A branched transport limit of the Ginzburg-Landau functional

The ground state energy of the two dimensional Ginzburg–Landau functional with variable magnetic field..

conductivity, SIAM Review, Vol. CHEN, Nonsymmetric vortices for the Ginzberg-Landau equations on the bounded domain, J. PETERSON, Analysis and approximation of

We find a vanishing gradient type property and then we obtain the renormalized energy by Bethuel, Brezis and Helein’s shrinking.. holes

Constructions (leading to the upper bounds in [19, 15, 13]), suggest that in this regime, typically, the penetra- tion length of the magnetic field inside the superconducting regions

We introduce a “Coulombian renormalized energy” W which is a logarithmic type of interaction between points in the plane, computed by a “renormalization.” We prove various of

The simplified Ginzburg- Landau energy (1) is essentially used to treat the case of a bounded number of vorticity defects (which essentially correspond to small neighborhoods of

It is proved that, when vorticity defects are trapped by a diluted impurity, then their lo- cation inside the impurity [the microscopic location] is independent of the

For sake of completeness, we give also the limit behaviour of the previous Ginzburg-Landau equation with homogeneous Dirichlet boundary condition (for scalar problems with