English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Open

We consider singular limits of the three-dimensional Ginzburg-Landaufunctional for a superconductor with thin-film geometry, in a constant externalmagnetic field. The superconducting domain has characteristic thickness on thescale $\eps>0$, and we consider the simultaneous limit as the thickness$\eps\rightarrow 0$ and the Ginzburg-Landau parameter$\kappa\rightarrow\infty$. We assume that the applied field is strong (on theorder of $\eps^{-1}$ in magnitude) in its components tangential to the filmdomain, and of order $\log\kappa$ in its dependence on $\kappa$. We prove thatthe Ginzburg-Landau energy $\Gamma$-converges to an energy associated with atwo-obstacle problem, posed on the planar domain which supports the thin film.The same limit is obtained regardless of the relationship between $\eps$ and$\kappa$ in the limit. Two illustrative examples are presented, each of whichdemonstrating how the curvature of the film can induce the presence of both(positively oriented) vortices and (negatively oriented) antivorticescoexisting in a global minimizer of the energy.

Singular Limits for Thin Film Superconductors in Strong Magnetic Fields - Maan Field Model for Thin Films