We study the Ginzburg-Landau energy functional for superconductors in an applied magnetic field. We focus on asymptotically large or small domains and establish the asymptotic behavior of the energy as a function of the Ginzburg-Landau parameter, applied magnetic field and domain size. For a large class of domain sizes, we calculate the critical field strength where vortex nucleation becomes en...

The cubic complex Ginzburg-Landau equation is one of the most-studied nonlinear equations in the physics community. It describes a vast variety of phenomena from nonlinear waves to secondorder phase transitions, from superconductivity, superfluidity and Bose-Einstein condensation to liquid crystals and strings in field theory. Our goal is to give an overview of various phenomena described the c...

We compute the elliptic genera of orbifolds associated with N = 2 super–conformal theories which admit a Landau-Ginzburg description. The identification of the elliptic genera of the macroscopic Landau-Ginzburg orbifolds with those of the corresponding microscopic N = 2 orbifolds further supports the conjectured identification of these theories. For SU(N) Kazama-Suzuki models the orbifolds are ...

We consider the relation between affine Toda field theories (ATFT) and Landau-Ginzburg Lagrangians as alternative descriptions of deformed 2d CFT. First, we show that the two concrete implementations of the deformation are consistent once quantum corrections to the Landau-Ginzburg Lagrangian are taken into account. Second, inspired by Gepner’s fusion potentials, we explore the possibility of a ...

Abstract Oscillons are spatially localized, time-periodic structures that have been observed in many natural processes, often under temporally periodic forcing. Near Hopf bifurcations, such systems can be formally reduced to forced complex Ginzburg–Landau equations, with oscillons then corresponding to stationary localized patterns. In this manuscript, stationary localized structures of the pla...

The existence, stability properties, and bifurcation diagram of the nematic umbilical defects is studied. Close to the Fréedericksz transition of nematic liquid crystals with negative anisotropic dielectric constant and homeotropic anchoring, an anisotropic Ginzburg-Landau equation for the amplitude of the tilt of the director away from the vertical axis is derived by taking the three-dimension...

In this paper we study the derived category of sheaves on the affine Grassmannian of a complex reductive group Ǧ, contructible with respect to the stratification by Ǧ(C[[x]])-orbits. Following ideas of Ginzburg and Arkhipov– Bezrukavnikov–Ginzburg, we describe this category (and a mixed version) in terms of coherent sheaves on the nilpotent cone of the Langlands dual reductive group G. We also ...

The moduli spaces of two (0, 2) compactifications of the heterotic string can share the same Landau-Ginzburg model even though at large radius they look completely different. It was argued that such a pair of (0, 2) models might be connected via a perturbative transition at the Landau-Ginzburg point. Situations of this kind are studied for some explicit models. By calculating the exact dimensio...

Ginzburg and Ivan A. Sag, published by CSLI Publications. ©2001 by CSLI Publications. All rights reserved. This text may be used and shared in accordance with the fair-use provisions of U.S. copyright law, and it may be archived and redistributed in electronic form, provided that this entire notice, including copyright information, is carried and provided that CSLI Publications is notified and ...

The Ginzburg–Landau equation has been used as a mathematical model for various pattern formation systems in mechanics, physics and chemistry. In this paper, we study the complex Ginzburg–Landau equation in two spatial dimensions with periodical boundary conditions. The method numerically approximates the solution by collocation method based on radial basis functions (RBFs). To improve the numer...