@Article{CiCP-6-673,
author = {Sangbum Kim, Max Gunzburger, Janet Peterson and Chia-Ren Hu},
title = {Computational Investigation of the Effects of Sample Geometry on the Superconducting-Normal Phase Boundary and Vortex-Antivortex States in Mesoscopic Superconductors},
journal = {Communications in Computational Physics},
year = {2009},
volume = {6},
number = {4},
pages = {673--698},
abstract = {<p style="text-align: justify;">A computational study of superconducting states near the superconducting-normal
phase boundary in mesoscopic finite cylinders is presented. The computational
approach uses a finite element method to find numerical solutions of the linearized
Ginzburg-Landau equation for samples with various sizes, aspect ratios, and cross-sectional
shapes, i.e., squares, triangles, circles, pentagons, and four star shapes. The
vector potential is determined using a finite element method with two penalty terms
to enforce the gauge conditions that the vector potential is solenoidal and its normal
component vanishes at the surface(s) of the sample. The eigenvalue problem for the
linearized Ginzburg-Landau equations with homogeneous Neumann boundary conditions
is solved and used to construct the superconducting-normal phase boundary
for each sample. Vortex-antivortex (V-AV) configurations for each sample that accurately
reflect the discrete symmetry of each sample boundary were found through the
computational approach. These V-AV configurations are realized just within the phase
boundary in the magnetic field-temperature phase diagram. Comparisons are made
between the results obtained for the different sample shapes.</p>},
issn = {1991-7120},
doi = {https://doi.org/},
url = {http://global-sci.org/intro/article_detail/cicp/7700.html}
}