International Journal of Partial Differential Equations
http://www.i-scholar.in/index.php/IjPDe
<p>International Journal of Partial Differential Equations is a peer-reviewed, open access journal that publishes original research articles as well as review articles related to all aspects of partial differential equations.</p>Hindawi Limiteden-USInternational Journal of Partial Differential Equations2356-7082Direct and Inverse Scattering Problems for Domains with Multiple Corners
http://www.i-scholar.in/index.php/IjPDe/article/view/98323
We proposed numerical methods for solving the direct and inverse scattering problems for domains with multiple corners. Both the near field and far field cases are considered. For the forward problem, the challenges of logarithmic singularity from Green's functions and corner singularity are both taken care of. For the inverse problem, an efficient and robust direct imaging method is proposed. Multiple frequency data are combined to capture details while not losing robustness.Songming HouYihong JiangYuan Cheng2015Development of a Nonlinear κ-ε Model Incorporating Strain and Rotation Parameters for Prediction of Complex Turbulent Flows
http://www.i-scholar.in/index.php/IjPDe/article/view/98326
The standard <em>Κ-ε</em> model has the deficiency of predicting swirling and vortical flows due to its isotropic assumption of eddy viscosity. In this study, a second-order nonlinear <em>Κ-ε</em> model is developed incorporating some new functions for the model coefficients to explore the models applicability to complex turbulent flows. Considering the realizability principle, the coefficient of eddy viscosity (<em>C</em><sub>μ</sub>) is derived as a function of strain and rotation parameters. The coefficients of nonlinear quadratic termare estimated considering the anisotropy of turbulence in a simple shear layer.Analytical solutions for the fundamental properties of swirl jet are derived based on the nonlinear <em>Κ-ε</em> model, and the values of model constants are determined by tuning their values for the best-fitted comparison with the experiments. The model performance is examined for two test cases: (i) for an ideal vortex (Stuart vortex), the basic equations are solved numerically to predict the turbulent structures at the vortex center and the (ii) unsteady 3D simulation is carried out to calculate the flow field of a compound channel. It is observed that the proposed nonlinear <em>Κ-ε</em> model can successfully predict the turbulent structures at vortex center, while the standard <em>Κ-ε</em> model fails.Themodel is found to be capable of accounting the effect of transverse momentum transfer in the compound channel through generating the horizontal vortices at the interface.Md. Shahjahan AliTakashi HosodaIchiro Kimura2015Weighted Pluricomplex Energy II
http://www.i-scholar.in/index.php/IjPDe/article/view/98334
We continue our study of the complex Monge-Ampere operator on the weighted pluricomplex energy classes. We give more characterizations of the range of the classes ξ<sub>χ</sub> by the complexMonge-Ampere operator. In particular, we prove that a nonnegative Borelmeasure μ is theMonge-Ampere of a unique function φεξ<sub>χ</sub> if and only if χ(ξ<sub>χ</sub>)CL<sup>1</sup> (δμ). Then we show that if μ = (dd<sup>c</sup>φ)<sup>η</sup> for some φεξ<sub>χ</sub> then μ = (dd<sup>c</sup>u)<sup>η</sup> for some φεξ<sub>χ</sub>, where f is given boundary data. If moreover the nonnegative Borel measure μ is suitably dominated by the Monge-Ampere capacity, we establish a priori estimates on the capacity of sublevel sets of the solutions. As a consequence, we give a priori bounds of the solution of the Dirichlet problemin the case when the measure has a density in some Orlicz space.Slimane Benelkourchi2015