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The Ginzburg -Landau theory for a thin superconducting loop in a large magnetic field.

Record Type:	Electronic resources : Monograph/item
Title/Author:	The Ginzburg -Landau theory for a thin superconducting loop in a large magnetic field./
Author:	Shieh, Tien-Tsan.
Published:	Ann Arbor : ProQuest Dissertations & Theses, : 2007,
Description:	88 p.
Notes:	Source: Dissertations Abstracts International, Volume: 69-05, Section: B.
Contained By:	Dissertations Abstracts International69-05B.
Subject:	Mathematics. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3274923
ISBN:	9780549157571

The Ginzburg -Landau theory for a thin superconducting loop in a large magnetic field.
Shieh, Tien-Tsan.

The Ginzburg -Landau theory for a thin superconducting loop in a large magnetic field. - Ann Arbor : ProQuest Dissertations & Theses, 2007 - 88 p.

Source: Dissertations Abstracts International, Volume: 69-05, Section: B.

Thesis (Ph.D.)--Indiana University, 2007.

When a temperature is lower than a certain critical value, a superconducting sample undergoes a phase transition from a normal state to a superconducting state. This onset process of superconductivity can be studied as a Rayleigh quotient under the framework of the Ginzburg-Landau theory. In particular, I study the onset problem for a thin superconducting loop in a large magnetic field. This double limit problem was first carried out by Richardson and Rubinstein by using formal asymptotic expansions. I rigorously show that a one-dimensional Rayleigh quotient in the spirit of Gamma-convergence. The full Gamma-convergence of the Ginzburg-Landau functional for a thin domain and a large field is also obtained. The rigorous analysis in this thesis shows the validity of Richardson and Rubinstein's formal results. It is also shown that the Rayleigh quotient related to this onset problem has a periodic variation with a parabolic background. The parabolic background effect can be explained by a non-ignorable effect if finite-width cross-section of a thin superconducting sample. This illustrate the observation of the Little-Parks experiment.

ISBN: 9780549157571Subjects--Topical Terms:

515831
Mathematics.
Subjects--Index Terms:

Asymptotic expansions

The Ginzburg -Landau theory for a thin superconducting loop in a large magnetic field.
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100 1 $a Shieh, Tien-Tsan. $3 3688859
245 1 4 $a The Ginzburg -Landau theory for a thin superconducting loop in a large magnetic field.
260 1 $a Ann Arbor : $b ProQuest Dissertations & Theses, $c 2007
300 $a 88 p.
500 $a Source: Dissertations Abstracts International, Volume: 69-05, Section: B.
500 $a Publisher info.: Dissertation/Thesis.
500 $a Advisor: Sternberg, Peter.
502 $a Thesis (Ph.D.)--Indiana University, 2007.
520 $a When a temperature is lower than a certain critical value, a superconducting sample undergoes a phase transition from a normal state to a superconducting state. This onset process of superconductivity can be studied as a Rayleigh quotient under the framework of the Ginzburg-Landau theory. In particular, I study the onset problem for a thin superconducting loop in a large magnetic field. This double limit problem was first carried out by Richardson and Rubinstein by using formal asymptotic expansions. I rigorously show that a one-dimensional Rayleigh quotient in the spirit of Gamma-convergence. The full Gamma-convergence of the Ginzburg-Landau functional for a thin domain and a large field is also obtained. The rigorous analysis in this thesis shows the validity of Richardson and Rubinstein's formal results. It is also shown that the Rayleigh quotient related to this onset problem has a periodic variation with a parabolic background. The parabolic background effect can be explained by a non-ignorable effect if finite-width cross-section of a thin superconducting sample. This illustrate the observation of the Little-Parks experiment.
590 $a School code: 0093.
650 4 $a Mathematics. $3 515831
650 4 $a Condensation. $3 942542
653 $a Asymptotic expansions
653 $a Gamma-convergence
653 $a Ginzburg-Landau theory
653 $a Magnetic field
653 $a Phase transitions
653 $a Superconducting loop
690 $a 0405
690 $a 0611
710 2 $a Indiana University. $b Mathematics. $3 1036206
773 0 $t Dissertations Abstracts International $g 69-05B.
790 $a 0093
791 $a Ph.D.
792 $a 2007
793 $a English
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3274923