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The Ginzburg–Landau approach to oscillatory media
Chaos: An Interdisciplinary Journal of Nonlinear Science, 1994Close to a supercritical Hopf bifurcation, oscillatory media may be described, by the complex Ginzburg–Landau equation. The most important spatiotemporal behaviors associated with this dynamics are reviewed here. It is shown, on a few concrete examples, how real chemical oscillators may be described by this equation, and how its coefficients may be ...
Kramer, Lorenz +3 more
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Sobolev Gradients and the Ginzburg--Landau Functional
SIAM Journal on Scientific Computing, 1998Summary: 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.
J. W. Neuberger, Robert J. Renka
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On the Ginzburg-Landau Wave Equation
Bulletin of the London Mathematical Society, 1990Consider the initial value problem of the Ginzburg-Landau wave equation with a general power self-interaction term: \[ (*)\quad \phi_ t=(1+i\alpha)\Delta \phi +(1+i\beta)\phi -(1+i\gamma)| \phi |^{\mu -1}\phi,\quad x\in {\mathbb{R}}^ n,\quad t>0, \] \[ \phi (x,0)=\phi_ 0(x),\quad x\in {\mathbb{R}}^ n, \] where \(\phi\) is a complex scalar function ...
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1999
This chapter discusses the extension of the theory to allow spatial variation in the order parameter and determining the shape of the interface and the surface contribution to the free energy. It describes the size of fluctuations of the order parameter, determining whether they are sufficiently small to be ignored or whether they dominate the ...
Roger Bowley, Mariana Sánchez
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This chapter discusses the extension of the theory to allow spatial variation in the order parameter and determining the shape of the interface and the surface contribution to the free energy. It describes the size of fluctuations of the order parameter, determining whether they are sufficiently small to be ignored or whether they dominate the ...
Roger Bowley, Mariana Sánchez
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Dynamic Bifurcation of the Ginzburg--Landau Equation
SIAM Journal on Applied Dynamical Systems, 2004Summary: We study in this article the bifurcation and stability of the solutions of the Ginzburg-Landau equation, using a notion of bifurcation called attractor bifurcation. We obtain in particular a full classification of the bifurcated attractor and the global attractor as \(\lambda\) crosses the first critical value of the linear problem ...
Tian Ma, Jungho Park, Shouhong Wang
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1997
The London theory (Chap. 2) did not take into account quantum effects. The first quantum (phenomenological) theory of superconductivity was the Ginzburg—Landau (GL) theory [23].
V. V. Schmidt +2 more
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The London theory (Chap. 2) did not take into account quantum effects. The first quantum (phenomenological) theory of superconductivity was the Ginzburg—Landau (GL) theory [23].
V. V. Schmidt +2 more
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2004
In the self-consistent field theory discussed in Chap. 3, the conformation entropy of the chains is evaluated accurately using the path integral formaliser. A further simplification of the model can be made by approximating the conformational entropy and the free energy. A typical example is the Ginzburg -Landau model. In this model, the free energy is
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In the self-consistent field theory discussed in Chap. 3, the conformation entropy of the chains is evaluated accurately using the path integral formaliser. A further simplification of the model can be made by approximating the conformational entropy and the free energy. A typical example is the Ginzburg -Landau model. In this model, the free energy is
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The Ginzburg–Landau Functional
2009Let us describe the mathematical problem. It is naturally posed for domains in \(\mathbb{R}^{3}\), but for cylindrical domains in \(\mathbb{R}^{3}\), it is natural (though not completely justified mathematically) to consider a functional defined in a domain Ω ⊂ \(\mathbb{R}^{3}\), where Ω is the cross-section of the cylinder.
Søren Fournais, Bernard Helffer
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SCATTERING OF GINZBURG–LANDAU VORTICES
Journal of Mathematical Sciences, 2022openaire +2 more sources
1979
We have seen in Sect.2 that a superconductor often resides in a state of high spatial inhomogeneity. Here the intermediate state and the situation near a domain wall are just an example showing spatial variations of the order parameter. Spatial inhomogeneity is displayed perhaps even more importantly in the case of the vortex state in type-II ...
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We have seen in Sect.2 that a superconductor often resides in a state of high spatial inhomogeneity. Here the intermediate state and the situation near a domain wall are just an example showing spatial variations of the order parameter. Spatial inhomogeneity is displayed perhaps even more importantly in the case of the vortex state in type-II ...
openaire +1 more source