Critical fluctuations in a mesoscopic superconducting ring

The nonlocal magnetoconductivity fluctuations in a superconducting submicron ring, with radius comparable to the Ginzburg-Landau coherence length, are studied. The order parameter mode separation yields to the solution of the time-dependent Ginzburg-Landau equation and the paraconductivity Fourier components are calculated in the vicinity of the critical temperature, including the critical fluctuation region. The homogeneous component has a logarithmic singularity at T(c) while the other components are found to be not singular.     

Phase separation in colloidal suspensions induced by a solvent phase transition

A colloidal suspension of macroparticles in a solvent is considered near a solvent first-order phase transition. The solvent phase transition is described by a Ginzburg-Landau model with a one-component order parameter which is coupled to the macroparticles coordinates. Wetting of the macroparticle surface by one of the two coexisting phases can induce phase separation of the colloidal particles. This phase separation is first explained by simple thermodynamic arguments and then confirmed by computer simulation of the Ginzburg-Landau model coupled to the macroparticles. Furthermore a topological diagnosis of the interface between the stable and metastable phase is given near phase separation and possible experimental consequences of the phase separation are discussed.     

Nonlinear interactions in a rotating disk flow: From a Volterra model to the Ginzburg-Landau equation

The physical system under consideration is the flow above a rotating disk and its cross-flow instability, which is a typical route to turbulence in three-dimensional boundary layers. Our aim is to study the nonlinear properties of the wavefield through a Volterra series equation. The kernels of the Volterra expansion, which contain relevant physical information about the system, are estimated by fitting two-point measurements via a nonlinear parametric model. We then consider describing the wavefield with the complex Ginzburg-Landau equation, and derive analytical relations which express the coefficients of the Ginzburg-Landau equation in terms of the kernels of the Volterra expansion. These relations must hold for a large class of weakly nonlinear systems, in fluid as well as in plasma physics. (c) 2000 American Institute of Physics.     

On the emergence of superconductivity and hysteresis in a cylindrical type I superconductor

One-dimensional vortex-free solutions of the system of Ginzburg-Landau equations (the so-called precursor states) are studied. These states describe the emergence of superconductivity in a long cylindrical type I superconductor, which was initially in the supercooled normal state in a magnetic field, and are formed upon subsequent reduction of the external field. The precursor states are responsible for the magnetic hysteresis in type I superconductors (for which κ < κ_c, where κ_c (R) is the critical value of the parameter κ in the Ginzburg-Landau theory, which is a function of radius). The range of fields is determined in which precursor states exist along with the Meissner state (and a hysteresis is possible) in the dependence of the cylinder radius R and parameter κ.     

Advection-induced spectrotemporal defects in a free-electron laser

We evidence numerically and experimentally that advection can induce spectrotemporal defects in a system presenting a localized structure. Those defects in the spectrum are associated with the breakings induced by the drift of the localized solution. The results are based on simulations and experiments performed on the super-ACO free-electron laser. However, we show that this instability can be generalized using a real Ginzburg-Landau equation with (i) advection and (ii) a finite-size supercritical region.     

Subcritical Kelvin-Helmholtz instability in a Hele-Shaw cell

We investigate experimentally the subcritical behavior of the Kelvin-Helmholtz instability for a gas-liquid shearing flow in a Hele-Shaw cell. The subcritical curve separating the solutions of a stable plane interface and a fully saturated nonlinear wave train is determined. Experimental results are fitted by a fifth order complex Ginzburg-Landau equation whose linear coefficients are compared to theoretical ones.     

Metastability of Ginzburg-Landau model with a conservation law

The hydrodynamics of Ginzburg-Landau dynamics has previously been proved to be a nonlinear diffusion equation. The diffusion coefficient is given by the second derivative of the free energy and hence nonnegative. We consider in this paper the Ginzburg-Landau dynamics with long-range interactions. In this case the diffusion coefficient is nonnegative only in the metastable region. We prove that if the initial condition is in the metastable region, then the hydrodynamics is governed by a nonlinear diffusion equation with the diffusion coefficient given by the metastable curve. Furthermore, the lifetime of the metastable state is proved to be exponentially large.     

Abrikosov Lattices in Finite Domains

In 1957 Abrikosov published his work on periodic solutions to the linearized Ginzburg-Landau equations. Abrikosov's analysis assumes periodic boundary conditions, which are very different from the natural boundary conditions the minimizer of the Ginzburg-Landau energy functional should satisfy. In the present work we prove that the global minimizer of the fully non-linear functional can be approximated, in every rectangular subset of the domain, by one of the periodic solution to the linearized Ginzburg-Landau equations in the plane. Furthermore, we prove that the energy of this solution is close to the minimum of the energy over all Abrikosov's solutions in that rectangle.     

Anisotropy of the upper critical field in MgB2: the two-gap Ginzburg-Landau theory

The upper critical field in MgB2 is investigated in the framework of the two-gap Ginzburg-Landau theory. A variational solution of linearized Ginzburg-Landau equations agrees well with the Landau level expansion and demonstrates that spatial distributions of the gap functions are different in the two bands and change with temperature. The temperature variation of the ratio of two gaps is responsible for the upward temperature dependence of in-plane Hc2 as well as for the deviation of its out-of-plane behavior from the standard angular dependence. The hexagonal in-plane modulations of Hc2 can change sign with decreasing temperature.     

On a coupled random walk process specified by a Hamiltonian

A coupled random walk process specified by an effective Hamiltonian in a potential field is proposed. The Hamiltonian is expressed in terms of a set of jumping probabilities which characterize the random walk processes. The steady state is expressed by the Hamiltonian. Conditions for the Hamiltonian to be reduced to the Ginzburg-Landau type are discussed.     

Dynamics of NLS solitons described by the cubic-quintic Ginzburg-Landau equation

The generalized moment method is applied to average the Ginzburg-Landau equation with quintic nonlinearity in the neighborhood of a soliton solution to the nonlinear Schrödinger equation. A qualitative analysis of the resulting dynamical system is presented. New soliton solutions bifurcating from a known exact soliton solution are obtained. The results of the qualitative analysis are compared with those obtained by direct numerical solution of the Ginzburg-Landau equation.     

Mesoscopic samples: the superconducting condensate via the Gross-Pitaevskii scenario

Mesoscopic superconductors are routinely investigated with the Ginzburg-Landau equations, whereby the confinement is taken into account by imposing that the normal component of the superconducting current vanishes through the sample boundary. We argue that this approach gives misleading results when applied to micron- and submicron-sized devices, and we introduce modified Ginzburg-Landau equations that take the confinement potential into account on the level of the free energy functional. For devices much larger than the Ginzburg-Landau coherence length, both approaches agree, but deviations appear for samples of the scale of the coherence length. In the absence of a magnetic field, the modified Ginzburg-Landau equation for the order parameter reduces to the Gross-Pitaevskii equation.     

External noise and the origin and dynamics of structure in convectively unstable systems

Some basic concepts and earlier work on external noise and the convectively unstable Ginzburg-Landau equation are reviewed, and some of the ideas presented in the earlier work are investigated further and extended. In particular, further consideration is given to convective chaos-chaos which only occurs in a moving frame of reference; and slugs-localized structures which are surrounded by a stable stationary state. Some new results on secondary convective instabilities and on periodic systems with a spatially varying instability are discussed. Work on the coupled Ginzburg-Landau equation is reviewed. Actual physical systems are discussed.     

Critical vortex line length near a zigzag of pinning centers

A vortex line passes through as many pinning centers as possible on its way from one extremety of the superconductor to the other at the expense of increasing its self-energy. In the framework of the Ginzburg-Landau theory we study the relative growth in length, with respect to the straight line, of a vortex near a zigzag of defects. The defects are insulating pinning spheres that form a three-dimensional cubic array embedded in the superconductor. We determine the depinning transition beyond which the vortex line no longer follows the critical zigzag path of defects.Received: 23 July 2004, Published online: 26 November 2004PACS: 74.80.-g Spatially inhomogeneous structures - 74.25.-q General properties; correlations between physical properties in normal and superconducting states - 74.20.De Phenomenological theories (two-fluid, Ginzburg-Landau, etc.)     

Superfluid 3He-A in a cylindrical pore

The Ginzburg-Landau free energy for superfluid ³He is reexpressed in arbitrary curvilinear coordinate systems. Application to ³He-A in a long cylindrical pore with large and small radii yields quantitative predictions for the stable configurations.     

Droplet Phases in Non-local Ginzburg-Landau Models with Coulomb Repulsion in Two Dimensions

We establish the behavior of the energy of minimizers of non-local Ginzburg-Landau energies with Coulomb repulsion in two space dimensions near the onset of multi-droplet patterns. Under suitable scaling of the background charge density with vanishing surface tension the non-local Ginzburg-Landau energy becomes asymptotically equivalent to a sharp interface energy with screened Coulomb interaction. Near the onset the minimizers of the sharp interface energy consist of nearly identical circular droplets of small size separated by large distances. In the limit the droplets become uniformly distributed throughout the domain. The precise asymptotic limits of the bifurcation threshold, the minimal energy, the droplet radii, and the droplet density are obtained.     

Synchronization in nonidentical complex Ginzburg-Landau equations

A cross-correlation coefficient of complex fields has been investigated for diagnosing spatiotemporal synchronization behavior of coupled complex fields. We have also generalized the subsystem synchronization way established in low-dimensional systems to one- and two-dimensional Ginzburg-Landau equations. By applying the indicator to examine the synchronization behavior of coupled Ginzburg-Landau equations, it is shown that our subsystem approach may be of better synchronization performance than the linear feedback method. For the linear feedback Ginzburg-Landau equation, the nonidentical system exhibits generalized synchronization characteristics in both amplitude and phase. However, the nonidentical subsystem may exhibit complete-like synchronization properties. The difference between complex fields for driven and response systems gives a linear scaling with the change of their parameter difference.     

Phase locking and periodic evolution of solitons in passively mode-locked fiber lasers with a semiconductor saturable absorber

Passively mode-locked lasers with intracavity weakly birefringent fiber are theoretically analyzed based on two coupled complex one-dimensional Ginzburg-Landau equations. The model includes fiber birefringence, spectral filtering, saturable gain, and saturable loss. Phase-locked soliton solutions are found for small amounts of birefringence and several types of soliton with periodic polarization evolution for higher amounts of birefringence. Numerical simulations show qualitative agreement with experimental results.