A generalized Ginzburg-Landau approach to second harmonic generation

Lower bounds for generalized Ginzburg-Landau functionals

An Approach to Quad Meshing Based on Harmonic Cross-Valued Maps and the Ginzburg-Landau Theory

A generalization of vector fields, referred to as N -direction fields or cross fields when N = 4, has been recently introduced and studied for geometry processing, with applications in quadrilateral (quad) meshing, texture mapping, and parameterization. We make the observation that cross field design for two-dimensional quad meshing is related to the well-known GinzburgLandau problem from mathe...

Limits of Solutions to the Generalized Ginzburg-Landau Functional

Here f(u) = (DF )(u) is the negative gradient of F w.r.t. u. Note that weak solutions to (1.2) are smooth for p = 2. It is also well-known that, for p 6= 2, weak solutions u to (1.2) are in C , for some 2 (0; 1) (see also [Tp]). The functional I has been used by Chen-Struwe [CS], where they proved the negative gradient ow of I converges to a global weak solution of the heat equations of harmoni...

Time - dependent Ginzburg - Landau approach and application to superconductivity

Abstract A time dependent generalization of the Ginzburg -Landau Lagrangian is proposed. It contains two terms determining the time dependence and the four arbitrary scalar functions. Relevant equations, which coincide with equations following from the suitable Hamiltonian, are derived by a standard variational technique. These equations determine the energy conservation law and admit twofold t...

Bifurcation and of the Generalized Complex Ginzburg–landau Equation

We study in this paper the bifurcation and stability of the solutions of the complex Ginzburg–Landau equation(CGLE). We investigate two different modes of CGLE. We study the first mode of CGLE which has only cubic unstable nonlinear term and later we also study the second mode of CGLE which has both cubic and quintic nonlinear terms. The solutions considered in cubic CGLE bifurcate from the tri...