TY - JOUR
T1 - Dynamics of vortices in Ginzburg-Landau theories with applications to superconductivity
AU - Weinan, E.
N1 - Funding Information:
Much of the work presented here was done during my visits to the Argonne N~ional Lab under the support of the Applied Mathematical Science subprogram of the Office of Energy Research, US Department of Energy contract W-31-109-Eng-38. I am especially grateful to Hans Kaper for his hospitality and many stimulating discussions. I also want to thank J. Chapman and A. Majda for suggestions on improving the first draft of this paper.
PY - 1994/10/15
Y1 - 1994/10/15
N2 - We study the dynamics of vortices in time-dependent Ginzburg-Landau theories in the asymptotic limit when the vortex core size is much smaller than the inter-vortex distance. We derive reduced systems of ODEs governing the evolution of these vortices. We then extend these to study the dynamics of vortices in extremely type-II superconductors. Dynamics of vortex lines is also considered. For the simple Ginzburg-Landau equation without the magnetic field, we find that the vortices are stationary in the usual diffusive scaling, and obey remarkably simple dynamic laws when time is speeded up by a logarithmic factor. For columnar vortices in superconductors, we find a similar dynamic law with a potential which is screened by the current. For curved vortex lines in curerconductors, we find that the vortex lines move in the direction of the normal with a speed proportional to the curvature. Comparisons are made with the previous results of John Neu.
AB - We study the dynamics of vortices in time-dependent Ginzburg-Landau theories in the asymptotic limit when the vortex core size is much smaller than the inter-vortex distance. We derive reduced systems of ODEs governing the evolution of these vortices. We then extend these to study the dynamics of vortices in extremely type-II superconductors. Dynamics of vortex lines is also considered. For the simple Ginzburg-Landau equation without the magnetic field, we find that the vortices are stationary in the usual diffusive scaling, and obey remarkably simple dynamic laws when time is speeded up by a logarithmic factor. For columnar vortices in superconductors, we find a similar dynamic law with a potential which is screened by the current. For curved vortex lines in curerconductors, we find that the vortex lines move in the direction of the normal with a speed proportional to the curvature. Comparisons are made with the previous results of John Neu.
UR - http://www.scopus.com/inward/record.url?scp=43949154992&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=43949154992&partnerID=8YFLogxK
U2 - 10.1016/0167-2789(94)90298-4
DO - 10.1016/0167-2789(94)90298-4
M3 - Article
AN - SCOPUS:43949154992
SN - 0167-2789
VL - 77
SP - 383
EP - 404
JO - Physica D: Nonlinear Phenomena
JF - Physica D: Nonlinear Phenomena
IS - 4
ER -