We construct exact solutions to the Bianchi equations on a flat spacetime background. When the constraints are satisfied, these solutions represent inand outgoing linearized gravitational radiation. We then consider the Bianchi equations on a subset of flat spacetime of the form [0, T ] × BR , where BR is a ball of radius R, and analyse different kinds of boundary conditions on ∂BR . Our main r...

A model is proposed of a collapsing quasi-spherical radiating star with matter content as shearfree isotropic fluid undergoing radial heat-flow with outgoing radiation. To describe the radiation of the system, we have considered both plane symmetric and spherical Vaidya solutions. Physical conditions and thermodynamical relations are studied using local conservation of momentum and surface red-...

The intent of this analysis is to explore the influence of thermal radiation paired with variable thermal conductivity on MHD micropolar fluid flow over an upper surface. The novelty of the present model is to consider the fluid flow along an upper horizontal surface of a paraboloid of revolution (uhspr) with the porous medium.  This physical phenomenon is described by a set of coupled...

A numerical analysis used to simulate the effects of wavy surfaces and thermal radiation on natural convection heat transfer boundary layer flow over an inclined wavy plate has been investigated. A simple coordinate transformation is employed to transform the complex wavy surface into a flat plate. The boundary layer equations and the boundary conditions are discretized by the finite difference...

The Helmholtz equation is solved within a three-dimensional rectangular duct with a sound source at the duct entrance plane, local admittance conditions on the side walls, and a new, nonlocal radiation boundary condition at the duct exit plane. The formulation employs a truncation of an infinite matrix, the generalized modal admittance tensor, that represents the transformation of the modal pre...

Solutions of linear elliptic partial differential equations in unbounded domains can be represented by boundary potentials if they satisfy certain conditions at infinity. These radiation conditions depend on the fundamental solution chosen for the integral representation. We prove some basic results about radiation conditions in a rather general framework. Fundamental solutions G are considered...

In the context of convection-di usion equation, we consider the use of open boundary conditions (also called radiation boundary conditons) in Block GaussSeidel algorithms. Theoretical results and numerical tests show that the convergence is thus accelerated.

This work examines the small-scale E and B patterns of the Cosmic Microwave Background Radiation (CMBR) polarization anisotropy. Particularly, we address the topological natures of the E and B modes, and how one may make use of the local measurements of Stokes parameters to separate these two modes in the real space. The analysis of a local map in the Fourier space for separating the E and B mo...

We study zero-temperature Ising Glauber Dynamics, on 2D slabs of thickness k ≥ 2. In this model, ±1-valued spins at integer sites update according to majority vote dynamics with two opinions. We show that all spins reaches a final state (that is, the system fixates) for k = 2 under free boundary conditions and for k = 2 or 3 under periodic boundary conditions. For thicker slabs there are sites ...