Abstract : In this paper origin of Saturn rings due to interaction of the protoplanetary icy particles moving on chaotic orbits with the planetary magnetic field is presented. Finally, all the particles orbits coming to the magnetic equator plane due to diamagnetic force of expulsion where locked within three-dimensional magnetic well due to the Meissner phenomenon and Abrikosov quantum vortex for a superconductor. The final picture is similar to the picture of iron particles forms the same shape around a magnet on laboratory table. The suggested model is confirmed by the data of the Cassini mission
Full article

Abstract : In this paper, the construction of Exponentially-Fitted (EF) versions of the third-order Adam-Bashfort method for oscillatory problems is presented. The convergence and stability properties of the constructed methods are investigated. Numerical experiments confirming the theoretical expectations regarding the constructed methods compared with other standard classical methods are also presented.
Full article

Abstract : In this paper, we considered the well-known parabolic velocity field of Poiseuille flow, as a Riemannian manifold. Calculations of both first and second fundamental forms allowed mean and Gauss curvatures of the paraboloid of revolution, to be calculated. From the Lamb form of Navier-Stokes equation, we calculated both the flexion product and enstrophy giving the Lamb vector divergence as a function of Gauss curvature of the laminar velocity field. These results allowed the stability of Poiseuille flow to be investigated through the influence of maximum flow curvature and the Lamb vector divergence. We showed that classical critical Reynolds number approach is not enough to explain the change from laminar to transition flow regime. A new method, based on Gauss curvature calculation of the Riemannian manifold is then proposed.
Full article