scholarly journals Local minimizers with vortex pinning to Ginzburg–Landau functional in three dimensions

2008 ◽  
Vol 345 (1) ◽  
pp. 535-544 ◽  
Author(s):  
Jian Zhai ◽  
Zhihui Cai
Keyword(s):  
Vortex Pinning ◽  
Three Dimensions ◽  
Local Minimizers ◽  
Ginzburg Landau

LOCAL MINIMIZERS WITH VORTEX PINNING FOR A GINZBURG–LANDAU FUNCTIONAL FOR SUPERCONDUCTING HOLLOW SPHERES

2012 ◽  
Vol 14 (01) ◽  
pp. 1250004
Author(s):  
JIAN ZHAI ◽  
SHUAI XUE
Keyword(s):  
Hollow Sphere ◽  
Hollow Spheres ◽  
Vortex Pinning ◽  
Local Minimizers ◽  
Ginzburg Landau ◽  
Pinning Effect

In this paper, we consider the pinning effect for full Ginzburg–Landau functional on a superconducting hollow sphere. The existence of local minimizers with vortices locating in the pinning regions is obtained.

Local Minimizers of the Ginzburg-Landau Energy with Magnetic Field in Three Dimensions

2004 ◽  
Vol 249 (3) ◽  
pp. 549-577 ◽  
Author(s):  
Robert Jerrard ◽  
Alberto Montero ◽  
Peter Sternberg
Keyword(s):  
Magnetic Field ◽  
Three Dimensions ◽  
Local Minimizers ◽  
Ginzburg Landau

Local minimizers with vortices to the Ginzburg-Landau system in three dimensions

2003 ◽  
Vol 57 (1) ◽  
pp. 99-125 ◽  
Author(s):  
J. Alberto Montero ◽  
Peter Sternberg ◽  
William P. Ziemer
Keyword(s):  
Three Dimensions ◽  
Local Minimizers ◽  
Ginzburg Landau

scholarly journals Analysis of a variational model for nematic shells

2016 ◽  
Vol 26 (10) ◽  
pp. 1865-1918 ◽  
Author(s):  
Antonio Segatti ◽  
Michael Snarski ◽  
Marco Veneroni
Keyword(s):  
Gradient Flow ◽  
Variational Model ◽  
Local Minimizers ◽  
Ginzburg Landau ◽  
Novel Approach ◽  
Existence Of Minimizers ◽  
Extrinsic Geometry ◽  
Global And Local ◽  
Intrinsic Energy

We analyze an elastic surface energy which was recently introduced by G. Napoli and L. Vergori to model thin films of nematic liquid crystals. We show how a novel approach in modeling the surface’s extrinsic geometry leads to considerable differences with respect to the classical intrinsic energy. Our results concern three connected aspects: (i) using methods of the calculus of variations, we establish a relation between the existence of minimizers and the topology of the surface; (ii) we prove, by a Ginzburg–Landau approximation, the well-posedness of the gradient flow of the energy; (iii) in the case of a parametrized torus we obtain a stronger characterization of global and local minimizers, which we supplement with numerical experiments.

Local minimizers for the Ginzburg-Landau energy

1997 ◽  
Vol 225 (4) ◽  
pp. 671-684 ◽  
Author(s):  
Manuel del Pino ◽  
Patricio L. Felmer
Keyword(s):  
Local Minimizers ◽  
Ginzburg Landau

LOCAL MINIMIZERS FOR THE GINZBURG–LANDAU ENERGY NEAR CRITICAL MAGNETIC FIELD: PART I

1999 ◽  
Vol 01 (02) ◽  
pp. 213-254 ◽  
Author(s):  
SYLVIA SERFATY
Keyword(s):  
Magnetic Field ◽  
Phase Transition ◽  
Critical Value ◽  
Critical Magnetic Field ◽  
Two Dimensional ◽  
Local Minimizers ◽  
Large Parameter ◽  
Ginzburg Landau

We find local minimizers of the two-dimensional Ginzburg–Landau functionals depending on a large parameter κ, which describe the behavior of a superconductor in a prescribed exterior magnetic field hex. We prove an estimate on the critical value Hc1 of hex(κ), corresponding to the first phase-transition in which vortices appear in the superconductor; and we locate these vortices.

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