The Ginzburg}Landau model for the radiation "eld of a free-electron laser (FEL) was originally derived for a high-gain ampli"er (S.Y. Cai and A. Bhattacharjee, Phys. Rev. A 43 (1991) 6934). With a view to making precise comparisons with experimental data from the long-pulse FEL oscillator at the University of California at Santa Barbara (UCSB) (L.R. Elias, G. Ramian, J. Hu, A. Amir, Phys. Rev. ...

We consider a time-dependent Ginzburg-Landau equation for superconductors with a strictly complex relaxation parameter, and derive motion laws for the vortices in the case of a finite number of vortices in a bounded magnetic field. The motion laws correspond to the flux-flow Hall effect. As our main tool, we develop a quantitative Γstability result relating the Ginzburg-Landau energy to the ren...

The scale hierarchy of wavelets provides a natural frame for renormalization. Expanding the order parameter of the Landau-Ginzburg/Φ model in a basis of compact orthonormal wavelets explicitly exhibits the coupling between scales that leads to non-trivial behavior. The locality properties of Daubechies’ wavelets enable us to derive the qualitative renormalization flow of the Landau-Ginzburg mod...

The magnetic response of a proximity-coupled superconductor–normal-metal sandwich is studied within the framework of the quasiclassical theory. The magnetization is evaluated for finite values of the applied magnetic field ~linear and nonlinear response! at arbitrary temperatures and is used to fit recent experimental lowtemperature data. The hysteretic behavior predicted from a Ginzburg-Landau...

We have measured the diffracted neutron scattering intensities from the square magnetic flux lattice in the perovskite superconductor Sr2RuO4, which is thought to exhibit p-wave pairing with a two-component order parameter. The relative intensities of different flux lattice Bragg reflections over a wide range of field and temperature have been shown to be inconsistent with a single component Gi...

We describe a generalized Levenberg-Marquardt method for computing critical points of the Ginzburg-Landau energy functional which models superconductivity. The algorithm is a blend of a Newton iteration with a Sobolev gradient descent method, and is equivalent to a trust-region method in which the trustregion radius is defined by a Sobolev metric. Numerical test results demonstrate the method t...

In this paper, we introduce baby Verma modules for symplectic reflection algebras of complex reflection groups at parameter t = 0 (the so–called rational Cherednik algebras at parameter t = 0) and present their most basic properties. As an example, we use baby Verma modules to answer several problems posed by Etingof and Ginzburg, [5], and give an elementary proof of a theorem of Finkelberg and...

We study the Ginzburg-Landau energy of a single vortex and prove a quantitative estimate for the anisotropy of the stress-energy tensor. In particular we establish an asymptotic rate of equipartitioning of the energy along each direction. By means of an explicit example, this rate is shown to be optimal up to a constant. The result has applications in the study of the nonlinear wave equation an...

Within Ginzburg-Landau theory, we study the structure of a magnetic vortex in color-flavor locked quark matter. This vortex is characterized by winding of the SU(3) phase in color-flavor space, as well as by the presence of a color-flavor unlocked condensate in the core. We estimate the upper and lower critical fields and the critical Ginzburg-Landau parameter that distinguishes between type I ...