Numerical analysis of a mean field model of superconducting vortices

2001 ◽  
Vol 21 (1) ◽  
pp. 1-51 ◽  
Author(s):  
C. M. Elliott
Keyword(s):  
Numerical Analysis ◽  
Field Model ◽  
Mean Field ◽  
Mean Field Model ◽  
Superconducting Vortices

A mean-field model of superconducting vortices

1996 ◽  
Vol 7 (2) ◽  
pp. 97-111 ◽  
Author(s):  
S. J. Chapman ◽  
J. Rubinstein ◽  
M. Schatzman
Keyword(s):  
Steady State ◽  
Field Model ◽  
Local Existence ◽  
Mean Field ◽  
State Problem ◽  
Mean Field Model ◽  
Type Ii Superconductor ◽  
Superconducting Vortices ◽  
Steady State Problem ◽  
Steady State Solutions

A mean-field model for the motion of rectilinear vortices in the mixed state of a type-II superconductor is formulated. Steady-state solutions for some simple geometries are examined, and a local existence result is proved for an arbitrary smooth geometry. Finally, a variational formulation of the steady-state problem is given which shows the solution to be unique.

Analysis of a mean field model of superconducting vortices

1999 ◽  
Vol 10 (4) ◽  
pp. 319-352 ◽  
Author(s):  
R. SCHÄTZLE ◽  
V. STYLES
Keyword(s):  
Weak Solution ◽  
Steady State ◽  
Free Boundary ◽  
Boundary Problem ◽  
Free Boundary Problem ◽  
Field Model ◽  
Mean Field ◽  
Two Dimensions ◽  
Mean Field Model ◽  
Superconducting Vortices

We study a mean-field model of superconducting vortices in one and two dimensions. The existence of a weak solution and a steady-state solution of the model are proved. A special case of the steady-state problem is shown to be of the form of a free boundary problem. The solutions of this free boundary problem are investigated. It is also shown that the weak solution of the one-dimensional model is unique and satisfies an entropy inequality.

scholarly journals Ill-posedness of the mean-field model of superconducting vortices and a possible regularisation

2000 ◽  
Vol 11 (2) ◽  
pp. 137-152 ◽  
Author(s):  
G. RICHARDSON ◽  
B. STOTH
Keyword(s):  
Stability Analysis ◽  
Linear Stability Analysis ◽  
Field Model ◽  
Mean Field ◽  
Average Density ◽  
Mean Field Model ◽  
Superconducting Vortices ◽  
Vorticity Vector ◽  
Ill Posed ◽  
The Mean

We conjecture that the mean-field model of superconducting vortices given in [10] is ill-posed wherever the electric current j has some component in the same direction as the vorticity vector ω (which gives the average density and direction of the superconducting vortices). The conjecture is illustrated with a linear stability analysis of a certain solution to the model. A regularised model is then proposed, and this is used to demonstrate the instability of force-free steady states in a certain geometry.

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