A formal asymptotic expansion is used to simplify the Ginzburg-Landau model of superconductivity in the limit of large values of the Ginzburg-Landau parameter and high applied magnetic field strengths. The convergence of solutions of the full Ginzburg-Landau equations to solutions of the leading order equations in the hierarchy is demonstrated for both boundary value and periodic problems. The ...

In this paper, we discuss elliptic genera of (2,2) and (0,2) supersymmetric Landau-Ginzburg models over nontrivial spaces, i.e. nonlinear sigma models on nontrivial noncompact manifolds with superpotential, generalizing old computations in Landau-Ginzburg models over (orbifolds of) vector spaces. For Landau-Ginzburg models in the same universality class as nonlinear sigma models, we explicitly ...

The first integral method is an efficient method for obtaining exact solutions of some nonlinear partial differential equations. This method can be applied to non integrable equations as well as to integrable ones. In this paper, the first integral method is used to construct exact solutions of the 2D Ginzburg-Landau equation.

ion and Ontology: questions as propositional abstracts in type theory with records Jonathan Ginzburg∗ Department of Computer Science King’s College, London The Strand, London WC2R 2LS [email protected] http://www.dcs.kcl.ac.uk/staff/ginzburg/papers

The initial-boundary value problem for the time-dependent Ginzburg-Landau equa, tions that model the macroscopic behavior of superconductors is considered. The convergence of finite-dimensional, semidiscrete Galerkin approximations is studied as is a fully-discrete scheme. The results of some computational experiments are presented. Keywords-Superconductivity, Timedependent Ginzburg-Landau equa...

In this paper we discuss correlation functions in certain A-twisted Landau-Ginzburg models. Although B-twisted Landau-Ginzburg models have been discussed extensively in the literature, virtually no work has been done on A-twisted theories. In particular, we study examples of Landau-Ginzburg models over topologically nontrivial spaces – not just vector spaces – away from large-radius limits, so ...

We present some mathematical aspects of Landau-Ginzburg string vacua in terms of toric geometry. The one-to-one correspondence between toric divisors and some of (−1, 1) states in Landau-Ginzburg model is presented for superpotentials of typical types. The Landau-Ginzburg interpretation of non-toric divisors is also presented. Using this interpretation, we propose a method to solve the so-calle...

In the asymptotic limit of a large Ginzburg-Landau parameter, we give a new asymptotic formula for the L-norm of the Ginzburg-Landau order parameter. The formula is valid in the bulk regime where the intensity of the applied magnetic eld is of the same order as the Ginzburg-Landau parameter and strictly below the second critical eld. Our formula complements the celebrated one of Sandier-Serfaty...

We introduce a duality construction for toric Landau-Ginzburg models, applicable to complete intersections in toric varieties via the sigma model / Landau-Ginzburg model correspondence. This construction is shown to reconstruct those of Batyrev-Borisov, Berglund-Hübsch, Givental, and HoriVafa. It can be done in more general situations, and provides partial resolutions when the above constructio...

We study the limit state of the inhomogeneous Ginzburg-Landau model as the Ginzburg-Landau parameter κ = 1/ →∞, and derive an equation to describe the limit state. We analyze the properties of solutions of the limit equation, and investigate the convergence of (local) minimizers of the Ginzburg-Landau energy with large κ. Our results verify the pinning effect of an inhomogeneous superconductor ...