The Experts below are selected from a list of 176280 Experts worldwide ranked by ideXlab platform
P. Zhuang - One of the best experts on this subject based on the ideXlab platform.
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Finite element method for space-time fractional diffusion equation
Numerical Algorithms, 2015Co-Authors: Libo Feng, P. Zhuang, Ian Turner, Yuantong GuAbstract:In this paper, we consider two types of space-time fractional diffusion equations(STFDE) on a Finite Domain. The equation can be obtained from the standard diffusion equation by replacing the second order space derivative by a Riemann-Liouville fractional derivative of order s (1
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numerical methods for the variable order fractional advection diffusion equation with a nonlinear source term
SIAM Journal on Numerical Analysis, 2009Co-Authors: P. Zhuang, Ian TurnerAbstract:In this paper, we consider a variable-order fractional advection-diffusion equation with a nonlinear source term on a Finite Domain. Explicit and implicit Euler approximations for the equation are proposed. Stability and convergence of the methods are discussed. Moveover, we also present a fractional method of lines, a matrix transfer technique, and an extrapolation method for the equation. Some numerical examples are given, and the results demonstrate the effectiveness of theoretical analysis.
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Finite difference approximations for the fractional fokker planck equation
Applied Mathematical Modelling, 2009Co-Authors: S Chen, P. ZhuangAbstract:The fractional Fokker–Planck equation has been used in many physical transport problems which take place under the influence of an external force field. In this paper we examine some practical numerical methods to solve a class of initial-boundary value problems for the fractional Fokker–Planck equation on a Finite Domain. The solvability, stability, consistency, and convergence of these methods are discussed. Their stability is proved by the energy method. Two numerical examples are also presented to evaluate these Finite difference methods against the exact analytical solutions.
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Finite difference approximation for two dimensional time fractional diffusion equation
Journal of Algorithms & Computational Technology, 2007Co-Authors: P. ZhuangAbstract:Fractional diffusion equations have recently been used to model problems in physics, hydrology, biology and other areas of application. In this paper, we consider a two-dimensional time fractional diffusion equation (2D-TFDE) on a Finite Domain. An implicit difference approximation for the 2D-TFDE is presented. Stability and convergence of the method are discussed using mathematical induction. Finally, a numerical example is given. The numerical result is in excellent agreement with our theoretical analysis.
Renaud De Landtsheer - One of the best experts on this subject based on the ideXlab platform.
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solving csp including a universal quantification
Lecture Notes in Computer Science, 2004Co-Authors: Renaud De LandtsheerAbstract:This paper presents a method to solve constraint satisfaction problems including a universally quantified variable with Finite Domain. Similar problems appear in the field of bounded model checking. The presented method is built on top of the Mozart constraint programming platform. The main principle of the algorithm is to consider only representative values in the Domain of the quantified variable. The presented algorithm is similar to a branch and bound search. Significant improvements have been achieved both in memory consumption and execution time compared to a naive approach.
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MOZ - Solving CSP including a universal quantification
Lecture Notes in Computer Science, 2004Co-Authors: Renaud De LandtsheerAbstract:This paper presents a method to solve constraint satisfaction problems including a universally quantified variable with Finite Domain. Similar problems appear in the field of bounded model checking. The presented method is built on top of the Mozart constraint programming platform. The main principle of the algorithm is to consider only representative values in the Domain of the quantified variable. The presented algorithm is similar to a branch and bound search. Significant improvements have been achieved both in memory consumption and execution time compared to a naive approach.
Yaolin Jiang - One of the best experts on this subject based on the ideXlab platform.
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analytical solutions for the multi term time space fractional advection diffusion equations with mixed boundary conditions
Nonlinear Analysis-real World Applications, 2013Co-Authors: Xiaoli Ding, Yaolin JiangAbstract:Abstract In this paper, we consider the analytical solutions of multi-term time–space fractional advection–diffusion equations with mixed boundary conditions on a Finite Domain. The technique of spectral representation of the fractional Laplacian operator is used to convert the multi-term time–space fractional advection–diffusion equations into multi-term time fractional ordinary differential equations. By applying Luchko’s theorem to the resulting fractional ordinary differential equations, the desired analytical solutions are obtained. Our results are applied to derive the analytical solutions of some special cases to demonstrate their practical applications.
Jing Wu - One of the best experts on this subject based on the ideXlab platform.
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minimum Domain impulse theory for unsteady aerodynamic force
Physics of Fluids, 2018Co-Authors: Linlin Kang, Weidong Su, Jing WuAbstract:We extend the impulse theory for unsteady aerodynamics from its classic global form to Finite-Domain formulation then to minimum-Domain form and from incompressible to compressible flows. For incompressible flow, the minimum-Domain impulse theory raises the finding of Li and Lu [“Force and power of flapping plates in a fluid,” J. Fluid Mech. 712, 598–613 (2012)] to a theorem: The entire force with discrete wake is completely determined by only the time rate of impulse of those vortical structures still connecting to the body, along with the Lamb-vector integral thereof that captures the contribution of all the rest disconnected vortical structures. For compressible flows, we find that the global form in terms of the curl of momentum ∇ × (ρu), obtained by Huang [Unsteady Vortical Aerodynamics (Shanghai Jiaotong University Press, 1994)], can be generalized to having an arbitrary Finite Domain, but the formula is cumbersome and in general ∇ × (ρu) no longer has discrete structures and hence no minimum-Domain...
Silke Guenther - One of the best experts on this subject based on the ideXlab platform.
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New Scaling Laws of Shear-Free Turbulent Diffusion and Diffusion-Waves
IUTAM Symposium on Reynolds Number Scaling in Turbulent Flow, 2004Co-Authors: Martin Oberlack, Silke GuentherAbstract:We consider the problem of turbulence generation at a vibrating grid in the x 2-x 3 plane. Turbulence diffuses in the x 1 direction. Analyzing the multi-point correlation equation using Lie-group analysis we find three different solutions (scaling laws): classical diffusion-like solution (heat equation like), decelerating diffusion-wave solution and Finite Domain diffusion due to rotation. All solution have been obtained using Lie- group (symmetry) methods. It is shown that models based on Reynolds averaging are only capable to model either the diffusion-like solution or the decelerating diffusion-wave solution. The latter solution is only admitted under certain algebraic constraints on the model constants. Turbulent diffusion on a Finite Domain induced by rotation is not admitted by any of the classical models.
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shear free turbulent diffusion classical and new scaling laws
Fluid Dynamics Research, 2003Co-Authors: Martin Oberlack, Silke GuentherAbstract:Abstract We consider the problem of turbulence generation at a vibrating grid in the x 2 – x 3 plane. Turbulence diffuses in the x 1 -direction. Analyzing the multi-point correlation equation using Lie-group analysis, we find three different invariant solutions (scaling laws): classical diffusion-like solution (heat equation like), decelerating diffusion-wave solution and Finite Domain diffusion due to rotation. All solutions have been obtained using Lie-group (symmetry) methods. It is shown that if only one spatial dimension is considered, models based on Reynolds averaging are only capable to model either the diffusion-like solution or the decelerating diffusion-wave solution. The latter solution is only admitted under certain algebraic constraints on the model constants; e.g. in case of the K – e model the model constants need to obey the relation c e 2 σ e / σ K =2. Turbulent diffusion on a Finite Domain induced by rotation is not admitted by any of the classical models. Finally, in the appendix it is shown that Lele's transformation (Phys. Fluids 28(1) (1985) 64) leads to a complete analytic solution of the steady diffusion problem modelled by the K – e equation.