The dynamics and interaction of quantized vortices in Ginzburg-Landau-Schroedinger equation
主 题: The dynamics and interaction of quantized vortices in Ginzburg-Landau-Schroedinger equation
报告人: Weizhu Bao (National University of Singapore)
时 间: 2008-12-30 下午 4:00 - 5:00
地 点: 理科一号楼 1303
In this talk, we study the dynamical laws of quantized vortex interactions in the Ginzburg-Landau-Schroedinger equation (GLSE) analytically and numerically. We begin with a review of the reduced dynamic laws governing the motion of vortex centers in GLSE and solve the nonlinear ordinary differential equations (ODEs) of the reduced dynamic laws analytically with a few types of initial data. By adopting the polar coordinates so as to effectively match and resolve the nonzero far-field conditions in phase space and applying a time-splitting technique for decoupling the nonlinearity in the GLSE, we propose an efficient and accurate numerical method for solving GLSE in two dimensions with nonzero far field conditions. By directly simulating the GLSE with our new numerical method for GLSE, we can compare quantized vortex interaction patterns of GLSE with those from the reduced dynamic laws qualitatively and quantitatively. Some conclusive findings on issues such as the stability of quantized vortex, interaction of two vortices, dynamics of the quantized vortex lattice and the motion of vortex with an inhomogeneous external potential are obtained, and discussions on numerical and theoretical results are made to provide further understanding of vortex interactions in GLSE. Finally, the vortex motion under an inhomogeneous potential in GLSE is also studied.
This is a joint work with Qiang Du and Yanzhi Zhang.
