Mathematics – Logic
Scientific paper
Jan 1992
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1992phdt........91h&link_type=abstract
Thesis (PH.D.)--RENSSELAER POLYTECHNIC INSTITUTE, 1992.Source: Dissertation Abstracts International, Volume: 53-07, Section: B,
Mathematics
Logic
Scientific paper
The finite element method has been used to solve the mass-tensor form of the phenomenological Ginzburg-Landau (G-L) equations. The spatial variations of the magnetic flux density, the super-electron pair density, and the supercurrents in anisotropic, type-II superconductors have been successfully modeled for a variety of problems, including the equilibrium vortex lattice structure, the superheated Meissner state, and the surface barrier to flux penetration. The Galerkin weighted-residual approach has been used to formulate the element stiffness and force matrices in two-dimensions, and triangular isoparametric elements with linear interpolation functions have been used to discretize the solution domains. A multi-dimensional Newton-Raphson scheme has been used to iteratively solve the nonlinear equations, with the convergence stability controlled by use of a successive under-relaxation method. Primitive solutions to each problem were generated by the use of either a simple analytical form or a continuation method in which the boundary conditions and forcing functions were gradually increased in successive iterations. A pre -conditioned conjugate gradient method was used to solve the sparse, non-symmetric matrix equations at each iteration step. The Gibbs free energy potential, the magnetization, and the lower critical field have been solved for the equilibrium vortex lattice with isotropic and anisotropic properties. Near the lower and upper critical fields the numerical results show excellent agreement with analytical solutions for both the isotropic and anisotropic cases. The Gibbs free energy of the triangular vortex lattice was found to be less than that of the square and rectangular vortex lattices for all applied fields between the lower and upper critical fields. The stability of the superheated Meissner state at a superconductor-insulator interface has been determined for surd 2 < kappa < 20 (where kappa is the G-L parameter). A two -dimensional instability was found to occur at fields less than the thermodynamic critical field, H_ {rm c}, for kappa > 5. The surface barrier to flux penetration at a superconductor-insulator interface was also studied for surd 2 < kappa < 20. The applied field at which it is energetically favorable for a single vortex to penetrate was determined by increasing the applied field from zero, with a vortex located at the surface. The numerical results show that the surface barrier field, H_{rm s}, exactly approaches the Bean-Livingston solution (H_ {rm s} = H_{ rm c}/surd2), for kappa gg 1..
No associations
LandOfFree
Finite Element Solutions to the Mass-Tensor Form of the Ginzburg-Landau Equations. does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Finite Element Solutions to the Mass-Tensor Form of the Ginzburg-Landau Equations., we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Finite Element Solutions to the Mass-Tensor Form of the Ginzburg-Landau Equations. will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-940143