Abstract/Details

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


2007 2007

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Abstract (summary)

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.

Indexing (details)


Subject
Mathematics;
Condensation
Classification
0405: Mathematics
0611: Condensation
Identifier / keyword
Pure sciences; Asymptotic expansions; Gamma-convergence; Ginzburg-Landau theory; Magnetic field; Phase transitions; Superconducting loop
Title
The Ginzburg -Landau theory for a thin superconducting loop in a large magnetic field
Author
Shieh, Tien-Tsan
Number of pages
88
Publication year
2007
Degree date
2007
School code
0093
Source
DAI-B 68/07, Dissertation Abstracts International
Place of publication
Ann Arbor
Country of publication
United States
ISBN
9780549157571
Advisor
Sternberg, Peter
Committee member
Rubinstein, Jacob; Torchinsky, Alberto; Wang, Shouhong
University/institution
Indiana University
Department
Mathematics
University location
United States -- Indiana
Degree
Ph.D.
Source type
Dissertations & Theses
Language
English
Document type
Dissertation/Thesis
Dissertation/thesis number
3274923
ProQuest document ID
304849497
Copyright
Database copyright ProQuest LLC; ProQuest does not claim copyright in the individual underlying works.
Document URL
http://search.proquest.com/docview/304849497
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