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.     

Interfacial growth in driven Ginzburg-Landau models: Short and long-time dynamics

Interfacial growth in driven systems is studied from the initial stage to the longtime regime. Numerical integrations of a Ginzburg-Landan type equation with a new flux term introduced by an external field are presented. The interfacial instabilities are induced by the external field. From the numerical results, we obtain the dispersion relation for the initial growth. During the intermediate temporal regime, fingers of a characteristic triangular shape could grow. Depending on the boundary conditions, the final state corresponds to strips, multifinger states, or a one-finger state. The results for the initial growth are interpreted by means of surface-driven and Mullins-Sekerka instabilities. The shape of the one-finger state is explained in terms of the characteristic length introduced by the external field.     

p-Ginzburg-Landau型极小元的渐近性质与p-调和映射的关系

本文考虑的是一类p-Ginzburg-Landau型泛函极小元,当p∈(1,n)时的极限行为．研究了极小元的零点与p-调和映射的奇点间的关系,并证明了极小元在Cloc1,γ意义下收敛到p-调和映射．     

Vortex matter in lead nanowires

Theoretical and experimental magnetizations of lead nanowire arrays well below the superconducting transition temperature T_c are described. The magnetic response of the array was investigated with a SQUID magnetometer. Hysteretic behaviour and phase transitions have been observed in sweeping up and down the external magnetic field at different temperatures. The Meissner and Abrikosov states were also experimentally observed in this apparently type-I superconductor. This fact brings to the fore the non-trivial behaviour of the critical boundary κ _c ( = 1/ in bulk materials) between type-I and type-II phase transitions at mesoscopic scales. The time-independent Ginzburg-Landau equations particularized to cylindrically symmetric configurations enable one to explain and reproduce the experimental magnetization curves within 10% of error. Received 16 January 2003 / Received in final form 27 March 2003 Published online 23 May 2003 RID="a" ID="a"e-mail: stenuit@fynu.ucl.ac.be     

On the stability of the critical state with inhomogeneous temperature in composite superconductors

The problem of the thermal and magnetic destruction of the critical state in composite superconductors is investigated. The initial distributions of temperature and electromagnetic field are assumed to be essentially inhomogeneous. The limit of the thermomagnetic instability in quasi-stationary approximation is determined. The obtained integral criterion, unlike the analogous criterion for a homogeneous temperature profile, is shown to take into account the influence of any part of the superconductor on the threshold for critical-state instability. Received 11 October 2001 / Received in final form 30 November 2002 Published online 14 February 2003 RID="a" ID="a"e-mail: taylanov@iaph.tkt.uz     

On the distributions of the form ∑i (δpi−δni)

We present some properties of the distributions T of the form ∑_i (δ_pi−δ_ni), with ∑_i d(p_i,n_i)<∞, which arise in the study of the 3-d Ginzburg–Landau problem; see Bourgain et al. (C. R. Acad. Sci. Paris, Ser. I 331 (2000) 119–124). We show that there always exists an irreducible representation of T. We also extend a result of Smets (C. R. Acad. Sci. Paris, Ser. I 334 (2002) 371–374) which says that T is a measure iff T can be written as a finite sum of dipoles.     

Variational problems on multiply connected thin strips III: Integration of the Ginzburg-Landau equations over graphs

We analyze the one-dimensional Ginzburg-Landau functional of superconductivity on a planar graph. In the Euler-Lagrange equations, the equation for the phase can be integrated, provided that the order parameter does not vanish at the vertices; in this case, the minimization of the Ginzburg-Landau functional is equivalent to the minimization of another functional, whose unknowns are a real-valued function on the graph and a finite set of integers.