Advanced Search

In this note we consider the Ginzburg-Landau functional $$I_a^{ϵ}(v)={\int }_0^1({ϵ}^2{v}^{\mathrm{\prime \prime }2}(s)+W(v^{\prime }(s))+a({ϵ}^{-\beta }s(v^2(s))ds$$ where $\beta >0$ and a is 1-periodic. We determine how (rescaled) minimal asymptotic energy associated to $I_a^{ϵ}$ depends on parameter $\beta >0$ as $ϵø0$. In particular, our analysis shows that minimizers of $I_a^{ϵ}$ are nearly ${ϵ}^{1/3}$-periodic.