The spin polarization of Sb overlayers on the semi-Heusler alloy NiMnSb is investigated in terms of the Landau-Ginzburg approach. The half-metallic semi-Heusler alloy NiMnSb acts as a ferromagnetic perturbation and induces a spin polarization in the semimetallic Sb overlayer. Using a Gaussian approximation, the propagation of the spin perturbation in the overlayer is calculated. The results are...

This paper is concerned with optimal control problems for a Ginzburg-Landau model of superconductivity that is valid for high values of the Ginzburg-Landau parameter and high external fields. The control is of Neumann type. We first show that optimal solutions exist. We then show that Lagrange multipliers may be used to enforce the constraints and derive an optimality system from which optimal ...

We address the striking coexistence of localized waves (‘pulses’) of different lengths which was observed in recent experiments and full numerical simulations of binary-mixture convection. Using a set of extended Ginzburg-Landau equations, we show that this multiplicity finds a natural explanation in terms of the competition of two distinct, physical localization mechanisms; one arises from dis...

Breaking the chiral symmetry, rotation induces a secondary Hopf bifurcation in weakly nonlinear hexagon patterns which gives rise to oscillating hexagons. We study the stability of the oscillating hexagons using three coupled Ginzburg-Landau equations. Close to the bifurcation point we derive reduced equations for the amplitude of the oscillation, coupled to the phase of the underlying hexagons...

The Ginzburg–Landau model of superconductivity is considered in three dimensions. We show, for smooth bounded domains, that the superconductivity order parameter decays exponentially fast away from the boundary as the Ginzburg–Landau parameter κ tends to infinity. We prove this result for applied magnetic fields satisfying |hex| − κ κ1/2. Additionally, we prove that for applied fields greater t...

The Ginzburg–Landau theory of phase transitions is one of the most successful and elegant theories that have a very general applicability to a large variety of phenomena. Moreover, its extension into time domain has produced a wealth of interesting new predictions and applications all the way from materials science to cosmology. Here, we describe applications of time-dependent Ginzburg–Landau t...

We develop techniques to compute the complete massless spectrum in heterotic string compactification on N=2 supersymmetric Landau-Ginzburg orbifolds. This includes not just the familiar charged fields, but also the gauge singlets. The number of gauge singlets can vary in the moduli space of a given compactification and can differ from what it would be in the large radius limit of the correspond...

We introduce a new class of algebras called Poisson orders. This class includes the symplectic reflection algebras of Etingof and Ginzburg, many quantum groups at roots of unity, and enveloping algebras of restricted Lie algebras in positive characteristic. Quite generally, we study this class of algebras from the point of view of Poisson geometry, exhibiting connections between their represent...

We compute topological correlators in Landau-Ginzburg models on a Riemann surface with arbitrary number of handles and boundaries. The boundaries may correspond to arbitrary topological D-branes of type B. We also allow arbitrary operator insertions on the boundary and in the bulk. The answer is given by an explicit formula which can be regarded as an open-string generalization of C. Vafa’s for...

Optical-fiber transmission of pulses can be modeled with the complex Ginzburg–Landau equation. We find novel stable soliton pairs and trains, which are relevant in this case, and analyze them. We suggest that the distance between the pulses and the phase difference between them is defined by energy and momentum balance equations, rather than by equations of standard perturbation theory. We pres...