s of courses Giovanni ALBERTI “Concentration phenomena for functionals of Ginzburg-Landau type. A variational approach” In these lectures I will describe an approach by Γ-convergence to certain concentration phenomena for minimizers of functionals of Ginzburg-Landau type, as developped in [ABO2] and [JS]. Consider the functionals

In this paper, we establish the global fast dynamics for the time-dependent Ginzburg}Landau equations of superconductivity. We show the squeezing property and the existence of "nite-dimensional exponential attractors for the system. In addition we prove the existence of the global attractor in ̧2] ̧2 for the Ginzburg}Landau equations in two spatial dimensions. Copyright ( 1999 John Wiley & Sons, ...

In this paper I examine what have often been considered the syntactic properties of Gapping constructions (Ross, 1970) and show that they are in fact discourse-pragmatic in nature. I offer a novel analysis of Gapping constructions by extending recent Question Under Discussion (QUD)-based accounts in Head-Driven Phrase Structure Grammar (Ginzburg and Sag, 2000; Ginzburg, 2012).

– We investigate vortex pinning in solutions to the Ginzburg–Landau equation. The coefficient, a(x), in the Ginzburg–Landau free energy modeling non-uniform superconductivity is nonnegative and is allowed to vanish at a finite number of points. For a sufficiently large applied magnetic field and for all sufficiently large values of the Ginzburg–Landau parameter κ = 1/ε, we show that minimizers ...

Gauge invariance is used to establish an equivalence relation between solutions of the time-independent and time-dependent Ginzburg-Landau equations that describe the same physical state of a superconductor. The equivalence relation shows how equilibrium conngurations are obtained as large-time asymptotic limits of solutions of the time-dependent Ginzburg-Landau equations.

This report is an extension of (Gregory 2001) and presents an overview of the implementation of the HPSG grammar currently used in SHARDS —a Semantically-based HPSG Approach to the Resolution of Dialogue Fragments (Ginzburg, Gregory, and Lappin 2001). The grammar is based on the theoretical framework presented in (Ginzburg and Sag 2001) and it is encoded in ProFIT (Erbach 1995).

We provide a study at the boundary for a class of equation including the Ginzburg-Landau equation as well as the equation of travelling waves for the Gross-Pitaevskii model. We prove Clearing-Out results and an orthogonal anchoring condition of the vortex on the boundary for the Ginzburg-Landau equation with magnetic field.

We shall show that the density of defects produced at a secondorder phase transition is determined by the correlation length of the fields. This is true both for defects appearing in the Ginzburg regime and for defects produced at a quench, when the Ginzburg regime is irrelevant.