Near boundary vortices in a magnetic Ginzburg–Landau model: Their locations via tight energy bounds

AbstractGiven a bounded doubly connected domain G⊂R2, we consider a minimization problem for the Ginzburg–Landau energy functional when the order parameter is constrained to take S1-values on ∂G and have degrees zero and one on the inner and outer connected components of ∂G, correspondingly. We show that minimizers always exist for 0<λ<1 and never exist for λ⩾1, where λ is the coupling constant (λ/2 is the Ginzburg–Landau parameter). When λ→1−0 minimizers develop vortices located near the boundary, this results in the limiting currents with δ-like singularities on the boundary. We identify the limiting positions of vortices (that correspond to the singularities of the limiting currents) by deriving tight upper and lower energy bounds. The key ingredient of our approach is the study of various terms in the Bogomol'nyi's representation of the energy functional

The Ginzburg-Landau functional with a discontinuous and rapidly oscillating pinning term. Part I: the zero degree case

International audienceWe consider minimizers of the Ginzburg-Landau energy with pinning term and zero degree Dirichlet boundary condition. Without any assumptions on the pinning term, we prove that these minimizers do not develop vortices in the limit $\varepsilon\to0$. We next consider the specific case of a periodic discontinuous pinning term taking two values. In this setting, we determine the asymptotic behavior of the minimizers as $\varepsilon\to0$

Long Time Behavior of Stochastic Thin Film Equation

In this paper we consider a stochastic thin-film equation with a one dimensional Gaussian Stratonovych noise. We establish the existence of non-negative global weak martingale solution, and study its long time asymptotic properties. In particular, we show the solution almost surely converges to the average value of the initial condition. Furthermore, using the regularized equations and adapted entropy functionals, we establish the exponential asymptotic decay of the solution in the uniform norm

Thin Film Equations with Nonlinear Deterministic and Stochastic Perturbations

In this paper we consider stochastic thin-film equation with nonlinear drift terms, colored Gaussian Stratonovych noise, as well as nonlinear colored Wiener noise. By means of Trotter-Kato-type decomposition into deterministic and stochastic parts, we couple both of these dynamics via a discrete-in-time scheme, and establish its convergence to a non-negative weak martingale solution

The equilibrium model of demand and supply at the Ukrainian Interbank Foreign Exchange Market: disclosure of problematic aspects

This article is devoted to building of the equilibrium model between demand and supply on foreign currency at the Ukrainian Interbank Foreign Exchange Market (non-cash share). The authors discussed that appeared trade-offs are a product of established current foreign arrangement, administrative measures provided by the National Bank of Ukraine and range of fundamental variables, which are traditionally significant for Ukrainian economy. By means of FAVAR modeling model of demand and supply equlibrium on non-cash foreign currency was built on empirical data of Ukrainian Interbank Foreign Exchange Market, splitted into the periods, proposed by the authors. Next, it was discussed disconnection properties in the model and shown log-linearized specification of the one. The efficiency of fulfillment hypothesis on decointegrating of the fundamental variables' time series has been provided in form of critical statistics values. Also, instrument of GAP analysis of deviation from equilibrium state was proposed and the further analysis of a regulation style of monetary authority was provided. In conclusion, it was summarized that increased share of the cash out of the banks has significantly jeopardized the price stability in Ukraine and the NBU interventions would become more effective if the flexible foreign exchange rate will be accompanied with flexible regime of inflation targeting