Branched microstructures in the Ginzburg-Landau model of type-I superconductors (Q2817452)

Superconductivity occurs at low temperature in some materials which lose their resistivity and generate an applied magnetic field. A standard model to describe this phenomenon is the Ginzburg-Landau equation, and the purpose herein is to study some features of this equation, and to determine the scaling of the minimum energy per cross-sectional area considered as a function of the physical parameters (such as temperature for instance) which define the system. One separates the bulk energy contribution and one defines the special equation which is dealt with. Ones derives lower bounds and upper bounds and to this end one begins with the sharp-interface problem and then extends the result to the full Ginzburg-Landau functional.