A New Formula for the Energy of Bulk Superconductivity

The energy of a type II superconductor submitted to an external magnetic field of intensity close to the second critical field is given by the celebrated Abrikosov energy. If the external magnetic field is comparable to and below the second critical field, the energy is given by a reference function obtained as a special (thermodynamic) limit of a non-linear energy. In this note, we give a new formula for this reference energy. In particular, we obtain it as a special limit of a linear energy defined over configurations normalized in the L4-norm.

ON THE SECOND CRITICAL FIELD FOR A GINZBURG–LANDAU MODEL WITH FERROMAGNETIC INTERACTIONS

We consider a two-dimensional Ginzburg–Landau model for superconductors which exhibit ferromagnetic ordering in the superconducting phase, introduced by physicists to describe unconventional p-wave superconductors. In this model the magnetic field is directly coupled to a vector-valued order parameter in the energy functional. We show that one effect of spin coupling is to increase the second critical field Hc2, the value of the applied magnetic field at which superconductivity is lost in the bulk. Indeed, when the spin coupling is strong we show that the upper critical field is no longer present, confirming predictions in the physics literature. We treat the energy density as a measure, and show that the order parameter converges (as the Ginzburg–Landau parameter κ→∞) in an average sense to a constant determined by the average energy.

DYNAMIC INTERFERENCE PATTERNS FROM FERROFLUIDS

Time-dependent interference was observed above a critical magnetic field Hc1 in ferrofluids by a novel technique — magnetic thermal lens effect. The onset of the dynamics is associated with the formation of linear structures in the system. When a second critical field, Hc2, was reached, a lattice of quasi-periodic columns was observed by optical microscopy and random rotating patterns were replaced by stable rings, indicating ordering in the system. This technique provides a useful way to detect microstructures that are much smaller than the optical wave length thus unobservable by conventional optical technique. We found that the result crucially depends on boundary conditions.