We study the minimizers of the Ginzburg-Landau model for variable thickness, superconducting, thin films with high k, placed in an applied magnetic field hex, when hex is of the order of the ＂first critical field＂, i.e. of the order of ｜lnε｜. We obtain the asymptotic estimates of minimal energy and describe the possible locations of the vortices.
Consider the motion of immersed hypersurfaces driven by surface diffusion flow and give anlower bound on the life span of a smooth immersed solution, which depends only on how muchthe curvature of the initial surface is concentrated in space.
LIU ZUHAN Department of Mathematics, Yangzhou University, Yangzhou 225002, Jiangsu, China.
The purpose of this paper is to investigate a new type of evolution problem for closed convex plane curves which will preserves the perimeter of the curve but expands the enclosed area and the final limiting curve is a circle in the Hausdorff metric in the plane.
Pan ShengliangDept. of Math.,East China Normal Univ.,Shanghai 200062.
This paper studies the asymptotic behavior of solutions to an evolutionary Ginzburg-Landau equation in 3 dimensions. It is shown that the motion of the Ginzburg-Landau vortex curves is the flow by its curvature. Away from the vortices, the author uses some measure theoretic arguments used by F. H. Lin in [16] to show the strong convergence of solutions.
LIU ZUHAN Department of Mathematics, Normal College. Yangzhou University. Yangzhou 225002, China. E-mail: zuhanl@yahoo.com
The effect of an applied magnetic field on an inhomogeneous superconductor is studied and the value of the lower critical magnetic field HC1 at which superconducting vortices appear is estimated. In addition, the authors locate the vortices of local minimizers, which depends on the inhomogeneous term a(x).
This paper is concerned with the minimization problem related to the superconductivity with thermal noise. We study the asymptotic behavior of the minimizes of this problem as the parameters tending to zero and prove the vortices-pinning mechanism.
The effect of an applied magnetic field on an inhomogeneous superconductor is studied and the value of the upper critical magnetic field Hc3 at which superconductivity can nucleate is estimated. In addition, the authors locate the concentration of the order parameter, which depends on the inhomogeneous term a(x). Unlikely to the homogeneous case, the order parameter may concentrate in the interior of the superconducting material, due to the influence of the inhomogeneous term a(x).
Stationary even single bump periodic solutions of the Swift Hohenberg equation are analyzed. The coefficient k in the equation is found to be a critical parameter. It is proved if 0
