Numerical studies on quantized vortex dynamics in superfludity and superconductivity

Abstract

This thesis mainly contains two topics. The first is to conduct extensive numerical studies for the vortex dynamics and interactions in superfluidity and superconductivity via solving Ginzburg-Landau-Schrodinger equation (GLSE) on different 2-D bounded domains and under different boundary conditions. The second one is to study Gross-Pitaevskii equation (GPE) with angular momentum rotation term and/or the long-range dipole-dipole interaction both analytically and numerically in the whole space.