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Juisheng Chen - One of the best experts on this subject based on the ideXlab platform.
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analytical power Series Solution for contaminant transport with hyperbolic asymptotic distance dependent dispersivity
Journal of Hydrology, 2008Co-Authors: Juisheng Chen, Chingping Liang, Chenchung ChiangAbstract:Summary A hyperbolic asymptotic function, which characterizes that the dispersivity initially increases with travel distance and eventually reaches an asymptotic value at long travel distance, is adopted and incorporated into the general advection–dispersion equation for describing scale-dependent solute transport in porous media in this study. An analytical technique for solving advection–dispersion equation with hyperbolic asymptotic distance-dependent dispersivity is presented. The analytical Solution is derived by applying the extended power Series method coupling with the Laplace transform. The developed analytical Solution is compared with the corresponding numerical Solution to evaluate its accuracy. Results demonstrate that the breakthrough curves at different locations obtained from the derived power Series Solution agree closely with those from the numerical Solution. Moreover, breakthrough curves obtained from the hyperbolic asymptotic dispersivity model are compared with those obtained from the constant dispersivity model to scrutinize the relationship of the transport parameters derived by Mishra and Parker [Mishra, S., Parker, J.C., 1990. Analysis of solute transport with a hyperbolic scale dependent dispersion model. Hydrol. Proc. 4(1), 45–47]. The result reveals that the relationship postulated by Mishra and Parker [Mishra, S., Parker, J.C., 1990. Analysis of solute transport with a hyperbolic scale dependent dispersion model. Hydrol. Proc. 4(1), 45–47] is only valid under conditions with small dimensionless asymptotic dispersivity (aa) and large dimensionless characteristic half length (b).
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two dimensional power Series Solution for non axisymmetrical transport in a radially convergent tracer test with scale dependent dispersion
Advances in Water Resources, 2007Co-Authors: Juisheng ChenAbstract:Abstract It has been known for many years that dispersivity increases with solute travel distance in a subsurface environment. The increase of dispersivity with solute travel distance results from the significant variation of hydraulic properties of heterogeneous media and was identified in the literature as scale-dependent dispersion. This study presents an analytical Solution for describing two-dimensional non-axisymmetrical solute transport in a radially convergent flow tracer test with scale-dependent dispersion. The power Series technique coupling with the Laplace and finite Fourier cosine transform has been applied to yield the analytical Solution to the two-dimensional, scale-dependent advection–dispersion equation in cylindrical coordinates with variable-dependent coefficients. Comparison between the breakthrough curves of the power Series Solution and the numerical Solutions shows excellent agreement at different observation points and for various ranges of scale-related transport parameters of interest. The developed power Series Solution facilitates fast prediction of the breakthrough curves at any observation point.
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two dimensional laplace transformed power Series Solution for solute transport in a radially convergent flow field
Advances in Water Resources, 2003Co-Authors: Juisheng Chen, Chungmin LiaoAbstract:This paper presents an analytical Solution for two-dimensional non-axisymmetric solute transport in a radially convergent flow field. We applied a Laplace-transformed power Series (LTPS) technique to solve the two-dimensional advection-dispersion equation in cylindrical coordinates. The Solution is compared with a numerical Solution to evaluate its robustness and accuracy. The applicable Peclet number range of the developed power Series Solution is also examined. Results show that the LTPS technique can effectively and accurately handle the two-dimensional radial advection-dispersion equation for a Peclet number up to 60. The two-dimensional power Series Solution is appropriate for hydrogeologic circumstances where temporally and spatially continuous Solutions are demanded.
Hina Khan - One of the best experts on this subject based on the ideXlab platform.
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The explicit Series Solution of SIR and SIS epidemic models
Applied Mathematics and Computation, 2009Co-Authors: Hina Khan, Ram N. Mohapatra, Kuppalapalle Vajravelu, Shijun LiaoAbstract:In this paper the SIR and SIS epidemic models in biology are solved by means of an analytic technique for nonlinear problems, namely the homotopy analysis method (HAM). Both of the SIR and SIS models are described by coupled nonlinear differential equations. A one-parameter family of explicit Series Solutions are obtained for both models. This parameter has no physical meaning but provides us with a simple way to ensure convergent Series Solutions to the epidemic models. Our analytic results agree well with the numerical ones. This analytic approach is general and can be applied to get convergent Series Solutions of some other coupled nonlinear differential equations in biology.
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Series Solution to the thomas fermi equation
Physics Letters A, 2007Co-Authors: Hina KhanAbstract:Abstract Here an analytic technique, namely the homotopy analysis method (HAM), is employed to solve the non-linear Thomas–Fermi equation. A new kind of transformation is being used here which has improved the results in comparison with Liao's work. We also present the comparison of this work with some well-known results and prove the importance of this transformation and the freedom of HAM.
M M Alipour - One of the best experts on this subject based on the ideXlab platform.
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a power Series Solution for vibration and complex modal stress analyses of variable thickness viscoelastic two directional fgm circular plates on elastic foundations
Applied Mathematical Modelling, 2013Co-Authors: M Shariyat, M M AlipourAbstract:Abstract In the present paper, a power Series Solution is developed for free vibration and damping analyses of viscoelastic functionally graded plates with variable thickness on elastic foundations. It is assumed that the material properties of the functionally graded material (FGM) vary in the transverse and radial directions, simultaneously. Therefore, the presented Solution can be employed for the transversely-graded and radially-graded viscoelastic circular plates, as special cases. In addition to the edge conditions, the plate may be resting on a two-parameter elastic foundation. The complex modulus approach in combination with the elastic–viscoelastic correspondence principle is employed to obtain the Solution for various edge conditions. A sensitivity analysis including effects of various edge conditions, geometric parameters, coefficients of the elastic foundation, parameters of the functionally graded material, and material loss factor is carried out. In the present paper, concept of the complex modal stresses of the viscoelastic plates is discussed in detail.
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an elasticity equilibrium based zigzag theory for axisymmetric bending and stress analysis of the functionally graded circular sandwich plates using a maclaurin type Series Solution
European Journal of Mechanics A-solids, 2012Co-Authors: M M Alipour, M ShariyatAbstract:Abstract The available semi-analytical Solutions for bending and stress analysis of the composite/sandwich plates have mainly been proposed for rectangular plates with specific material properties and edge conditions. In the present paper, axisymmetric bending and stress analysis of circular functionally graded sandwich plates subjected to transversely distributed loads is performed. The governing equations are derived based on an elasticity-equilibrium-based (rather than the traditional constitutive-equations-based) zigzag theory. Therefore, both ideas of using the local variations of the displacement field and satisfying a priori the continuity conditions of the transverse stresses at the layer interfaces for predicting the global and local responses of the sandwich circular plates are employed, for the first time. The resulting governing equations are then solved by a semi-analytical Maclaurin-type power-Series Solution. Each layer of the plate may be made of functionally graded materials. The transverse shear and normal stresses are determined based on the three-dimensional theory of elasticity. Comparisons made with results of a numerical finite element code (ABAQUS software) reveal that even for thick sandwich plates with soft cores, accuracy of results of the present formulation is comparable with that of the three-dimensional theory of elasticity.
Shijun Liao - One of the best experts on this subject based on the ideXlab platform.
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A general approach to get Series Solution of non-similarity boundary-layer flows
Communications in Nonlinear Science and Numerical Simulation, 2009Co-Authors: Shijun LiaoAbstract:Abstract An analytic method for strongly non-linear problems, namely the homotopy analysis method (HAM), is applied to give convergent Series Solution of non-similarity boundary-layer flows. As an example, the non-similarity boundary-layer flows over a stretching flat sheet are used to show the validity of this general analytic approach. Without any assumptions of small/large quantities, the corresponding non-linear partial differential equation with variable coefficients is transferred into an infinite number of linear ordinary differential equations with constant coefficients. More importantly, an auxiliary artificial parameter is used to ensure the convergence of the Series Solution. Different from previous analytic results, our Series Solutions are convergent and valid for all physical variables in the whole domain of flows. This work illustrates that, by means of the homotopy analysis method, the non-similarity boundary-layer flows can be solved in a similar way like similarity boundary-layer flows. Mathematically, this analytic approach is rather general in principle and can be applied to solve different types of non-linear partial differential equations with variable coefficients in science and engineering.
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The explicit Series Solution of SIR and SIS epidemic models
Applied Mathematics and Computation, 2009Co-Authors: Hina Khan, Ram N. Mohapatra, Kuppalapalle Vajravelu, Shijun LiaoAbstract:In this paper the SIR and SIS epidemic models in biology are solved by means of an analytic technique for nonlinear problems, namely the homotopy analysis method (HAM). Both of the SIR and SIS models are described by coupled nonlinear differential equations. A one-parameter family of explicit Series Solutions are obtained for both models. This parameter has no physical meaning but provides us with a simple way to ensure convergent Series Solutions to the epidemic models. Our analytic results agree well with the numerical ones. This analytic approach is general and can be applied to get convergent Series Solutions of some other coupled nonlinear differential equations in biology.
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A Series Solution of the Unsteady Von Kármán Swirling Viscous Flows
Acta Applicandae Mathematicae, 2007Co-Authors: Shijun LiaoAbstract:A new analytic technique is applied to solve the unsteady viscous flow due to an infinite rotating disk, governed by a set of two fully coupled nonlinear partial differential equations deduced directly from the exact Navier-Stokes equations. The system of coupled nonlinear partial differential equations is replaced by a sequence of uncoupled systems of linear ordinary differential equations. Different from all other previous analytic results, our Series Solution is accurate and valid for all time in the whole spatial region. Accurate expressions for skin friction coefficients are given, which are valid for all time. Such kind of Series Solutions have not been reported, to the best of our knowledge.
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explicit Series Solution of travelling waves with a front of fisher equation
Chaos Solitons & Fractals, 2007Co-Authors: Yue Tan, Shijun LiaoAbstract:Abstract In this paper, an analytic technique, namely the homotopy analysis method, is employed to solve the Fisher equation, which describes a family of travelling waves with a front. The explicit Series Solution for all possible wave speeds 0 c c
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Series Solution of unsteady boundary layer flows of non newtonian fluids near a forward stagnation point
Journal of Non-newtonian Fluid Mechanics, 2006Co-Authors: Shijun Liao, Ioan PopAbstract:Abstract In this paper, the unsteady viscous flow of non-Newtonian fluids near the forward stagnation point of a two-dimensional body is studied analytically. By using the homotopy analysis method, a convergent Series Solution is obtained, which is uniformly valid for all dimensionless time in the whole spatial region 0 ≤ η ∞ . Besides, the effects of integral power-law index of the non-Newtonian fluids on the flow are investigated. To the best of our knowledge, such kind of Series Solutions have never been reported for this problem.
Guy Bonnet - One of the best experts on this subject based on the ideXlab platform.
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A Series Solution for the effective properties of incompressible viscoelastic media
International Journal of Solids and Structures, 2014Co-Authors: H. Hoang-duc, Guy BonnetAbstract:This paper presents a Series Solution for the homogenization problem of a linear viscoelastic periodic incompressible composite. The method uses the Laplace transform and the correspondence principle which are combined with the classical expansion along Neumann Series of the Solution of the periodic elasticity problem in Fourier space. The terms of the Neumann Series appear as decoupled, containing geometry dependent terms and viscoelastic properties dependent terms which are polynomial fractions whose inverse Laplace transforms are provided explicitly.
