Gravitational Field Equations with Cross-terms and Static Equilibrium Configurations

Considering Einstein's equations modified by additional cross-terms we calculate spherically symmetric equilibrium configurations of cold degenerated matter. The effects of such modifications proposed by TREDER [5] to describe properties of a unitary field theory depend on the sign of the coupling and on some critical energy density. If this density is higher than the nuclear density, we do not find significantly larger equilibrium masses than in general relativity. However the modifications of the gravitional dynamics resulting from the cross-terms become physically significant.     

Time‐dependent flow across a step: the slip with friction boundary condition

The paper studies numerically the slip with friction boundary condition in the time‐dependent incompressible Navier–Stokes equations. Numerical tests on two‐ and three‐dimensional channel flows across a step using this boundary condition on the bottom wall are performed. The influence of the friction parameter on the flow field is studied and the results are explained according to the physics of the flow. Due to the stretching and tilting of vortices, the three‐dimensional results differ in many respects from the two‐dimensional ones. Copyright © 2005 John Wiley & Sons, Ltd.