The authors consider two models, the Lawrence-Doniach and the anisotropic Ginzburg-Landau models for layered superconductors such as the recently discovered high-temperature superconductors. A mathematical description of both models is given and existence results for their solution are derived. The authors then relate the two models in the sense that they show that as the layer spacing tends to...

2.5 *The Laplacian 2.6 Bibliography 3. Fiber bundles and their topology 3.1 Introduction 3.2 Local symmetries. Connexion and curvature 3.3 Chern classes 3.4 Manifolds with a boundary: Chern-Simons classes 3.4.1 The Gauss-Bonnet theorem 3.4.2 Surfaces with boundary 3.4.3 Secondary characteristic classes 3.5 *The Weitzenböck formula 4. The dual point of Ginzburg-Landau equations for an infinite s...

The publication of this special section offers a chance to reflect on a topic of perennial interest in psychiatry: the ethics of commenting on public figures. Since at least the election of 1964, when publisher Ralph Ginzburg became concerned about Barry Goldwater’s psychological fitness, psychiatrists have debated the ethics of speaking out about the mental health of public figures. In that ye...

London theory was developed by Fritz London in 1935 to describe the Meissner effect. This theory leads to the introduction of the penetration depth to describe the extent of magnetic field penetration, λ into type I superconductors. The penetration depth is also important in type II superconductors and describes the extent of flux penetration near vortices as well as at surfaces. Prior to his s...

We formulate a constructive theory of noncommutative Landau-Ginzburg models mirror to symplectic manifolds based on Lagrangian Floer theory. The construction comes with natural functor from the Fukaya category matrix factorizations constructed model. As applications, it is applied elliptic orbifolds, punctured Riemann surfaces and certain non-compact Calabi-Yau threefolds construct their mirror...

Abstract By generalizing the Landau–Ginzburg/Calabi–Yau correspondence for hypersurfaces, we can relate a Calabi–Yau complete intersection to hybrid Landau–Ginzburg model: family of isolated singularities fibered over projective line. In recent years Fan, Jarvis, and Ruan have defined quantum invariants this type, Clader Clader–Ross provided an equivalence between these Gromov–Witten intersecti...