Studies of the formation of ne structures on free-surfaces in liquids, such as curvature singularities or interface pinching, demand that the motion of the interface must be computed very accurately. Boundary integral techniques are a popular choice in such studies because they reduce the dimension of the problem by one. On the other hand, the boundary integrals are singular, and their accurate...

The general solution of equations of saturated porous media with incompressible fluid for two dimensional axi-symmetric problem is obtained in the transformed domain. The Laplace and Hankel transforms have been used to investigate the problem. As an application of the approach concentrated source and source over circular region have been taken to show the utility of the approach. The transforme...

We examine gravitational waves in an isolated axi–symmetric reflexion symmetric NGT system. The structure of the vacuum field equations is analyzed and the exact solutions for the field variables in the metric tensor are found in the form of expansions in powers of a radial coordinate. We find that in the NGT axially symmetric case the mass of the system remains constant only if the system is s...

We derive all the axi-symmetric, vacuum and electrovac extremal isolated horizons. It turns out that for every horizon in this class, the induced metric tensor, the rotation 1-form potential and the pullback of the electromagnetic field necessarily coincide with those induced by the monopolar, extremal Kerr– Newman solution on the event horizon. We also discuss the general case of a symmetric, ...

We study models of axi-dilaton gravity in space-time geometries with torsion. We discuss conformal rescaling rules in both Riemannian and non-Riemannian formulations. We give static, spherically symmetric solutions and examine their singularity behaviour. PACS numbers: 04.50.+h, 04.20.Jb, 04.70.Bw E.mail: [email protected] E.mail: [email protected] 1

In connection with the recent proposal for possible singularity formation at the boundary for solutions of 3d axi-symmetric incompressible Euler’s equations (Luo and Hou, 2014a), we study models for the dynamics at the boundary and show that they exhibit a finite-time blow-up from smooth data.

We discuss the gravitationally interacting system of a thick domain wall and a black hole. We numerically solve the scalar field equation in the Schwarzschild spacetime and obtain a sequence of static axi-symmetric solutions representing thick domain walls. We find that, for the walls near the horizon, the Nambu–Goto approximation is no longer valid.

Let D denote the class of bounded real analytic plane domains with the symmetry of an ellipse. We prove that if Ω1,Ω2 ∈ D and if the Dirichlet spectra coincide, Spec(Ω1) = Spec(Ω2), then Ω1 = Ω2 up to rigid motion.

In this paper we present a mathematical analysis for the magneto hydrodynamic (MHD) axi-symmetric stagnation-point flow and heat transfer over a shrinking sheet which shrinks axi-symmetrically in its own plane. The governing partial differential equations along with the boundary conditions are first cast into a dimensionless form and then these equations are solved numerically by shooting techn...