We derive the fractional generalization of the Ginzburg–Landau equation from the variational Euler–Lagrange equation for fractal media. To describe fractal media we use the fractional integrals considered as approximations of integrals on fractals. Some simple solutions of the Ginzburg–Landau equation for fractal media are considered and different forms of the fractional Ginzburg–Landau equatio...

In 1957 Abrikosov published his work on periodic solutions to the linearized Ginzburg-Landau equations. Abrikosov’s analysis assumes periodic boundary conditions, which are very different from the natural boundary conditions the minimizer of the Ginzburg-Landau energy functional should satisfy. In the present work we prove that the global minimizer of the fully non-linear functional can be appr...

The authors consider the Ginzburg-Landau model for superconductivity. First some well-known features of superconducting materials are reviewed and then various results concerning the model, the resultant differential equations, and their solution on bounded domains are derived. Then, finite element approximations of the solutions of the Ginzburg-Landau equations are considered and error estimat...

We study a gradient-flow version of the Ginzburg-Landau equations with an addition of a compactly supported potential term. We consider initial data close to a magnetic vortex solution of the Ginzburg-Landau equations and find the dynamical law governing the motion of the vortex center in the presence of the potential.

Using a recent construction of Bezrukavnikov and Etingof, [BE], we prove that there is a factorization of the Etingof-Ginzburg sheaf on the generalized Calogero-Moser space associated to a complex reflection group. In the case W = Sn, this confirms a conjecture of Etingof and Ginzburg, [EG].

We study the fate of the 2d kinetic q-state Potts model after a sudden quench to zero temperature. Both ground states and complicated static states are reached with non-zero probabilities. These outcomes resemble those found in the quench of the 2d Ising model; however, the variety of static states in the q-state Potts model (with q ≥ 3) is much richer than in the Ising model, where static stat...

Abstract The hybrid model is the Landau–Ginzburg-type theory that expected, via Landau–Ginzburg/ Calabi–Yau correspondence, to match Gromov–Witten of a complete intersection in weighted projective space. We prove wall-crossing formula exhibiting dependence genus-zero on its stability parameter, generalizing work [21] for quantum singularity and paralleling Ciocan-Fontanine–Kim [7] quasimaps. Th...

This article concerns annular ring solutions of the Gray–Scott model. In the monostable regime, annular rings are far-fromequilibrium patterns supported on annuli inside of which the activator is concentrated. The diffusive flux of inhibitor over long length scales toward such an annulus feeds the production of activator there, and the interaction is semi-strong. Numerical and experimental obse...