Several issues in mathematical modeling and numerical simulation for the time dependent Ginzburg-Landau equations are investigated. A key point of this study is the influence of the mesh for the spatial discretization on the simulation results. In particular, we demonstrate that a fine mesh resolution in space is necessary, and that an inadequate mesh resolution will often give rise to spurious...

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 ...

A bstract As put forward in [1] topological quantum field theories can be projected using so-called projection defects. The theory and its correlation functions completely realized within the unprojected one. An interesting example is case of associated to IR fixed points renormalization group flows, which by this method inside UV. In note we show that defects triangulated defect categories (su...

For a Bose-Einstein condensate placed in a rotating trap and strongly confined along the z axis, we set a framework of study for the Gross-Pitaevskii energy in the Thomas-Fermi regime for an effective twodimensional ~2D! situation in the x-y plane. We investigate an asymptotic expansion of the energy, the critical angular velocities of nucleation of vortices with respect to a small parameter « ...

In a seminal paper [9] Ginzburg and Adler analyzed the bounce-back boundary conditions for the lattice Boltzmann scheme and showed that it could be made exact to second order for the Poiseuille flow if some expressions depending upon the parameters of the method were satisfied, thus defining so-called “magic parameters”. Using the Taylor expansion method that one of us developed, we analyze a s...

This paper considers a wavelet analogue of the classical Ginzburg-Landau energy, where the Hseminorm is replaced by the Besov seminorm defined via an arbitrary regular wavelet. We prove that functionals of this type converge, in the Γ-sense, to a weighted analogue of the TV functional on characteristic functions of finite-perimeter sets. The Γ-limiting functional is defined explicitly, in terms...

The thermodynamics and kinetics of the self-assembly of cylinder-forming diblock copolymers directed by the lateral confinement of hexagons have been studied by the combination of self-consistent field theory (SCFT) calculation and time-dependent Ginzburg-Landau (TDGL) theory simulation. The SCFT calculations are used to determine the stability of candidate 2D and 3D equilibrium phases formed i...

We describe a Sobolev gradient method for finding minima of the Ginzburg–Landau functional for superconductivity. This method leads to a particularly simple algorithm which avoids consideration of the nonlinear boundary conditions associated with the Ginzburg–Landau equations.

We propose a unified method for the analytically exact vortex extraction and tracking of superconducting magnetic flux vortices for both structured and unstructured mesh data. In the Ginzburg-Landau theory, magnetic flux vortices are well-defined features in a complex-valued order parameter field, and their dynamics determine electromagnetic properties in type-II superconductors. Our method rep...