Verres de Spin et optimisation combinatoire
Vortex motion and phase-vortex interaction in dissipative Ginzburg-Landau dynamics
We discuss the asymptotics of the parabolic Ginzburg-Landau equation in dimension Our only asumption on the initial datum is a natural energy bound. Compared to the case of “well-prepared” initial datum, this induces possible new energy modes which we analyze, and in particular their mutual interaction. The two dimensional case is qualitatively different and requires a separate treatment.
Vortex pinning with bounded fields for the Ginzburg–Landau equation
Vortex rings for the Gross-Pitaevskii equation
We provide a mathematical proof of the existence of traveling vortex rings solutions to the Gross–Pitaevskii (GP) equation in dimension . We also extend the asymptotic analysis of the free field Ginzburg–Landau equation to a larger class of equations, including the Ginzburg–Landau equation for superconductivity as well as the traveling wave equation for GP. In particular we rigorously derive a curvature equation for the concentration set (i.e. line vortices if ).
Vortices for a variational problem related to superconductivity
Vortices in Ginzburg-Landau equations.
Vorticité dans les équations de Ginzburg-Landau de la supraconductivité
Vorticité dans les modèles de Ginzburg-Landau pour la supraconductivité