Recent studies of impinging jet flows have shown that momentum and heat transfer can be significantly improved if the jet flow is pulsed (Zumbrunnen, 1996). Moreover, when the jet holes are elliptical, jet free surfaces are formed into a helical structure. These helical structures in a jet flow can be readily observed by squeezing a garden hose into an elliptic shape. Upon pulsating the jet flo...

the mordell-weil theorem states that the group of rational points‎ ‎on an elliptic curve over the rational numbers is a finitely‎ ‎generated abelian group‎. ‎in our previous paper, h‎. ‎daghigh‎, ‎and s‎. ‎didari‎, on the elliptic curves of the form $ y^2=x^3-3px$‎, ‎‎bull‎. ‎iranian math‎. ‎soc‎.‎‎ 40 (2014)‎, no‎. ‎5‎, ‎1119--1133‎.‎, ‎using selmer groups‎, ‎we have shown that for a prime $p$...

We present a method for construction of the topological derivatives in plane elasticity. It is assumed that a hole is created in the subdomain of the elastic body which is filled out with isotropic material. The asymptotic analysis of elliptic boundary value problems in singularly perturbed geometrical domains is used in order to derive the asymptotics of the shape functionals depending on the ...

A new algorithm for solving the general relativistic MHD equations is described in this paper. We design our scheme to incorporate black hole excision with smooth boundaries, and to simplify solving the combined Einstein and MHD equations with AMR. The fluid equations are solved using a finite difference Convex ENO method. Excision is implemented using overlapping grids. Elliptic and hyperbolic...

This paper is concerned with the Einstein equations in axisymmetric vacuum spacetimes. We consider numerical evolution schemes that solve the constraint equations as well as elliptic gauge conditions at each time step. We examine two such schemes that have been proposed in the literature and show that some of their elliptic equations are indefinite, thus potentially admitting nonunique solution...

Two distinct redistribution grids - adaptation techniques, spring analogy and elliptic grid generator are applied to two-dimensional steady, inviscid, shocked flows, and the ability of each technique is examined and compared. Euler equations are solved base on Roe's Reimann solver approach to simulate supersonic flow around a sphere, transonic flow about an airfoil and supersonic flow in a symm...

Recent progress in the understanding of the statistical nature of black hole entropy shows that the counting functions in certain classes of models are determined by automorphic forms of higher rank. In this paper we combine these results with Langlands’ reciprocity conjecture to view black holes as probes of the geometry of spacetime. This point of view can be applied in any framework leading ...

Self-adjoint extensions of elliptic operators are used to model the solution of a partial differential equation defined in a singularly perturbed domain. The asymptotic expansion of the solution of a Laplacian with respect to a small parameter ε is first performed in a domain perturbed by the creation of a small hole. The resulting singular perturbation is approximated by choosing an appropriat...

This paper treats boundary conditions on black hole horizons for the full 3+1D Einstein equations. Following a number of authors, the apparent horizon is employed as the inner boundary on a space slice. It is emphasized that a further condition is necessary for the system to be well posed; the “prescribed curvature conditions” are therefore proposed to complete the coordinate conditions at the ...