Amer Rasheed

Amer Rasheed, Imtiaz Ali

This article presents the phase dynamics of an inline long Josephson junction in voltage state under the influence of constant external magnetic field. Fractional calculus approach is used to model the evolution of the phase difference between the macroscopic wave functions of the two superconductors across the junction. The governing non-linear partial differential equation is then solved using finite difference-finite element schemes. Other quantities of interest like Josephson current density and voltage across the junction are also computed. The effects of various parameters in the model on phase difference, Josephson current density and voltage are analyzed graphically with the help of numerical simulations.

Amer Rasheed, Aziz Belmiloudi

In this article, we study the error and stability of the proposed numerical scheme in order to solve a two dimensional anisotropic phase-field model with convection and externally applied magnetic field in an isothermal solidification of binary alloys. The proposed numerical scheme is based on mixed finite element method satisfying the CFL condition. A particular application with real physical parameters of Nickel-Copper(Ni-Cu) is considered in order to validate the numerical scheme employed. The results of stability and error analysis substantiates complete accordance with the postulated theoretical error estimates which demonstrates the efficiency of the presented method.