of Lines Combined with Chebyshev Spectral Method respect to weighted residual (Collocation Points) for Space-Time fractional diffusion equation is considered, the direct way will be used for approximating Time fractional and the expiation of shifted first kind of Chebyshev polynomial will be used to approximate unknown functions, the str...
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The Taylor Vortex and the Driven Cavity Problems in the Stream Function-Vorticity Formulation
Blanca Bermúdez Juárez,
René Posadas Hernández,
Wuiyevaldo Fermín Guerrero Sánchez
Issue:
Volume 3, Issue 6, December 2014
Pages:
337-342
Received:
15 December 2014
Accepted:
24 December 2014
Published:
4 January 2015
Abstract: In this work, two problems will be presented: The Taylor Vortex problem and the Driven Cavity problem. Both problems are solved using the Stream function-Vorticity formulation of the Navier-Stokes equations in 2D. Results are obtained using two methods: A fixed point iterative method and another one working with matrixes A and B resulting from the discretization of the Laplacian and the advective term, respectively. This second method resulted faster than the fixed point iterative one.
Abstract: In this work, two problems will be presented: The Taylor Vortex problem and the Driven Cavity problem. Both problems are solved using the Stream function-Vorticity formulation of the Navier-Stokes equations in 2D. Results are obtained using two methods: A fixed point iterative method and another one working with matrixes A and B resulting from the ...
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A Cubic Bézier Model with Shape Parameters
Issue:
Volume 3, Issue 6, December 2014
Pages:
343-348
Received:
16 December 2014
Accepted:
28 December 2014
Published:
8 January 2015
Abstract: A novel extension of the cubic Bézier curve with two shape parameters is presented in this work. The proposed curve is still a cubic polynomial model, which has simpler structure than other similar models. The proposed curve has the same properties with the usual cubic Bézier curve and its shape can be adjusted by altering values of the two shape parameters while the control points are fixed. With the two shape parameters, the proposed curve can approach to its control polygon farther or closer. The corresponding surface with four shape parameters has the similar properties with the proposed curve and enjoys the shape adjustable property.
Abstract: A novel extension of the cubic Bézier curve with two shape parameters is presented in this work. The proposed curve is still a cubic polynomial model, which has simpler structure than other similar models. The proposed curve has the same properties with the usual cubic Bézier curve and its shape can be adjusted by altering values of the two shape p...
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